Internal Design of Mechanically Stabilized Earth (MSE) Retaining Walls Using Crimped Bars

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Bernardo A. Castellanos Utah State University

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INTERNAL DESIGN OF MECHANICALLY STABILIZED EARTH (MSE) RETAINING WALLS

USING CRIMPED BARS

Bernardo A. Castellanos

A thesis submitted in partial fulfillment of the requirements for the degree

MASTER OF SCIENCE

Civil and Environmental Engineering

Approved:

______James A. Bay John D. Rice Major Professor Committee Member

______Marvin W. Halling Byron R. Burnham Committee Member Dean of Graduate Studies

UTAH STATE UNIVERSITY Logan, Utah

2010 ii

ABSTRACT

Internal Design of Mechanically Stabilized Earth (MSE) Retaining

Walls Using Crimped Bars

Bernardo A. Castellanos, Master of Science

Utah State University, 2010

Major Professor: Dr. James A. Bay Department: Civil and Environmental Engineering

Current design codes of Mechanically Stabilized Earth (MSE) Walls allow the use lower lateral earth pressure coefficient (K value) for designing geosynthetics walls than those used to design steel walls. The reason of this is because geosynthetics walls are less rigid permitting the wall to deform enough to work under active pressures instead of at rest pressures as in steel walls.

A new concept of crimped steel bars was recently introduced. This new type of bar was tested for tension and pullout behavior. Results on tests made on crimped bars show that putting those crimps in the steel bar will give us a better pullout behavior and a more flexible tensile behavior. This new type of steel bar will behave more like geosynthetics, allowing the wall to deform sufficiently to reach the necessary deflection to reach the active condition. iii

The use of steel by current design codes is pushing MSE walls to be designed

with more steel than needed. Measurements of the force in different walls showed that

the steel is not being used even close to the maximum stress allowed by the code which is 50%.

The proposed design methodology using crimped bars will help us save around

52% of steel volume compared to the actual design procedures. This means a huge improvement in the usage of steel versus actual designs. This improvement is obtained because of the efficient behavior of rounded bars under corrosion and because of the flexibility in the bars obtained with the crimps that will allow us to reach the active condition.

(137 pages)

DEDICATION

This thesis is dedicated first to God for all the opportunities given and for being

the guide of my life. To the Dominican government, for providing me the necessary

funds to attend Utah State University. To my family, for their unconditional support all these years. To friends and all others that motivated me throughout this process. The

gratitude I have for the inspiration and confidence conferred upon me by these people

is indescribable.

Bernardo A. Castellanos

ACKNOWLEDGMENTS

I would like to thank my committee members, Drs. James Bay, for all his unconditional support and dedication to this project, Loren Anderson, John Rice, and

Marv Halling, for their support and insight throughout this process. Finally, I would like to thank Hilkfiker Retaining Walls in the person of Bill Hilfiker for providing the funds and steel bars for the realization of this project.

Bernardo A. Castellanos

CONTENTS

Page ABSTRACT ...... ii

DEDICATION ...... iv

ACKNOWLEDGMENTS ...... v

LIST OF TABLES ...... viii

LIST OF FIGURES ...... xi

CHAPTER

1 INTRODUCTION, OBJECTIVES AND ORGANIZATION ...... 1

1.1 Introduction ...... 1 1.2 Objectives of the Research ...... 2 1.3 Report Organization ...... 3

2 LITERATURE REVIEW ...... 4

2.1 Introduction ...... 4 2.2 American Association of State Highway and Transportation Official (AASHTO) MSE Walls Design Code ...... 4

2.2.1 General ...... 4 2.2.2 Loads in the MSE walls ...... 7 2.2.3 Overall stability ...... 10 2.2.4 Sliding ...... 10 2.2.5 Bearing capacity ...... 11 2.2.6 Overturning ...... 16 2.2.7 Loads in the reinforcement ...... 16 2.2.8 Load at the connection to the face of the wall...... 19 2.2.9 Reinforcement strength ...... 20 2.2.10 Pullout resistance ...... 27

2.3 K-Stiffness Method...... 30

2.3.1 General ...... 30 vii

2.3.2 Strength limit state design for internal stability for geosynthetic walls ...... 39 2.3.3 Strength Limit state design for internal stability for steel walls 41

3 DESIGN METHODOLOGY ...... 43

3.1 Concept ...... 43 3.2 Crimp Properties ...... 44

3.2.1 Pullout resistance ...... 44 3.2.2 Crimp deflection ...... 46

3.3 Model Definition ...... 55

3.3.1 Tensile design of the wall ...... 62 3.3.2 Pullout design of the reinforcement ...... 64 3.3.3 Wall deflections ...... 67

4 DESIGN OF A 40 FT. HEIGHT MECHANICALLY STABILIZED EARTH (MSE) WALL USING THE PROPOSED METHODOLOGY ...... 69

4.1 Introduction ...... 69 4.2 Description of the Wall ...... 69 4.3 Wall Design ...... 70 4.4 Designs Summary ...... 74

5 COMPARISON BETWEEN DESIGN METHODOLOGIES ...... 79

5.1 Introduction ...... 79 5.2 Other Design Methodologies ...... 79 5.3 Designs Comparison ...... 80

6 CONCLUSIONS AND RECOMMENDATIONS ...... 83

REFERENCES ...... 85

APPENDICES ...... 87

APPENDIX A. Visual Basic Scripts for Crimps Properties Calculation ...... 88 APPENDIX B. MSE Walls Complete Designs ...... 105

viii

LIST OF TABLES

Table Page

2.1 Load factors for permanent loads ...... 5

2.2 Resistance factors for permanent MSE walls ...... 6

2.3 Coefficients Cw1 for various groundwater depths ...... 13

2.4 Bearing capacity factor N for footings on cohesionless soil ...... 14

2.5 Shape factor S for footings on cohesionless soil ...... 14

2.6 Soil compressibility factor C for square footings on cohesionless soil ...... 14

2.7 Soil compressibility factor C for Strip footings on cohesionless soil ...... 15

2.8 Load Inclination Factor i for load inclined in direction of footing width ...... 15

2.9 Minimum requirements for geosynthetic products to allow use of default reduction factor for long-term degradation...... 26

2.10 Default and minimum values for the total geosynthetic ultimate limit strength reduction factor, RF...... 27

2.11 Default values for the scale effect correction factor  ...... 29

2.12 Load factors for permanent loads for internal stability of MSE walls designed using the K-Stiffness method, p ...... 32

2.13 Resistance factors for the strength and extreme event limit states for MSE walls designed using the K-Stiffness method ...... 33

4.1 Design summary table for the wall designed with crimp 1 and Sc = 2 ft ...... 75

4.2 Design summary table for the wall designed with crimp 1 and Sc = 1.5 ft .... 76

4.3 Design summary table for the wall designed with crimp 2 and Sc = 2 ft ...... 77

4.4 Summary table for the wall designed with crimp 2 and Sc = 1.5 ft ...... 77

5.1 Summary table of the AASHTO design approach using RECO straps ...... 80 ix

5.2 Summary table of the K-Stiffness method using RECO straps ...... 81

B.1 Properties of the select fill for the MSE wall...... 105

B.2 Corrosion considerations ...... 105

B.3 Reinforcement information ...... 105

B.4 General information of the wall designed with crimp 1 and Sc = 2.00 ft ...... 106

B.5 Pullout resistance calculations of the wall designed with crimp 1 and Sc = 2.00 ft ...... 107

B.6 Calculations of the tension in the connections of the wall designed with crimp 1 and Sc = 2.00 ft...... 108

B.7 Calculations of the deflections of the wall designed with crimp 1 and Sc = 2.00 ft...... 109

B.8 General information of the wall designed with crimp 1 and Sc = 1.50 ft ...... 110

B.9 Pullout resistance calculations of the wall designed with crimp 1 and Sc = 1.50 ft ...... 111

B.10 Calculations of the tension in the connections of the wall designed with crimp 1 and Sc = 1.50 ft...... 112

B.11 Calculations of the deflections of the wall designed with crimp 1 and Sc = 1.5 ft...... 113

B.12 General information of the wall designed with crimp 2 and Sc = 2.00 ft ...... 114

B.13 Pullout resistance calculations of the wall designed with crimp 2 and Sc = 2.00 ft ...... 116

B.14 Calculations of the tension in the connections of the wall designed with crimp 2 and Sc = 2.00 ft...... 117

B.15 Calculations of the deflections of the wall designed with crimp 2 and Sc = 2.00 ft...... 118

B.16 General information of the wall designed with crimp 2 and Sc = 1.50 ft ...... 119

B.17 Pullout resistance calculations of the wall designed with crimp 2 and Sc = 1.50 ft ...... 120

B.18 Calculations of the tension in the connections of the wall designed with crimp 2 and Sc = 1.50 ft...... 121

B.19 Calculations of the deflections of the wall designed with crimp 2 and Sc = 1.5 ft...... 122

B.20 General information of the wall designed with AASHTO approach ...... 124

B.21 General information of the wall designed with K-Stiffness approach using RECO straps ...... 125

LIST OF FIGURES

Figure Page

1.1 Percentage of the yield stress used measured in existing MSE Walls...... 2

2.1 Earth pressure distribution for MSE Wall with level backfill surface ...... 8

2.2 Earth pressure distribution for MSE wall with sloping backfill surface ...... 9

2.3 Earth pressure distribution for MSE wall with broken back backfill surface. ... 9

2.4 Location of potential failure surface for inextensible reinforcements for internal stability design of MSE walls ...... 16

2.5 Location of potential failure surface for extensible reinforcements for internal stability design of MSE walls ...... 17

2.6 Variation of the coefficient of lateral stress ratio kr/ka with depth in a MSE wall ...... 18

2.7 Calculation of vertical stress for horizontal backslope condition, including live load and dead load surcharges for internal stability analysis...... 19

2.8 Calculation of vertical stress for sloping backslope condition for internal stability analysis ...... 20

2.9 Reinforcement coverage ratio for metal reinforcement...... 21

2.10 Reinforcement coverage ratio for geosynthetic reinforcement ...... 22

2.11 Default values for the pullout friction factor F* ...... 29

2.12 Dtmax as a function of normalized depth below wall top plus average surcharge depth ...... 39

3.1 Example of a crimp in a steel rebar...... 44

3.2 Straight steel reinforcement bar pullout resistance ...... 47

3.3 1/2'' dia. steel reinforcement bar crimp 1 pullout resistance ...... 48

3.4 3/8'' dia. steel reinforcement bar crimp 1 pullout resistance ...... 49 xii

3.5 1/4'' dia. steel smooth bar crimp 1 pullout resistance ...... 50

3.6 1/2'' dia. steel reinforcement bar crimp 2 pullout resistance ...... 51

3.7 3/8'' dia. steel reinforcement bar crimp 2 pullout resistance ...... 52

3.8 1/4'' dia. steel reinforcement bar crimp 2 pullout resistance ...... 53

3.9 3/8'' dia. steel reinforcement bar crimp 1 measured vs. extrapolated pullout resistance ...... 54

3.10 3/8'' dia. steel reinforcement bar crimp 2 measured vs. extrapolated pullout resistance ...... 54

3.11 1/2'' dia. steel reinforcement bar crimp 1 displacement curve ...... 56

3.12 3/8'' dia. steel reinforcement bar crimp 1 displacement curve ...... 57

3.13 1/4'' dia. steel reinforcement bar crimp 1 displacement curve...... 58

3.14 1/2'' dia. steel reinforcement bar crimp 2 displacement curve...... 59

3.15 3/8'' dia. steel reinforcement bar crimp 2 displacement curve...... 60

3.16 1/4'' dia. steel reinforcement bar crimp 2 displacement curve...... 61

3.17 Tension distribution along the reinforcement behind the wall face...... 65

4.1 Displacement of the face of the wall vs. depth of the wall designed using crimp 1 ...... 76

4.2 Displacement of the face of the wall vs. depth of the wall designed using crimp 2...... 78

5.1 Steel usage for the existing and proposed design methodologies...... 82

CHAPTER 1

INTRODUCTION, OBJECTIVES AND ORGANIZATION

1.1 Introduction

Current design codes allow lower lateral earth pressure coefficient (K value) for designing geosynthetics walls than those used to design steel walls. This is because geosynthetics walls are less rigid, permitting the wall to deform sufficiently to work under actives pressures instead of at rest pressures as in steel walls.

After Suncar (2010), a new concept of crimped steel bars was proved to be useful. These bars provided sufficient pullout resistance and the flexibility needed build a flexible wall using steel reinforcement. This new type of steel bars will behave more like geosynthetics, allowing the wall to deform sufficiently to lower the stresses to active stresses.

The usage of steel by current design codes are making that the MSE walls are designed with a lot of more steel than needed. Looking at the measurement on various

MSE walls presented by Wong (1989) and Goodsell (2000) and illustrated in Fig. 1.1 is well shown that the steel is not being used efficiently because any but one is nearly close to the maximum stress allowed by the code which is 50% and the average percentage of the yield stress that is being used is 17.65%.

Idaho Wall 30 Grayback RD. Wall, California Rainier Ave. Wall, Washington

20 I-15 R-346-1C Wall Sect. 1, Utah I-15 R-346-1C Wall Sect. 2, Utah Height Of Fill Above the Mat (ft) Of Fill Above Height

0 0% 10% 20% 30% 40% 50% σ/σy

Fig. 1.1 Percentage of the yield stress used measured in existing MSE walls.

1.2 Objectives of the Research

The objective of this research is to develop a design procedure that will allow the

use of crimped bars to build MSE walls. This new procedure will be more efficient in the

usage of steel than current design methods. One of the problems with the materials

used in the construction of MSE walls is the large cross-sectional area. In order to use

the steel at the maximum capacity allowed by the code (about 50% of yield stress) a

large horizontal spacing (larger than the allowed by the code) is needed. The use of 3

smaller bars, which will allow the wall to resist the stresses behind it, is proposed. Doing so, the wall will be more flexible, with lower stresses, steel volume and cost.

1.3 Report Organization

Chapter 2 presents the literature review needed to understand the thesis and

gives the reader a background in the current designs methodologies that are currently

being used. The newly proposed design methodology is presented in Chapter 3. Chapter

4 presents a 40 ft MSE wall designed with the new proposed methodology and Chapter

5 provides a comparison between walls designed with current design procedures and

the proposed design procedure.

CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

The concept of MSE walls is fairly new. The development of this type of reinforced wall began in the decade of 1980. In the last decade notorious improvement have been made in the understanding of the wall behaviors, how the stresses are distributed based on the stiffness of the wall components, factors affecting the durability of the materials, soil behavior behind the wall and now we have more walls constructed that can be used as case studies to gather information an calibrate models.

All this facts together now make possible the design and construction of more efficient and secure walls.

As we all know in this world the design codes varies from country to country and sometimes from state to state. In this chapter we are going to present a literature review of everything concerning MSE wall design codes that are going to be applied along this thesis and that will help us in the understanding of the problem.

2.2 American Association of State Highway and Transportation

Official (AASHTO) MSE Walls Design Code

2.2.1 General

The American Association of State Highway and Transportation Official (ASSHTO) included the MSE wall section in their Bridge Design Manual. Since that it has been 5

evolving till presents day where now it is focused on the new Load and Resistance

Factor Design (LRFD) concepts. In this new design philosophy we do not use factors of safety anymore as we used to know them. Now we amplify the loads and reduce the capacity of the materials with what they call load and resistance factors.

The AASHTO method is based on the classic linearly distributed earth pressure behind the wall and it does not take into account the stiffness of the elements that forms the wall.

2.2.1.1 Load and resistance factors

LRFD methodology introduces a new way of using factor of safety in engineering.

Instead of using the traditional definition of factor of safety LRFD introduces the load

factor which increment the loads (Table 2.1) and the resistance factor that are in

charge of reducing the resistance of the material (Table 2.2).

Table 2.1 Load factors for permanent loads (AASHTO, 2004)

Load Factor Type of Load Maximum Minimum DC: Component and Attachments 1.25 0.90 EH: Horizontal Earth Pressure  Active 1.50 0.90  At-Rest 1.35 0.90 EL: Locked-in Erection Stresses 1.00 1.00 EV: Vertical Earth Pressure

 Overall Stability 1.00 N/A  Retaining Walls and 1.35 1.00 Abutments ES: Earth Surcharge 1.50 0.75

Table 2.2 Resistance factors for permanent MSE walls (AASHTO, 2004)

Condition Resistance Factor Bearing Resistance - Sand  Semiempirical Procedure using SPT Data. 0.45  Semiempirical Procedure using CPT Data. 0.55  Rational Method . Using ϕf Estimated from SPT Data. 0.35 . Using ϕf Estimated from CPT Data. 0.45 Plate Load Test 0.55 Sliding - Precast Concrete Placed on Sand (ϕτ)  Using ϕf Estimated from SPT Data. 0.90  Using ϕf Estimated from CPT Data. 0.90

- Concrete Cast in Place on Sand (ϕτ)  Using ϕf Estimated from SPT Data. 0.80  Using ϕf Estimated from CPT Data. 0.80

- Passive Earth Pressure Component of Sliding 0.50 Resistance (ϕep) Tensile Resistance of Metallic Reinforcement and Connectors: - Strip Reinforcement(1):  Static Loading 0.75  Combined Static/Earthquake Loading. 1.00

- Grid Reinforcements(1) (2):  Static Loading 0.65  Combined Static/Earthquake Loading. 0.85 Tensile Resistance of Geosynthetic Reinforcement and Connectors: 0.90  Static Loading 1.20  Combined Static/Earthquake Loading.

Pullout Resistance of Tensile Reinforcement: 0.90  Static Loading 1.20  Combined Static/Earthquake Loading. (1) Apply to gross cross-section less sacrificial area, (2) Applies to grid reinforcement connected to a rigid facing element, e.g., a concrete panel or block. For grid reinforcement connected to a flexible facing mat or which are continuous with the facing mat, use the resistance factor for strip reinforcement. 7

2.2.1.2 Minimum length of soil reinforcement

The minimum length of reinforcement that should be used is 8.0 ft or 70% of the

wall height measured from the leveling pad. In the case that we have small compaction

equipments used in the wall a 6.0 ft reinforcement length can be considered if it is not

less than the 70% of the wall height. Longer reinforcement should be used to resist

external loads if needed.

2.2.2 Loads in the MSE walls

The stress distribution behind a MSE wall is considered to vary linearly with

depth, Fig. 2.1, Fig. 2.2, and Fig. 2.3 show different scenarios that we might encounter

when designing a wall and its stress distribution and the force per unit width behind the

wall (Pa).

=0.5ℎ (2.1)

where:

Pa = Force resultant per unit width (kip/ft.).

s = Total unit weight of the backfill (kcf)

h = Height of the horizontal earth pressure diagram taken as shown in Fig. 2.1, Fig. 2.2 and Fig. 2.3 (ft)

Ka = Active earth pressure coefficient with the angle of backfill slope taken as as specified in Fig. 2.2, B, as specified in Fig. 2.3, and = and B in Fig. 2.2 and Fig. 2.3 respectively (dim.).

sin2θ+ϕ' K = f (2.2) a ϑ[sin2θ sinθ-δ)

( ) ( ) =1+ (2.3) () ()

where:

 = Friction angle between fill and wall.

 = Angle of fill to the horizontal.

θ = Angle of back face of wall to the horizontal.

’ ϕ f = Effective angle of internal friction.

Fig. 2.1 Earth pressure distribution for MSE Wall with level backfill surface (AASHTO, 2004).

Fig. 2.2 Earth pressure distribution for MSE wall with sloping backfill surface (AASHTO, 2004).

Fig. 2.3 Earth pressure distribution for MSE wall with broken back backfill surface (AASHTO, 2004).

The maximum friction angle used to calculate the horizontal forces in the reinforced soil mass shall be assumed to be 34° unless results from triaxial or direct shear tests methods (AASHTO T 234-74 and T 236-72) specifies a higher friction angle, and it should never be more than 40°.

2.2.3 Overall stability

This is the case where we have a slope failure plane beneath the foundation of

the wall. This should be evaluated using limit equilibrium methods of analysis. The

resistance factor  should be taken as follow in case we do not have any better

information:

1) 0.75 where we have well defined geotechnical parameters and the slope

does not support or contain a structural element.

2) 0.65 where we do not have well defined geotechnical parameter and the

slope support or contain a structural element.

2.2.4 Sliding

Sliding along the base of the wall can occur sometimes. To prevent this from

happening, the summation of forces in the X direction should be equal to zero. The

factored resistance against failure by sliding may be taken as:

= = + (2.4)

where:

QR = Sliding factored resistance (tons). 11

Φ = Resistance factor.

Qn = Nominal resistance (tons).

ϕτ = Resistance factor for shear between soil and foundation as in Table 2.2.

Qτ = Maximum shear resistance between the foundation and the soil (tons).

Φep = Resistance factor for passive pressure as in Table 2.2.

Qep = Passive resistance of soil available throughout the design life of the structure (tons).

For cohesionless soil:

= (2.5)

where: tan δ = tan(ϕf ) for concrete cast against soil. 0.8 tan(ϕf) for precast concrete footing.

ϕf = Internal friction angle of the soil.

V = Total vertical force (tons).

2.2.5 Bearing capacity

The bearing capacity of the soil is highly influenced by the position of the water

table below the foundation. This is because the weight of the soil is not the same when

submerged in water and so the effective parameters. Based on that, the bearing

resistance of the soil must be calculated using the highest elevation of the water table

expected during the design life of the structure.

= = (2.6)

where:

Φ = Resistance factor as in Table 2.2.

qn = qult = Nominal bearing resistance (tsf).

qR = v = Vertical stress at the base (tsf).

The bearing capacity must be estimated using the standards soil parameters of

the soil beneath the foundation. As we might know there are different soil shear

strength depending of the stress path used. In this case we must use the soils

parameters that most resemble the state of stress that we are going to have in the field.

The bearing resistance of footings on cohesionless soils shall be evaluated using

effective stress analyses and drained soil strength parameter. For footings over

compacted soils, the bearing resistance shall be evaluated using the most critical of

either total or effective stress analysis.

For cohesionless soil the bearing capacity should be calculated as follows:

=0.5 (2.7)

where:

 = Soil Unit Weight (tcf)

B = Footing Width. To account for eccentricity the B should be changed to B’ = B – 2e (ft).

Cw1 = Coefficients as Specified in Table 2.3 as Function of Dw (dim.).

Dw = Depth to Water Surface Taken From the Ground Surface (ft).

Nm = Modified bearing capacity factor (dim.).

The bearing capacity factors should be calculated as follows:

= (2.8)

where:

N = Bearing capacity factor as specified in Table 2.4 for footings on relatively level ground.

S = Shape factor specified in

Table 2.5.

c = Soil compressibility factor specified in Table 2.6 and

Table 2.7.

i = Load inclination factor specified in Table 2.8.

Table 2.3 Coefficients Cw1 for various groundwater depths (AASHTO, 2004).

DW CW1* 0.0 0.5 > 1.5B 1.0 *For intermediate positions of the ground water table, the values of Cw1 should be linearly interpolated.

Table 2.4 Bearing capacity factor N for footings on cohesionless soil (Barker et al. 1991)

Friction Ndim.) 28 17 30 22 32 30 34 41 36 58 38 78 40 110 42 155 44 225 46 330

Table 2.5 Shape factor S for footings on cohesionless soil (Barker et al. 1991)

L/B S (dim.) 10.60 20.80 50.92 10 0.96

Table 2.6 Soil compressibility factor C for square footings on cohesionless soil (Barker et al. 1991)

Relative Friction C (dim.) Density, D Angle, ϕ r f q = 0.25 tsf q = 0.50 tsf q = 1.00 tsf q = 2.00 tsf (%) (°) 20 28 1.00 1.00 0.92 0.89 30 32 1.00 1.00 0.85 0.77 40 35 1.00 0.97 0.82 0.75 50 37 1.00 0.96 0.81 0.73 60 40 1.00 0.86 0.72 0.65 70 42 0.96 0.80 0.66 0.60 80 45 0.79 0.66 0.54 0.48 100 50 0.52 0.42 0.35 0.31 Note: q should be taken as the initial vertical effective stress at the footing depth, i.e., vertical stress at the bottom of the footing prior to excavation, corrected for water pressure.

Table 2.7 Soil compressibility factor C for Strip footings on cohesionless soil (Barker et al. 1991)

Relative Friction C (dim.) Density, D Angle, ϕ r f q = 0.25 tsf q = 0.50 tsf q = 1.00 tsf q = 2.00 tsf (%) (°) 20 28 0.85 0.75 0.65 0.60 30 32 0.80 0.68 0.58 0.53 40 35 0.76 0.64 0.54 0.49 50 37 0.73 0.61 0.52 0.47 60 40 0.62 0.52 0.43 0.39 70 42 0.56 0.47 0.39 0.35 80 45 0.44 0.36 0.30 0.27 100 50 0.25 0.21 0.17 0.15 Note: q should be taken as the initial vertical effective stress at the footing depth, i.e., vertical stress at the bottom of the footing prior to excavation, corrected for water pressure.

Table 2.8 Load Inclination Factor i for load inclined in direction of footing width (Barker et al. 1991)

H/V i (dim.) Strip L/B = 2 Square 0.0 1.00 1.00 1.00 0.10 0.73 0.76 0.77 0.15 0.61 0.65 0.67 0.20 0.51 0.55 0.57 0.25 0.42 0.46 0.49 0.30 0.34 0.39 0.41 0.35 0.27 0.32 0.34 0.40 0.22 0.26 0.28 0.45 0.17 0.20 0.22 0.50 0.13 0.16 0.18 0.55 0.09 0.12 0.14 0.60 0.06 0.09 0.10 0.65 0.04 0.06 0.07 0.70 0.03 0.04 0.05 Note: H and V shall be taken as the unfactored horizontal and vertical loads, respectively.

2.2.6 Overturning

Rotation of the wall around the tail of the base should be checked. The flexibility

of the MSE walls should make the potential for overturning highly unlikely to occur.

However, the overturning criteria should always be satisfied. To check for overturning

the moment summation in the tail of the base should be equal to zero.

2.2.7 Loads in the reinforcement

The load in the reinforcement is calculated at the zone of maximum stresses and

at the connection with the face of the wall. This zone is assumed to be between the

active zone and the resistance zone (Fig. 2.4 and Fig. 2.5). Those two locations are

where the maximum loads are and there is where we need to check for pullout

resistance and rupture.

Fig. 2.4 Location of potential failure surface for inextensible reinforcements for internal stability design of MSE walls (AASHTO, 2004). 17

Fig. 2.5 Location of potential failure surface for extensible reinforcements for internal stability design of MSE walls (AASHTO, 2004).

To calculate the maximum load in the reinforcement the Simplified Method should be used. In this method the load is calculated multiplying the vertical stress at the reinforcement layer by a lateral earth pressure coefficient and dividing that into the tributary area for that specific reinforcement.

= ( +∆) (2.9)

where:

p = Load factor for vertical earth pressure as specified in Table 2.1.

Kr = Horizontal pressure coefficient as specified in Fig. 2.6 (dim.).

v = Pressure due to resultant of gravity forces from soil self weight within and immediately above the reinforced wall backfill and any surcharge loads present (ksf).

H = Horizontal stress at reinforcement level resulting from any applicable concentrated horizontal surcharge load (ksf). 18

Fig. 2.6 Variation of the coefficient of lateral stress ratio kr/ka with depth in a MSE wall (AASHTO, 2004).

The maximum tension (Tmax) shall be calculated in a per unit of wall width basis

as follow:

= (2.10)

where:

H = Factored horizontal soil stress at the reinforcement level (ksf).

Sv = Vertical spacing of the reinforcement (ft).

Vertical spacing (Sv) greater than 2.7 ft. should only be allowed if full scale wall

data (e.g. reinforcement loads and strains and overall deflections) is available to support

the use of higher spacing.

Fig. 2.7 Calculation of vertical stress for horizontal backslope condition, including live load and dead load surcharges for internal stability analysis (AASHTO, 2004).

2.2.8 Load at the connection to the face of the wall.

The maximum load applied to the connection to the face of the wall (To) should

be equal to the maximum force in the reinforcement (Tmax) independently of the facing

and reinforcement type. 20

Fig. 2.8 Calculation of vertical stress for sloping backslope condition for internal stability analysis (AASHTO, 2004).

2.2.9 Reinforcement strength

The capacity of the reinforcement to resist the tension force that it is going to be

applied to it should be checked at every level of the wall at the boundary between the

active and resistant zone (Fig. 2.4 and Fig. 2.5) and in the connection of the

reinforcement to the wall face.

At the zone of maximum stress:

≤ (2.11)

Fig. 2.9 Reinforcement coverage ratio for metal reinforcement (AASHTO, 2004). where:

Tmax = Applied factored load to the reinforcement (kips/ft).

Φ = Resistance factor for reinforcement tension as specified in Table 2.2.

Tal = Nominal long-term reinforcement design strength (kips/ft).

Rc = Reinforcement coverage ratio as specified in Fig. 2.9 and Fig. 2.10.

2.2.9.1 Design life considerations

A minimum design life of 75 years is required for permanent walls and 36 month

or less for temporary walls. For walls which its failure will have severe consequences a grater design life (100 years) should be considered (i.e. bridge support, buildings, and critical utilities among others). 22

Fig. 2.10 Reinforcement coverage ratio for geosynthetic reinforcement (AASHTO, 2004).

2.2.9.2 Steel reinforcement

The design of MSE Walls using steel reinforcement must account for the lost in

cross sectional area due to corrosion of the steel. All the steel reinforcement used for

soil shall comply with the provisions of AASHTO LRFD Bridge Construction Specification,

Article 7.6.4.2, Steel Reinforcement (AASHTO, 1998).

To calculate the thickness of the reinforcement at the end of the service life the

following equation should be used:

= − (2.12)

Where:

Ec = Thickness of metal at the end of service life (mil.).

En = Nominal thickness of steel reinforcement at construction (mil.).

Es = Sacrificial thickness of metal expected to be lost by uniform corrosion during the service life of the structure (mil.).

The corrosion rates where summarized in Yannas (1985) and should be taken as

follow for nonaggressive materials:

 Loss of galvanizing = 0.58 mil./yr. for first 2 years.

= 0.16 mil./yr. for subsequent years.

 Loss of carbon steel = 0.47 mil./yr. after zinc depletion.

For a soil to be considered nonaggressive it must meet the following criteria:

 pH = 5 to 10.

 Resistivity ≥ 3,000 ohm-cm.

 Chlorides ≤ 100 ppm.

 Sulfates ≤ 200 ppm.

 Organic Content ≤ 1%.

For soils with resistivity equal or greater than 5,000 ohm-cm the chloride and

sulfate criteria may be waived. Galvanized coating thickness should be a minimum of 2

oz/ft2 or 3.4 mils. in accordance to AASHTO M 111 (ASTM A 123) for strip reinforcement

or ASTM 641 for bar mat or grid type steel reinforcement. 24

To calculate the nominal reinforcement tensile resistance the corroded cross sectional area must be used. This value is obtained by multiplying the corroded sectional area by the yield stress and dividing it by the width of the reinforcement to have it in a per foot basis.

= (2.13)

where:

Tal = Nominal long term reinforcement design strength (kips/ft).

Fy = Minimum yield strength of steel (ksi).

2 Ac = Area of reinforcement corrected for corrosion (in ).

b = Unit width of reinforcement (ft).

2.2.9.3 Geosynthetic reinforcement

The use of Geosynthetic reinforcement to MSE Walls design and construction is

limited to some wall application, soil conditions and polymer type to be able to use a

single default reduction factor (RF) and to assure the degradation due to environmental

factors will be minimal.

These limitations consist in the following:

 Failure or poor performance will not have severe consequences.

 The soil is nonaggressive.

 The requirements provided in Table 2.9 are met.

A soil is considered to be nonaggressive for Geosynthetics when: 25

 pH = 4.5 to 9 for permanent applications and 3 to 10 for temporary applications.

 Maximum soil particle size is 0.75 in. unless full scale installation damage tests

are conducted in accordance to ASTM D 5818.

 Soil organic content for material finer than the No. 10 Sieve ≤ 1%.

 Design temperature at wall site is ≤ 89°F for permanent applications and ≤ 95°F

for temporary applications.

If any drainage or seepage will occur from the surrounding soil to the backfill, the surrounding soil must also meet the nonaggressive criteria unless a drainage preventing the water coming from the aggressive soil reach the reinforced soil can be assure for the life of the project.

If those requirements are not met then a product-specific durability studies shall be carried to determine the short and long term properties of the Geosynthetic under those circumstances to determine the reduction factor (RF).

To calculate the long term tensile resistance of the Geosynthetics the following equation should be used:

= (2.14)

where:

= (2.15)

Table 2.9 Minimum requirements for geosynthetic products to allow use of default reduction factor for long-term degradation (AASHTO, 2004).

Criteria to Polymer Type Property Test Method Allow Use of Default RF Minimum 70% strength Polypropylene UV Oxidation Resistance ASTM D4355 retained after 500 hrs. in weatherometer Polyethylene UV Oxidation Resistance ASTM D4355 Minimum 70% strength retained after

500 hrs. in weatherometer Intrinsic Viscosity Minimum Method (ASTM D4603) Number And GRI Test Method Average Polyester Hydrolysis Resistance GG8, or Determine Molecular Directly Using Gel Weight of Permeation 25,000 Chromatography Maximum of Carboxyl End Polyester Hydrolysis Resistance GRI Test Method GG7 Group Content of 30 Weight per Unit Area Minimum 270 All Polymers Survivability (ASTM D5261) g/m2 % Post-Consumer Certification of Materials Maximum of All Polymers Recycled Material by Used 0% Weight

And:

Tal = Nominal long-term reinforcement design strength (kips/ft).

Table 2.10 Default and minimum values for the total geosynthetic ultimate limit strength reduction factor, RF (AASHTO, 2004).

Application Total Reduction Factor, RF All applications, but with product-specific All reduction factors shall be based on data obtained and analyzed in accordance product specific data. Neither RFID nor with Elias (2001) and Elias, et al. (2001). RFD shall be less than 1.1 Permanent applications not having severe consequences due poor performance or failure occur, nonaggressive soils, and 7.0 polymers meeting requirements listed in Table 2.9. Temporary applications not having severe consequences due poor performance or failure occur, nonaggressive soils, and 3.5 polymers meeting requirements listed in Table 2.9 and provided product specific data are not available.

Tult = Minimum average roll value (MARV) ultimate tensile strength (kips/ft).

RF = Combined strength reduction factor to account for potential long-term degration due to installation damage, creep and chemical aging (dim.).

RFID = Strength reduction factor to account for installation damage (dim.).

RFCR = Strength reduction factor to prevent long-term creep rupture of reinforcement (dim.).

RFD = Strength reduction factor to prevent rupture of reinforcement due to chemical and biological degradation (dim.).

2.2.10 Pullout resistance

The pullout resistance should be checked in every reinforcement level to prevent

the reinforcement from being pulled out of the soil. The length of reinforcement needed

to resist the pullout force must be extended beyond the active edge (Resistance Zone) 28

because that is the soil that is not moving, and this cannot be less than 3 ft. The total reinforcement length is equal to La + Le (Fig. 2.4 and Fig. 2.5).

The length beyond the active edge is calculated by the following equation:

= ∗ (2.16)

where:

Le = Length of reinforcement in resisting zone (ft.).

Tmax = Applied factored load in the reinforcement.

Φ = Resistance factor for reinforcement pullout.

F* = Pullout friction factor (dim.)

α = Scale effect correction factor (dim.)

σv = Unfactored vertical stress at the reinforcement level in the resistant zone (ksf).

C = Overall reinforcement surface area geometry factor based on the gross perimeter of the reinforcement and is equal to 2 for strip, grids and sheet type reinforcements, i.e., two sides (dim.)

Rc = Reinforcement coverage ratio as specified in (Fig. 2.9 and Fig. 2.10)

The values for F* and α shall be determined from the product specifics pullout tests in the project backfill material or equivalent soil or they can be determined

empirically or theoretically.

If standards backfill materials as specified in AASHTO LRFD Bridge Construction

Specification, Article 7.3.6.3 with the exception of uniform sand (Cu < 4) is used. In the absence of test data conservative values from Table 2.11 and Fig. 2.11 can be used for α 29

and F*, respectively. If we are using ribbed steel and the Cu is unknown at the moment

of the design it could be assumed as 4 to determine F*.

Table 2.11 Default values for the scale effect correction factor  (AASHTO, 2004) Reinforcement Type Default Value for α All Steel Reinforcement 1.0 Geogrids 0.8 Geotextiles 0.6

Fig. 2.11 Default values for the pullout friction factor F* (AASHTO, 2004).

2.3 K-Stiffness Method

2.3.1 General

The K-Stiffness method was first proposed by Allen and Bathurst (2003). The

calculations used in this method were empirically derived from full scale walls at

working conditions where reinforcement strain measurements were used to back

calculate the force in each reinforcement level. This method relies on the difference in

stiffness of the wall components to distribute the loads and also take into consideration

the wall toe restraint that produces lower pressures in the lowest part of the wall.

This method can be used as an alternative to the Simplified Method provided in

AASHTO LRFD Bridge Design Specification and summarized in the Section 2.1 to design the internal stability of MSE Walls up to 25 ft and that are not directly supporting other structures or in location where high settlement is expected. The use of the K-Stiffness method in areas where these requirements are not met must be considered experimental and will require the use of special monitoring equipments and the approval of the State Geotechnical Engineer.

The load factor provided in Table 2.12 must be used as minimum values to be used for the K-Stiffness method although the factors provided in Table 2.1 still apply.

These load factors were calculated assuming that the soil parameters are well known at the time of design. In practice this is not always true, so the soil parameters are assumed based in previous experiences with the material that is going to be used as backfill. The K-Stiffness method was calibrated to use plane strain soil friction angle. The 31

following equations should be used to approximate the plane strain soil friction angle from a triaxial or direct shear results:

For triaxial test data (Lade and Lee, 1976):

=1.5 − 17 (2.17)

For direct shear test data (based in interpretation of data presented by Bolton

(1986) and Jewell and Wroth (1987)):

= tan (1.2 tan ) (2.18)

Note that the use of the triaxial or direct shear friction angle will only introduce

some conservatism in the prediction of the loads.

This method was calibrated for a mean value of K0 of 0.3 so friction angles higher

than 44° shall not be used.

The maximum resistance factors to be used for the K-Stiffness Method are listed

in Table 2.13 for the strength and extreme event limit states for internal stability. For

service limit state a resistance factor of 1.00 should be used, except for the evaluation

of overall slope stability as described in AASHTO LRFD specification. These resistance

factors are consistent with the use of select granular backfill and used in conformance

with WSDOT Standard Specifications.

Table 2.12 Load factors for permanent loads for internal stability of MSE walls designed using the K-Stiffness method, p (WSDOT, 2006)

Minimum Type of Load Load Factor EV: Vertical Earth Pressure:

 MSE Wall soil reinforcement loads (K-Stiffness Method, 1.55 steel strips and grids).  MSE Wall soil reinforcement/facing connection loads (K- Stiffness Method, steel grids attached to rigid facings). 1.80

 MSE Walls soil reinforcement loads (K-Stiffness Method, 1.60 geosynthetics).  MSE Wall soil reinforcement/facing connection loads (K- Stiffness Method, geosynthetics). 1.85

As in the Simplified Method presented by AASHTO the critical reinforcement

load must be determined in two locations, the boundary between the active and

resistance zone (Fig. 2.4 and Fig. 2.5). The design of MSE Walls assumes that the wall

facing and the reinforced backfill acts as a coherent unit to form a gravity structure. The

effect of large vertical spacing (> 2.7 ft.) is not well understood and the use of these

higher spacing must be avoided unless full scale wall data is available.

The factored vertical stress v at each reinforcement level shall be:

=+++∆ (2.19)

Table 2.13 Resistance factors for the strength and extreme event limit states for MSE walls designed using the K-Stiffness method (WSDOT, 2006)

Limit State and Reinforcement Type Resistance Internal Stability of MSE Walls, K-Stiffness Method Factor Metallic 0.85 rr Reinforcement Rupture (3) Geosynthetic 0.80 Metallic 0.85 sf Soil Failure (1) Geosynthetic 1.00 Metallic 0.85 cr Connection Rupture Geosynthetic 0.80(3) Steel Ribbed Strips (at z < 2) 1.10 Steel Ribbed Strips (at z > 2) 1.00 (2) po Pullout Steel Smooth Strips 1.00 Steel Grids 0.60 Geosynthetic 0.50 Combined static/earthquake Metallic 1.00 EQr loading (Reinforcement and (3) Geosynthetic 0.95 connector rupture) Steel Ribbed Strips (at z < 2) 1.25 Combined static/earthquake EQp (2) Steel Ribbed Strips (at z > 2) 1.15 loading (Pullout) Steel Smooth Strips 1.15 Steel Grids 0.75  Geosynthetic 0.65 (1) If default value for the critical reinforcement strain of 3.0% or less is used for flexible wall facings, and 2.00% or less for stiff wall facing (for a facing stiffness factor of less than 0.9).

(2) Resistance factor values in table for pullout assume that the default values for F* and  provided in Fig. 2.11 and Table 2.11 respectively are used and are applicable.

(3) This resistance factor applies if installation damage is not severe (i.e., RFID < 1.7). Severe installation damage is likely if very light weight reinforcement is used. Note that when installation damage is severe, the resistance factor needed for this limit state can drop to approximately 0.15 or less due to greatly increased variability in the reinforcement strength, which is not practical for design.

where:

σV = The factored pressure due to resultant of gravity forces from soil self weight within and immediately above the reinforced wall backfill and any surcharge loads present (ksf).

p = The load factor for vertical earth pressure EV in Table 2.1 and Table 2.12 (dim.).

LL = The load factor for live load surcharge per the AASHTO LRFD Specifications (dim.). q = Live Load Surcharge (ksf).

H = The total vertical height at the wall face (ft.).

S = Average soil surcharge depth above wall top (ft.).

∆σV = Vertical stress increase due to concentrated surcharge load above the wall (ksf).

The K-Stiffness method differs from the other that it determines the maximum

reinforcement load from the gravity forces acting in the wall and then it adjust the

maximum load per level of reinforcement using a load distribution factor (Dtmax) and some others empirical factors that account the stiffness of the facing and reinforcement, the facing batter, etc. to determine Tmax.

To calculate the maximum factored load at each reinforcement level, the

following equation shall be used:

=0.5 +∆ (2.20)

where:

SV = Vertical spacing (ft.).

K = Index lateral earth pressure coefficient equal to K0 = 1-sinϕ (dim.).  v = The factored pressure due to resultant of gravity forces from soil self weight within and immediately above the reinforced wall backfill and any surcharge loads present (ksf).

Dtmax = Distribution factor to calculate Tmax for each layer as a function of depth fig (dim.).

Sglobal = Global reinforcement stiffness (ksf).

Φg = Global stiffness factor (dim.).

Φlocal = Local stiffness factor (dim.).

Φfb = Facing batter factor (dim.).

Φfs = Facing stiffness factor (dim.).

∆σH = Horizontal stress increase resulting from concentrated horizontal surcharge (ksf).

The following equation shall be used to calculate the global reinforcement stiffness (Sglobal) which takes into account the stiffness of the entire wall section.

∑ = = (2.21) ( )

where:

Jave = Average stiffness of all reinforcement layers within then entire wall section on a per foot of wall width basis (kips/ft).

Ji = Stiffness of an individual reinforcement layer on a per foot of wall width basis (kips/ft).

H = Total wall height (ft.).

n = Number of reinforcement layers within the wall section (dim.).

The global stiffness factor shall be calculated as follows:

. =0.25 (2.22)

where:

Pa = Atmospheric pressure (2.11 ksf).

The local stiffness factor shall be calculated as follows:

= (2.23)

where:

= (2.24)

And:

Slocal = Local stiffness that consider the stiffness and reinforcement density at a given layer (ksf).

a = 1.0 for geosynthetic walls and 0.0 for steel reinforced walls.

J = Stiffness of an individual reinforcement layer (kips/ft.).

SV = Vertical spacing (ft.).

The wall face batter factor (Φfb), which takes into account the influence of the

reduced soil weight on reinforcement loads, shall be calculated as follows:

= (2.25)

where:

Kabh = Horizontal component of the active earth pressure coefficient accounting for wall face batter (dim.).

Kavh = Horizontal component of the active earth pressure coefficient assuming that the wall is vertical (dim.). d = Constant coefficient recommended to be 0.25 to provide the best fit to empirical data (dim.).

To determine Kabh and Kavh Coulomb’s equation can be used assuming that there

is no friction between the wall and the soil and a horizontal backslope as follows:

() = (2.26)

where:

Φ = Peak friction angle (°).

ω = Wall face inclination, positive in a clockwise direction from vertical. This should be set to 0 to calculate Kav (°).

To calculate the horizontal component of the active earth pressure coefficient the following equation shall be used assuming no wall-soil friction:

= cos (2.27)

= (2.28)

The data obtained from geosynthetics walls using segmental concrete blocks and

propped panel wall facing, shows a significantly reduced stress in the reinforcement. To

account for that was derive the facing stiffness factor (ϕfs). This factor is not well known

how it will affect steel walls and should be set to 1.00 for steel and flexible faced wall.

The recommended formula for this is:

. = (2.29)

and

= (2.30)

where:

bw = Thickness of the facing column.

L = Unit length of the wall.

H = Total wall face height.

E = Modulus of the facing material. 39

heff = Equivalent height of an un-jointed facing column that is 100% efficient in transmitting moment throughout the facing column.

Pa = Atmospheric pressure used to preserve dimensional consistency (2.11 Ksf.)

η, k = Dimensionless coefficients determined from empirical data, 0.5 and 0.14, respectively.

Dtmax shall be determined using Fig. 2.12. This distribution only applies to wall constructed in firm soil. The rock and soft soil distribution should be different; it

becomes more triangular as the soil becomes more compressible.

2.3.2 Strength limit state design for internal stability for geosynthetic walls

The design of geosynthetics wall must check four possibilities of failures: 1) Soil failure,

2) Reinforcement failure, 3) Connection failure and 4) Reinforcement Pullout. In this

Fig. 2.12 Dtmax as a function of normalized depth below wall top plus average surcharge depth: a) generally applies to geosynthetic walls, b) generally applies to polymer strap walls and extensible or very lightly reinforced steel systems, and c) generally applies to steel reinforced systems (WSDOT, 2006). 40

section we are just going to explain the soil failure and how to obtain the parameter needed for Equation 2.20 because in this method the others failure methods are treated as specified in the AASHTO Bridge Design Specification (2004) described in the section

2.2 with the differences that Tmax is obtained from Equation 2.20 and the load factor

provided in Table 2.12 must be used as minimum values to be used for the K-Stiffness

method although the factors provided in Table 2.1 still apply.

Soil failure is considered when the soil reaches its peak shear strain, because at

strains higher than that the soil lowers its friction angle. The purpose of this part of the

design is to select a geosynthetic that at the working conditions (strain, stress,

temperature, etc.) its stiffness is large enough to prevent soil failure to occur.

The stiffness for final design must be obtained using products specific

isochronous creep data obtained in accordance with WSDOT Standard Practice T925

(WSDOT, 2006). For design the secant stiffness should be used. If the reinforcement

ratio (Rc) is less than 1, the reinforcement stiffness must be calculated as follow:

= (2.31)

where:

J = Reinforcement Stiffness modified for Rc.

JEOC = Reinforcement Stiffness at the end of construction, which can be assumed to be after 1,000 hours.

Rc = Reinforcement coverage ratio as in Fig. 2.10.

To calculate the factored strain in the reinforcement at the end of design life (75 years for permanent structures is typically used) the following equation shall be used:

= (2.32)

where:

εrein = Factored reinforcement strain.

Tmax = Maximum factored load from Equation 2.20

JDL = Reinforcement stiffness at the end of design life.

sf = Resistance factor from (Table 2.13).

The reinforcement strain (εr) should be limited to the maximum soil strain which can be assumed for granular soils to be 3% for flexible faced wall and 2% for stiff faced wall if a ϕfs of less than 0.9 is used for design.

2.3.3 Strength Limit state design for internal stability for steel walls

The design of steel reinforced wall must check four possibilities of failures: 1) soil

failure, 2) reinforcement failure, 3) connection failure and 4) reinforcement pullout. In

this section we are just going to explain how to obtain the parameter needed for

Equation 2.20 and any difference with AASHTO. In this kind of wall we do not have to

worry about soil failure because if we keep the stress below yield (Equation 2.33) the

reinforcement strain will not be higher than the soil peak strain. The others failure

methods are treated as specified in the AASHTO Bridge Design Specification (2004) 42

described in the section 2.2 with the differences that Tmax is obtained from Equation

2.20 and the load factor provided in Table 2.12 must be used as minimum values to be

used for the K-Stiffness method although the factors provided in Table 2.1 still apply.

To begin with the design a trial spacing and steel area based on the end of

construction (EOC) conditions (no corrosion) must be chosen to calculate the

reinforcement stiffness and Sglobal (Equation 2.21).

The reinforcement rupture has to be checked at the end of life of the wall. In this

method this limit state is verified using the ultimate strength of the steel instead if the

yield strength as follows:

≤ = (2.33)

CHAPTER 3

DESIGN METHODOLOGY

3.1 Concept

As noticed in the literature review the lateral earth pressure coefficient (K values) used for design geosynthetics walls are lower than those used to design steel walls. This is because geosynthetics walls are less rigid permitting the wall to yield and work under actives pressures instead of at rest pressures as in steel walls.

The concept for this design is based on steel bars that will behaves more like a geosynthetic, allowing the wall to deform sufficient to lower the stresses to active stresses. To be able to do that, crimps (Fig. 3.1) were made in steel reinforcing bars like the ones we used in reinforced concrete. These crimps allow the steel bar to be more flexible and permit bigger deformations and lowers working loads. Also having crimps in the bars creates additional pullout resistance.

Another problem in current designs is that actual steel straps and wires have a large cross sectional area and in order to use the steel at the maximum capacity allowed by the code (about 50% of yield stress) we need to have large horizontal spacing between bars which is not allowed in the code for wire facings and is not economically suitable for concrete panels facings. Therefore a more efficiently way to use the steel is proposed with the use of smaller bars with crimps which will resist the stresses behind the wall, make the wall more flexible and lower the cost of it. 44

Fig. 3.1 Example of a crimp in a steel rebar.

3.2 Crimp Properties

A variety of tests were performed by Suncar (2010) to characterize the pullout

resistance and the tensile behavior of the steel bar with crimps when buried under soil

at different overburden pressures. The data presented in this thesis to obtain the

different properties needed for the design is based on the data presented by Suncar

(2010).

The crimps properties presented by Suncar (2010) are based on a soil with a

friction angle of at least 38°. More testing has to be done in order to characterize the

effect of the friction angle in the properties of the crimps. There are two sizes of crimp

on each bar. The crimp 1 is the biggest crimp and the crimp 2 is the medium crimp of

each bar size as presented by Suncar (2010). This crimps where made taking into

account the minimum radii as specified in the AASHTO LRFD Bridge Design Specifications

(2004).

3.2.1 Pullout resistance

The first property needed for the design is the crimp pullout resistance. In this

case the pullout resistance is going to be divided in two parts. The first one consider the 45

pullout resistance of a single straight steel bar (Fig. 3.2) because the crimps are going to be separated by a certain spacing and the resistance provided by that straight section needs to be taken into account. The second part is the pullout resistance provided by the crimp itself. As the crimp are pulled trough the soil, friction and passive forces are developed preventing the crimp from sliding. The crimp pullout resistance is going to be dependent on two variables: The effective vertical stress in the crimp and the tension at which the crimp is working. The results from the pullout resistance test are illustrated in

Fig. 3.3 thru Fig. 3.8 along with a fit made to come up with the design charts.

The data presented by Suncar (2010) shows all the information obtained from the pullout tests made in crimped bars. The pullout resistance of the straight bar and the crimps were defined at a displacement of 0.75”.

Several tests were performed on 5/8’’ and 1/2'’ steel reinforcing crimped bars to characterize its pullout behavior using different sizes of crimps. The pullout behavior of the 3/8’’ steel reinforcing bar and 1/4'’ steel smooth crimped bars were extrapolated based on the results from the 5/8’’ and 1/2'’ crimped bars. Those extrapolated results were compared with a measured curve of each crimp size of the 3/8’’ diameter bar and the results show a difference of less than 10% between the extrapolated and the measured curves (Fig. 3.9 and Fig. 3.10).

The 1/4'’ bar properties were extrapolated assuming half pullout resistance of the 1/2’’ bar at the same percentage of the working stress referenced to the yield stress.

This results were not verified and taking into account that the 1/4’’ bar is smooth and the 1/2'’ has some corrugation the behavior is not expected to be the same. 46

For the crimp 1 of the 1/2'’ bar the pullout resistance (Fig. 3.3 ) was just obtained till a working load of 6,000 lbs (about 50% of yield strength) because that was the maximum working load. When doing the pullout design of the wall as we apply the safety factor to the maximum tension the tensions in the crimp might increase above

6,000 lbs. To be able to account for that, an assumption that the bar is totally straighten at 8,500 lbs was made so there is no crimp resistance left.

3.2.2 Crimp deflection

When dealing with retaining structures the deflection in the wall is a determining

factor that indicates if the wall is going to be working at active state of stress or at-rest

state of stress. The deflection of the wall is preferred to be enough to work in active

state of stress because these stresses are about 50% lower than the at-rest allowing the

wall to be less expensive.

There have been various publication about the deflection needed to reach the

active condition. Bonaparte (1988) stated that at 0.2% strain of the steel reinforcement is required to reach the active condition behind the wall. Terzaghi reported that only a

0.5% of the wall height is required to reach the active condition and Clough and Duncan

(1991) reported that 0.1% of the wall height is required for dense sand, 0.2% for

medium dense sand and 0.4% for loose sand.

Tension test of crimped bars at different effective vertical stress were also made

and presented by Suncar (2010). The results of these tests are presented in Fig. 3.11

thru Fig. 3.15.

350

300

250

200 5/8'' dia. (Suncar, 2009) 5/8'' dia. (Fitted) 1/2'' dia. (Suncar, 2009) 150 1/2'' dia. (Fitted) 3/8'' dia. (Suncar, 2009)

100 3/8'' dia. (Fitted) Resistance @ 0.75 in of displacement (lbs/ft) @ in of displacement 0.75 Resistance

0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 Vertical Stress (psf)

Fig. 3.2 Straight steel reinforcement bar pullout resistance. 47

900 850 800

750 360 psf (Suncar, 2009) 700 360 psf (Fitted) 650 720 psf (Suncar, 2009) 600 720 psf (Fitted) 550 1080 psf (Suncar, 2009) 500 1080 psf (Fitted) 450 1440 psf (Suncar, 2009) 1440 psf (Fitted) 400 2160 psf (Suncar, 2009) 350 2160 psf (Fitted) 300 Crimp Pullout Resistance (lbs) Resistance Crimp Pullout 2880 psf (Suncar, 2009) 250 2880 psf (Fitted) 200 3600 psf (Suncar, 2009) 150 3600 psf (Fitted) 100 4320 psf (Suncar, 2009) 50 4320 psi (Fitted) 0 0 1000 2000 3000 4000 5000 6000 7000 8000 Tension Load in the Crimp (lbs)

Fig. 3.3 1/2'' dia. steel reinforcement bar crimp 1 pullout resistance. 48

700

650

600

550

500

450 360 psf (Extrapolated) 400 720 psf (Extrapolated)

350 1080 psf (Extrapolated) 1440 psf (Extrapolated) 300 2160 psf (Extrapolated) 250 2880 psf (Extrapolated)

Crimp Pullout Resistance (lbs) Resistance Crimp Pullout 3600 psf (Extrapolated) 200 4320 psf (Extrapolated) 150

100

0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 Tension Load in the Crimp (lbs)

Fig. 3.4 3/8'' dia. steel reinforcement bar crimp 1 pullout resistance. 49

450

400

350

300 360 psf (Extrapolated)

250 720 psf (Extrapolated) 1080 psf (Extrapolated) 1440 psf (Extrapolated) 200 2160 psf (Extrapolated) 2880 psf (Extrapolated) 150 Crimp Pullout Resistance (lbs) Resistance Crimp Pullout 3600 psf (Extrapolated) 4320 psf (Extrapolated) 100

0 0 500 1000 1500 2000 Tension Load in the Crimp (lbs)

Fig. 3.5 1/4'' dia. steel smooth bar crimp 1 pullout resistance. 50

800

750

700

650 360 psf 600 360 psf (Fitted) 720 psf 550 720 psf (Fitted) 500 1080 psf 450 1080 psf (Fitted)

400 1440 psf 1440 psf (Fitted) 350 2160 psf 300 2160 psf (Fitted)

Crimp Pullout Resistance (lbs) Resistance Crimp Pullout 250 2880 psf 2880 psf (Fitted) 200 3600 psf 150 3600 psf (Fitted) 100 4320 psf

50 4320 psf (Fitted)

0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Tension Load in the Crimp (lbs)

Fig. 3.6 1/2'' dia. steel reinforcement bar crimp 2 pullout resistance. 51

600

550

500

450

400

360 psf (Extrapolated) 350 720 psf (Extrapolated)

300 1080 psf (Extrapolated) 1440 psf (Extrapolated) 250 2160 psf (Extrapolated) 2880 psf (Extrapolated) 200 Crimp Pullout Resistance (lbs) Resistance Crimp Pullout 3600 psf (Extrapolated) 4320 psf (Extrapolated) 150

100

0 0 1000 2000 3000 4000 5000 Tension Load in the Crimp (lbs)

Fig. 3.7 3/8'' dia. steel reinforcement bar crimp 2 pullout resistance. 52

400

350

300

250 360 psf (Extrapolated) 720 psf (Extrapolated)

200 1080 psf (Extrapolated) 1440 psf (Extrapolated) 2160 psf (Extrapolated) 150 2880 psf (Extrapolated)

Crimp Pullout Resistance (lbs) Resistance Crimp Pullout 3600 psf (Extrapolated) 100 4320 psf (Extrapolated)

0 0 500 1000 1500 2000 2500 Tension Load in the Crimp (lbs)

Fig. 3.8 1/4'' dia. steel reinforcement bar crimp 2 pullout resistance. 53 54

400

350

300

250

200 3/8'' Meassured 150 3/8'' Extrapolated

100 Crimp Pullout Resistance (lbs) Crimp Pullout

0 0 2000 4000 6000 Tension Load in the Crimp (lbs)

Fig. 3.9 3/8'' dia. steel reinforcement bar crimp 1 measured vs. extrapolated pullout resistance.

300

250

200

150 Measssured 100 Extrapolated

Crimp Pullout Resistance (lbs) Crimp Pullout 50

0 0 1000 2000 3000 4000 5000 6000 Tension Load In the Crimp (lbs)

Fig. 3.10 3/8'' dia. steel reinforcement bar crimp 2 measured vs. extrapolated pullout resistance. 55

The 1/4'’ bar properties were extrapolated assuming half deflection of the 1/2’’ bar at the same percentage of the working stress referenced to the yield stress. This results were not verified and taking into account that the 1/4’’ bar is smooth and the

1/2'’ has some corrugation the behavior is not expected to be the same.

All the deflection presented in the graph is assumed to come from the crimps because the deflection of the straight bar is negligible compared to the deflection of the crimp. The design graph presented does not take into account the difference in effective vertical pressures because the data shows a negligible difference between tests so one fitting was made with all the data.

3.3 Model Definition

The model presented in this thesis is for internal design of the wall only. For

external equilibrium the requirements of AASHTO must be met.

The definition of this model is going to be based in the assumption that with the

crimps the wall is going to yield enough to work under the active state of stress. Based

on this assumption the forces on the wall are going to be defined as follows:

= +∆ (3.1)

where:

H = Horizontal pressure in the wall (psf).

Ka = Horizontal pressure active coefficient as specified in Equation 2.2 (dim.).

13000

12000

11000

10000

9000

8000

7000 1/2'' dia. (Fitted) 6000 1/2'' dia 5 psi (Suncar, 2009) 1/2'' dia. 10 psi (Suncar,2009) 5000 1/2'' dia. 30 psi (Suncar, 2009)

Tension Force in the Crimp (lbs) Force in the Tension 4000

3000

2000

1000

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Displacement of the Crimp (in)

Fig. 3.11 1/2'' dia. steel reinforcement bar crimp 1 displacement curve. 56

3500

3000

2500

2000

3/8'' dia. Measured (Suncar, 2009) 1500 3/8'' dia. Fitted Tension Force in the Crimp (lbs) Force in the Tension 1000

500

0 0 0.1 0.2 0.3 0.4 0.5 0.6 Displacement of the Crimp (in)

Fig. 3.12 3/8'' dia. steel reinforcement bar crimp 1 displacement curve. 57

4000

3000

2000

1/4'' dia. Extrapolated Tension Force in the Crimp (lbs) Force in the Tension

1000

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Displacement of the Crimp (in)

Fig. 3.13 1/4'' dia. steel reinforcement bar crimp 1 displacement curve. 58

10000

9000

8000

7000

6000

5000 1/2'' dia 5 psi (Suncar, 2009) 1/2'' dia. 10 psi (Suncar,2009)

4000 1/2'' dia. 30 psi (Suncar, 2009) 1/2'' Crimp 2 (Fitted)

Tension Force in the Crimp (lbs) Force in the Tension 3000

2000

1000

0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Displacement of the Crimp (in)

Fig. 3.14 1/2'' dia. steel reinforcement bar crimp 2 displacement curve. 59

3500

3000

2500

2000

3/8'' dia. Measured (Suncar, 2009) 1500 3/8'' dia. Fitted Tension Force in the Crimp (lbs) Force in the Tension 1000

500

0 0 0.05 0.1 0.15 0.2 0.25 0.3 Displacement of the Crimp (in)

Fig. 3.15 3/8'' dia. steel reinforcement bar crimp 2 displacement curve. 60

3000

2000

1/4'' in dia Extrapolated

1000 Tension Force in the Crimp (lbs) Force in the Tension

0 0 0.05 0.1 0.15 0.2 0.25 Displacement of the Crimp (in)

Fig. 3.16 1/4'' dia. steel reinforcement bar crimp 2 displacement curve. 61 62

v = Pressure due to resultant of gravity forces from soil self weight within and immediately above the reinforced wall backfill and any surcharge loads present (psf).

H = Horizontal stress at reinforcement level resulting from any applicable concentrated horizontal surcharge load (psf).

The maximum force supported by the each reinforcement is going to be

calculated based on the tributary area concept as follow:

= (3.2)

where:

Tmax = Maximum load in each reinforcement (lbs).

H = Horizontal pressure in the wall as in Equation 3.1 (psf).

Sv = Vertical spacing ≤ 2.7 ft (ft).

SH = Horizontal spacing (ft).

The maximum tensile force in the reinforcement (Tmax) can also be calculated using

any other method approved by AASHTO like the K-Stiffness method presented in this

thesis.

3.3.1 Tensile design of the wall

The tensile design of the wall takes into consideration the loads that are going to

be received by the steel cross-sectional area during the design life of the structure. The

purpose if this step of the design process is to prevent the rupture of the reinforcement

at the calculated workings loads. 63

The maximum load that the steel can handle is going to be limited by a percentage of the yield stress of the steel used in the design. The maximum force allowable by the steel shall be calculated as follows:

= (3.3)

where:

Tal = Allowable tension force in the steel (lbs).

Fy = Yield stress of the steel (psi).

Ac = Steel cross sectional area after corrosion as specified in Sections 0 and 2.2.9.2 (in2).

Combining equations 3.2 and 3.3 a basic equation for the tensile design of the

wall can be obtained:

∅ ≤ (3.4)

where:

Ø = Factor of safety against rupture. In this case 2 is going to be used (dim.).

Tmax = Maximum load in each reinforcement (lbs).

Tal = Allowable tensile force in the steel (lbs).

So:

≤ (3.5) ∅

The maximum horizontal spacing should be limited by the maximum spacing permitted by the facing that is going to be used. For flexible wall facing the maximum horizontal spacing allowed by the code is 3 ft.

3.3.2 Pullout design of the reinforcement

The pullout design takes into consideration the friction resistance provided by

the soil to the reinforcement to prevent it from being pulled out from the soil mass by

the soil pressures making the wall collapse.

The distribution of the tensile force along the reinforcement without crimp will

be assumed to vary linearly with a slope defined by the pullout resistance per unit

length of the reinforcement (Fig. 3.17). In this case the contribution of the crimp will be

defined as a step localized value that will be located at the center of the crimp. This

value is going to be a function of the effective vertical stress and the tension in that

crimp.

The spacing between crimps needs to be assumed before entering in the design.

The values proved to be useful and efficiently range from 1.50 ft. to 2.00 ft. Other

spacing can be used if they meet the required displacement and length of reinforcement

for the specific project.

Fig. 3.17 Tension distribution along the reinforcement behind the wall face.

To calculate the total length needed for pullout resistance a detailed analysis must be made in each reinforcement level to calculate the tension in each crimp as we go farther from the wall face and select the correspondence pullout resistance value for each crimp. This analysis has to be done from the locus of maximum tension (Fig. 2.5), assuming the behavior of an extensible reinforcement, and moving away from the wall face. The followings formulas define the pullout resistance for each part of the bar:

= + = (3.6)

= (3.7)

= ∑ (3.8)

where: 66

F = Total friction force resisted by the crimped bar (lbs).

Fstraight = Friction force resisted by the straight part of the bar (lbs).

fstraight = Straight bar friction factor per unit length for a given effective vertical stress as show in Fig. 3.2 (lbs/ft).

Le = Length of reinforcement in resisting zone (ft.).

Fcrimp = Friction force resisted by the crimps in the bar (lbs).

fcrimp = Crimp friction resistance for a given effective vertical stress and working tensile load as shown in Fig. 3.3 to Fig. 3.8 (lbs). p = Load factor against pullout taken as 1.44 (dim.).

Tmax = Maximum load in each reinforcement (lbs).

The total length of reinforcement needed in each layer is going to be defined as

the summation of the length of the reinforcement in the active edge for extensible

reinforcement (La) and the length of reinforcement in the resisting zone (Le) (Fig. 2.5).

∅ =ℎtan(45− ) (3.9)

= + (3.10)

where:

La = Length of reinforcement in the active edge assuming an extensible reinforcement (ft.).

h = Height from the bottom of the wall to the reinforcement layer (ft.).

Ø = Effective friction angle of the soil (°). 67

Lt = Total length of reinforcement needed (ft.).

Le = Length of reinforcement in the resisting zone (ft.).

3.3.3 Wall deflections

In this section the deflection in each reinforcement layer is going to be

calculated so the designer can know its values and can make decisions with them. The

deflection in each reinforcement level is going to be dependent on the crimp spacing

and the tensions in the crimps. In this model we will make the assumption that all the

deflection is coming from the deformations of the crimps and the bar deformation is

going to be neglected because it is expected to be too small compared to the crimp

deflection.

To calculate the deflection in the crimped bar the tension force is each crimp

must be known first. The total deflection in each layer is going to be defined as the

summation of all the deformations of all the crimps in the bar (the ones in the active

zone and the ones in the resistance zone).

= ∑ (3.11)

where:

δt = Total wall deflection in a given layer (in.).

n = Number of crimps in a given layer (dim.).

δi = Deflection in a given crimp in a layer (in.).

A detailed analysis must be made in each reinforced level. This analysis has to be done from the locus of maximum tension toward the front of the wall and also toward the end of the reinforcement so all the crimps are taken into account. To calculate the expected deflection in the wall is recommended to use unfactored loads to obtain a real value for deflection and not an overestimated value caused by the factored loads.

To reach the active condition this model is going to consider, based on past investigation, a minimum deflection of 0.20% of the wall height is required with an average deflection of 0.35% of the wall height preferred taking into consideration that we will be dealing with dense to medium dense soil in the reinforced zone.

CHAPTER 4

DESIGN OF A 40 FT. HIGH MECHANICALLY STABILIZED EARTH (MSE) WALL USING THE

PROPOSED METHODOLOGY

4.1 Introduction

This chapter is going to present the design of wall that is going to be constructed and monitored to see the behavior of an actual constructed wall using the newly proposed crimped bars and design methodology. A detailed design of one layer is going to be explained while all the calculations are going to be presented in Appendix B.

4.2 Description Of The Wall

The wall that is going to be analyzed and designed is a 40 ft. wall with concrete panel facing. The concrete panels will be 12.5 ft. x 2.5 ft. Each panel needs to be attached at least to two rods or straps so the maximum horizontal spacing will be limited to 6.25 ft and the vertical spacing will be used as 2.5 ft. The crimps spacing proved to be useful for this design are 2.00 ft and 1.50 ft. This example calculation is going to be based in the 1.50 ft spacing between crimps and using crimp 1 although the summary table is presented for both crimp spacing and sizes all the calculations tables are presented in Appendix A.

The yield stress of the reinforcement that is going to be used in this design is 60 ksi. 70

The soil that is going to be used in the design will be a well graded sand with a friction angle of 38° and a unit weight of 130 pcf.

This wall is going to be considered a permanent wall with a design life of 75 years.

4.3 Wall Design

For the step by step explanation of the design the last layer of this wall will be

selected. This example will cover everything from the calculation of the soils properties to the calculation of the deflection in the layer.

The first thing to do to design the wall is calculate the vertical and horizontal stress in the desired layer. To do this Equation 2.2 reduced for vertical walls and 3.1 will

be used.

∅ 38 = tan (45− ) =tan (45− ) = 0.23788308 2 2

= = 130 18.75 = 2,437.50

= ( +∆) = (2437.50 0.23788308 + 0) = 579.84

Now that the horizontal stress is calculated the next step is calculate the

corroded area expected at the end of the life of the structure using considerations

specified in Sections 0 and 2.2.9.2 . After the calculation of the corroded area the

horizontal spacing needed in that layer can be calculated using Equation 3.5. In this layer

we are using a 3/8’’ diameter steel reinforcing bar. 71

= 0.00047 75 = 0.03525

( − 2 ) (0.375 − 2(0.03525)) = = = 0.07282 4 4

60000 0.07282 ≥ = = 1.51 ∅ 2 579.84 2.5

The horizontal spacing needs to be rounded down to fits the facing allowable

spacings and also to help the construction of the wall. Also the length of the

reinforcement need to be taken into account because it is not efficient to have a very

large length is better instead to have smaller horizontal spacing (Sh). For the purpose of

this thesis the horizontal spacing is going to be used as calculated just for the

comparison of the methods.

After calculating the horizontal spacing needed between bars to limit the

internal stresses on it to be 50% of the yield stress we are done with the tension design

of the wall. Now the pullout analysis needs to be done in order to complete the internal

design of the wall.

To begin with the pullout design the maximum pullout force to be resisted by the reinforcement needs to be calculated using Equations 3.2 and 3.6 and the location of

the maximum tension using Equation 3.9.

= = 579.84 2.5 1.51 = 2,188.90

= + = = 1.44 2188.90 = 3,152.01 72

∅ 38 =ℎtan(45− ) = 21.25 tan(45 − ) = 10.36 2 2

Now that we have the location of the maximum pullout force an analysis needs

to be done from this point and moving away from the wall face using the model

presented in Fig. 3.17 to know the length of reinforcement needed. First of wall a

calculation needs to be done to know the portion of straight bar that is just between the point of maximum force and the first crimp.

= −( −) (4.1)

= (4.2)

where:

X = Straight bar length between the point of maximum tension and the first crimp behind that (ft.).

Sc = Spacing between crimps (ft.).

La = Length of reinforcement in the active edge assuming an extensible reinforcement (ft.).

N = Number of crimps in the active edge length rounded down to the nearest integer (dim.).

10.36 = = =6.91≅6 1.5

= −( −) = 1.5 − (10.36 − 1.5 6) = 0.14

Now the pullout resistance of the straight bar is needed. Using the effective vertical stress at that level and knowing the size of the bar from Fig. 3.2 can be obtained the value of the pullout resistance per unit length of bar. Then multiplying that value times the straight bar length between the point of maximum tension and the first crimp and subtracting that from the total friction force we can find the tension in the first crimp. Having the tension in the crimp the pullout resistance of the crimp can be obtained using Fig. 3.3 thru Fig. 3.8.

=7.68

=− = 3152.01 − 0.14 7.68 = 3,044.49

= 170.59

Now that those values are calculated the tension in the second crimp can be

calculated and its deflection and pullout resistance can be obtained.

= − − = 3044.49 − 170.59 − 1.50 7.68 = 2,868.38

= 195.38

Following this procedure the tension in every crimp can be calculated. This

procedure can also be done from the point of maximum tension toward the wall face to

know the value of the tension in the connection. 74

To calculate the deflection of the crimps is better to use unfactored loads so a more precise value is obtained instead of a big value because of the factor in the loads.

The same procedure needs to be followed but using the value of Tmax.

= − = 2188.90 − 0.14 7.68 = 2,187.82

= 247.74

= 0.38

= − − = 2187.82 − 247.74 − 1.50 7.68 = 1,928.56

= 278.72

= 0.31

Following that procedure the displacement of all the crimps can be obtained and

the total deflection is the summation of the deflection of each individual crimp. The

crimps in the active zone need to be taken into account to calculate the total displacement of the wall face at that layer.

4.4 Designs Summary

Below are the summary tables of the walls designed using the proposed

methodology and the new type of reinforcement. The complete information of the

design of these walls is presented in Appendix B. These walls where designed with both

the crimp 1 and the crimp 2 using two different crimp spacing of 2.00 ft. and 1.50 ft.

Table 4.1 Design summary table for the wall designed with crimp 1 and Sc = 2 ft

Depth S T T L L h Bar max c t tdesign Steel Volume (in3)/ft of wall (ft) (ft) (lbs) (lbs) (ft) (ft) 1.25 1 1/4'' dia. 96.64 0.00 28.90 29.00 17.08 3.75 1 1/4'' dia. 289.92 0.00 27.68 29.00 17.08 6.25 1.8 3/8'' dia. 869.76 0.00 27.40 29.00 21.35 8.75 1.8 3/8'' dia. 1217.66 0.00 28.09 29.00 21.35 11.25 1.9 3/8'' dia. 1652.54 142.57 28.02 29.00 20.23 13.75 1.9 3/8'' dia. 2019.78 885.58 28.80 29.00 20.23 16.25 1.74 3/8'' dia. 2184.67 1291.89 27.58 29.00 22.09 18.75 1.51 3/8'' dia. 2184.67 1203.08 24.36 29.00 25.45 21.25 1.33 3/8'' dia. 2184.67 1406.91 23.71 29.00 28.90 23.75 1.19 3/8'' dia. 2184.67 1684.57 20.61 29.00 32.30 26.25 1.08 3/8'' dia. 2184.67 1750.97 18.84 29.00 35.59 28.75 0.99 3/8'' dia. 2184.67 2128.38 16.66 29.00 38.82 31.25 0.91 3/8'' dia. 2184.67 2270.71 14.27 29.00 42.24 33.75 0.84 3/8'' dia. 2184.67 2716.80 13.05 29.00 45.76 36.25 0.78 3/8'' dia. 2184.67 2849.54 11.83 29.00 49.28 38.75 0.73 3/8'' dia. 2184.67 3041.04 9.44 29.00 52.65 Total: 490.40

The wall design with crimp 1 shows a good behavior in terms of the deflection.

Although the minimum deflection was not reached in the first three and last one layers of the wall it is expected to reach the active condition. The deflection at the top will always be a problem because in order to get a reasonable bar length shorter horizontal spacing was used.

The amount of steel used in this wall is very low because of the long term behavior of the round bars that will lose less cross-sectional area due to the corrosion of the steel and that the deformation in the wall will allow the reach of the active condition.

Table 4.2 Design summary table for the wall designed with crimp 1 and Sc = 1.5 ft

Depth S T T L L h Bar max c t tdesign Steel Volume (in3)/ft of wall (ft) (ft) (lbs) (lbs) (ft) (ft) 1.25 1.3 1/4'' dia. 125.63 0.00 27.90 29.00 13.14 3.75 1.3 1/4'' dia. 376.90 0.00 28.18 29.00 13.14 6.25 2.3 3/8'' dia. 1111.36 0.00 28.46 29.00 16.71 8.75 2.4 3/8'' dia. 1623.55 0.00 28.30 29.00 16.01 11.25 2.1 3/8'' dia. 1826.50 0.00 27.52 29.00 18.30 13.75 2.06 3/8'' dia. 2184.67 700.22 27.80 29.00 18.66 16.25 1.74 3/8'' dia. 2184.67 725.18 25.08 29.00 22.09 18.75 1.51 3/8'' dia. 2184.67 824.16 22.36 29.00 25.45 21.25 1.33 3/8'' dia. 2184.67 726.52 19.64 29.00 28.90 23.75 1.19 3/8'' dia. 2184.67 994.22 18.43 29.00 32.30 26.25 1.08 3/8'' dia. 2184.67 1336.54 15.71 29.00 35.59 28.75 0.99 3/8'' dia. 2184.67 1732.71 14.49 29.00 38.82 31.25 0.91 3/8'' dia. 2184.67 2167.43 14.18 29.00 42.24 33.75 0.84 3/8'' dia. 2184.67 2345.95 10.55 29.00 45.76 36.25 0.78 3/8'' dia. 2184.67 2838.46 9.33 29.00 49.28 38.75 0.73 3/8'' dia. 2184.67 3041.04 8.11 29.00 52.65 Total: 469.04

Displacement (in) 0123 0

5 Sc = 2.0 ft 10 Sc=1.5 ft 15 Min. Disp. For 20 Active Condition

25Depth (ft) Max. Disp. For Active Condition 30

Fig. 4.1 Displacement of the face of the wall vs. depth of the wall designed using crimp 1. 77

Table 4.3 Design summary table for the wall designed with crimp 2 and Sc = 2 ft

Depth S T T L L h Bar max c t tdesign Steel Volume (in3)/ft of wall (ft) (ft) (lbs) (lbs) (ft) (ft) 1.25 1.2 1/4'' dia. 115.97 0.00 28.29 29.00 14.24 3.75 1 1/4'' dia. 289.92 0.00 27.07 29.00 17.08 6.25 2.1 3/8'' dia. 1014.72 0.00 29.00 29.00 18.30 8.75 2 3/8'' dia. 1352.96 19.16 28.63 29.00 19.22 11.25 1.8 3/8'' dia. 1565.57 365.50 28.71 29.00 21.35 13.75 1.8 3/8'' dia. 1913.47 774.74 28.19 29.00 21.35 16.25 1.74 3/8'' dia. 2184.67 1334.18 27.30 29.00 22.09 18.75 1.51 3/8'' dia. 2184.67 1469.45 27.75 29.00 25.45 21.25 1.33 3/8'' dia. 2184.67 1424.92 22.54 29.00 28.90 23.75 1.19 3/8'' dia. 2184.67 1702.57 19.32 29.00 32.30 26.25 1.08 3/8'' dia. 2184.67 1749.13 16.32 29.00 35.59 28.75 0.99 3/8'' dia. 2184.67 2142.96 14.88 29.00 38.82 31.25 0.91 3/8'' dia. 2184.67 2589.68 13.66 29.00 42.24 33.75 0.84 3/8'' dia. 2184.67 2756.89 12.44 29.00 45.76 36.25 0.78 3/8'' dia. 2184.67 2948.33 11.22 29.00 49.28 38.75 0.73 3/8'' dia. 2184.67 3145.92 8.24 29.00 52.65 Total: 484.62

Table 4.4 Summary table for the wall designed with crimp 2 and Sc = 1.5 ft

Depth S T T L L h Bar max c t tdesign Steel Volume (in3)/ft of wall (ft) (ft) (lbs) (lbs) (ft) (ft) 1.25 1.6 1/4'' dia. 154.62 0.00 28.79 29.00 10.68 3.75 1.4 1/4'' dia. 405.89 0.00 27.57 29.00 12.20 6.25 2.6 3/8'' dia. 1256.32 0.00 28.96 29.00 14.78 8.75 2.3 3/8'' dia. 1555.90 0.00 28.13 29.00 16.71 11.25 2.2 3/8'' dia. 1913.47 533.45 28.76 29.00 17.47 13.75 2.06 3/8'' dia. 2184.67 804.25 27.19 29.00 18.66 16.25 1.74 3/8'' dia. 2184.67 813.21 24.47 29.00 22.09 18.75 1.51 3/8'' dia. 2184.67 895.42 21.81 29.00 25.45 21.25 1.33 3/8'' dia. 2184.67 1063.25 20.54 29.00 28.90 23.75 1.19 3/8'' dia. 2184.67 1312.91 17.82 29.00 32.30 26.25 1.08 3/8'' dia. 2184.67 1328.48 15.10 29.00 35.59 28.75 0.99 3/8'' dia. 2184.67 1725.00 13.83 29.00 38.82 31.25 0.91 3/8'' dia. 2184.67 2175.71 11.94 29.00 42.24 33.75 0.84 3/8'' dia. 2184.67 2673.37 10.25 29.00 45.76 36.25 0.78 3/8'' dia. 2184.67 2948.33 8.93 29.00 49.28 38.75 0.73 3/8'' dia. 2184.67 3145.92 7.50 29.00 52.65 Total: 463.57 78

Displacement (in)

00.511.522.53 0

10 Sc = 2.0 ft 15 Sc=1.5 ft Min. Disp. For Active Condition 20 Max. Disp. For Active Condition Depth (ft) 25

Fig. 4.2 Displacement of the face of the wall vs. depth of the wall designed using crimp 2.

Although the wall designed with crimp 2 uses little less amount of steel than the one designed with crimp 1 the deflection in all the layer did not reach the minimum displacement required to reach the active condition. For this reason this size of crimp cannot be used to design MSE walls using the active condition.

CHAPTER 5

COMPARISON BETWEEN DESIGN METHODOLOGIES

5.1 Introduction

One of the biggest concerns when planning a project is choosing the design

approach to be used. This decision is going to be based by analyzing some aspects like:

safety, material availability, construction difficulty, time and money. The design

approach which can give us more benefits in each of those categories will be the winner.

A comparison between all three design methodology (AASHTO, K-Stiffness and Crimps) is presented in this chapter.

Although the K-Stiffness method only deals with the calculation of the maximum tension in the reinforcement a final designs using current materials (RECO Strap) is

presented. AASHTO guidelines for the internal design of the wall using RECO straps are

used with the maximum forces obtained from the K-Stiffness method.

A final design of the wall presented in Chapter 4 was made for the other two

methodologies (AASHTO and K-Stiffness) and is presented in this chapter so the reader

can analyze each design and arrive to his own conclusion.

5.2 Other Design Methodologies

A summary table of the wall designed using AASHTO approach and RECO strap is

presented in Table 5.1. The complete design information is presented in Appendix B. 80

Table 5.1 Summary table of the AASHTO design approach using RECO straps

Depth S S T L L h v max t tdesign Steel Volume (in3) / ft of wall (ft) (ft) (ft) (lbs) (ft) (ft) 1.25 6.25 2.50 1133.92 25.01 28.00 16.13 3.75 6.25 2.50 3274.34 25.53 28.00 16.13 6.25 4.32 2.50 3623.96 21.65 28.00 23.34 8.75 3.21 2.50 3623.96 19.46 28.00 31.36 11.25 2.61 2.50 3623.96 18.35 28.00 38.61 13.75 2.23 2.50 3623.96 17.77 28.00 45.11 16.25 1.98 2.50 3623.96 17.50 28.00 50.86 18.75 1.80 2.50 3623.96 17.49 28.00 55.85 21.25 1.63 2.50 3623.96 16.10 28.00 61.69 23.75 1.46 2.50 3623.96 14.01 28.00 68.95 26.25 1.32 2.50 3623.96 12.03 28.00 76.21 28.75 1.21 2.50 3623.96 10.14 28.00 83.46 31.25 1.11 2.50 3623.96 8.31 28.00 90.72 33.75 1.03 2.50 3623.96 6.52 28.00 97.98 36.25 0.96 2.50 3623.96 4.78 28.00 105.24 38.75 0.90 2.50 3623.96 3.07 28.00 112.49 Total: 974.13

The design presented in Table 5.2 was done with the maximum tensions

calculated using the k-Stiffness method and taking the consideration presented by

AAHSTO to do the internal design of the wall. The complete information of the design is

presented in Appendix B.

5.3 Designs Comparison

After seeing the designs made of the same wall using the different

methodologies used actually to design MSE walls and the one proposed in this thesis is

good to compare them to find the pros and cons of each one.

Table 5.2 Summary table of the K-Stiffness method using RECO straps

Depth S S T L L h v max t tdesign Steel Volume (in3) / ft of wall (ft) (ft) (ft) (lbs) (ft) (ft) 1.25 6.25 2.50 67.37 12.02 28.00 16.13 3.75 0.61 2.50 606.35 12.90 28.00 16.13 6.25 1.68 2.50 1684.30 13.92 28.00 16.13 8.75 3.30 2.50 3301.22 15.15 28.00 16.13 11.25 5.46 2.50 5457.12 16.62 28.00 16.13 13.75 5.48 2.50 5476.21 16.21 28.00 24.01 16.25 5.48 2.50 5476.21 16.01 28.00 33.53 18.75 5.48 2.50 5476.21 16.00 28.00 44.64 21.25 5.48 2.50 5476.21 14.67 28.00 57.34 23.75 5.48 2.50 5476.21 12.73 28.00 70.12 26.25 5.48 2.50 5476.21 10.88 28.00 77.50 28.75 5.48 2.50 5476.21 9.09 28.00 84.88 31.25 5.48 2.50 5476.21 7.34 28.00 92.26 33.75 5.48 2.50 5476.21 5.63 28.00 99.65 36.25 5.48 2.50 5476.21 3.95 28.00 107.03 38.75 5.48 2.50 5476.21 2.29 28.00 114.41 Total: 886.01

First of all the three design methodologies showed about the same required

length of reinforcement which means that the cost on excavation and selected fill will

be about the same. Any of the methods showed advantage over the others in this

aspect. This aspect can be improved with the use of bars with bigger deformations as

the one presented by Suncar, 2010 in addition to the crimp.

One of the most important parts of the total cost of a steel reinforced MSE wall

is the amount of steel needed to build the wall. In this aspect the proposed

methodology shows an impressive decrement in the steel needed to design a wall. As

shown in Fig. 5.1 the amount of steel needed to build a MSE wall with the proposed

methodology is about 50% lower than the amount needed using AASHTO methodology 82

and current reinforcing materials and 45% better than using the K-Stiffness method with the current reinforcing materials.

The K-Stiffness method was not used with the proposed reinforcing materials because this is an empirical method derived from the measurements of MSE walls and the effect in the calibration and factors in the model is not well known as the behavior of the materials is totally different.

974.13 1000 886.01

900

800

700

600 490.4 469.04

500

400

300 Steel Volume (in3) / ft of Wall 200

100

0 Crimp 1 Sc = 2.00 Crimp 1 Sc = 1.50 AASHTO Wall K-Stiffness Wall ft ft

Fig. 5.1 Steel usage for the existing and proposed design methodologies.

CHAPTER 6

CONCLUSIONS AND RECOMMENDATIONS

A new methodology for the design of MSE walls is proposed with the use of crimped rounds bar which behaves more efficiently under corrosion and that allows more deformation that will lead the wall to work under an active state of stress. This type of reinforcement proved to be useful. The length of reinforcement needed to take the pullout forces is the same for the others design methodologies. This total length is limited by AASHTO by 70% of the wall height and a single length must be used.

The proposed design methodology helps us save around 50% of steel compared to the actual designs. This means a huge improvement in the usage of steel versus the actual designs. This improvement is obtained because of the efficient behavior of rounded bars under corrosion and because of the flexibility in the bars that will allow us to reach the active condition.

With the results obtained from crimp 1 and crimp 2 can also be concluded that the number 2 crimp cannot be used in a design under the active state of stress because it did not met the requirements to reach the active condition.

Although all the theory behind the design of MSE walls and the theory about the displacement needed to reach the active condition have been met a real wall needs to be constructed and instrumented to prove the concepts proposed in this research. The construction and instrumentation of a wall using the proposed methodology not only will help us prove the theory behind this new type of bar also will help us adjust the design charts with the actual pullout resistance obtained from the field measurements 84

and will help us calibrate the K-Stiffness method with this new type of bar, which will help us to design with lowers load than the ones obtained using AASHTO.

More testing need to be done in order to characterize the behavior of smaller bars (1/4’’ dia.). Doing that more precise design in the upper part of the wall can be done.

More sizes of crimped needs to be tested in order to reach the minimum displacement to reach the active condition in every layer and more testing needs to be done with different soils to characterize the effect of the soil friction angle in the behavior of crimped bars.

REFERENCES

AASHTO. (1998). AASHTO LRFD bridge construction specifications. American Association of State Highway and Transportation Officials, Washington D.C.

AASHTO. (2004). LRFD bridge design specifications (3rd ed.). American Association of State Highway and Transportation Officials, Washington D.C.

Allen, T. M., & Bathurst, R. J. (2003). Prediction of reinforcement loads in reinforced soil walls. Washington State Department of Transportation, Seattle, Wa.

Barker, R. M., Duncan, J. M., Rojiani, K. B., Ooi, P. S., Tan, C. K., & Kim, S. G. (1991). Manual for the design of bridge foundation. NCHRP Report 343. TRB, National Research Council, Washington D.C.

Bolton, M. D. (1986). “The strength and dilatancy of sands”. Geotechnique , 36(1), 65-78.

Bonaparte, R. a. (1988). Reinforcement extensibility in reinforced soil wall design. Kluvwer Academic Publishers, London.

Clough, G. W. (1991). “Earth pressures”. Foundation engineering handbook (2nd ed.). In H. Y. Fang, & V. N. Reinhold, New York, pags. 224–235.

Elias, V. (2001). Corrosion/degradation of soil reinforcement of mechanically stabilized earth wall and reinforced soil slopes. Federal Highway Administration, Washington D.C.

Elias, V., Christopher, B. R., & Berg, R. R. (2001). Mechanically stabilized earth walls and reinforced soil slopes. Federal Highway Administration, Washington D.C.

Goodsell, M. W. (2000). Instrumentation and installation scheme on a mechanically stabilized earth wall On I-15. Utah State University, Logan, Utah.

Jewell, R. A., & Wroth, C. P. (1987). Direct shear test on reinforced sand. Geotechnique, 37(1), 53-68.

Lade, & Lee. (1976). Engineering properties of soils. Report UCLA-ENG-7652, University of California, Los Angeles.

Suncar, O. (2010). Pullout and tensile behavior of crimped steel reinforcement for MSE walls. Utah State University, Logan, Utah.

Wong, W. L. (1989). Field performance of welded wire retaining walls. Utah State University, Logan, Utah.

WSDOT. (2006). Geotechnical design manual. M-46-03. Washington State Department of Transportation, Seattle, Wa.

Yannas, S. F. (1985). Corrosion susceptibility of internally reinforced soil-retaining walls. FHWA RD-83-105. Federal Highway Administration, U.S. Department of Transportation, Washington D.C.

APPENDICES

APPENDIX A. Visual Basic Scripts For Crimps Properties Calculation

A.1 Scripts for the properties of crimp 1

Bar 1 is referred to the 1/2'’’ diameter bar, Bar 2 is the 3/8’’ diameter bar and

Bar 3 is the 1/4'’ diameter bar. The pressure needs to be used in psi and the tension in pounds. The straight function gives the pullout resistance at a given pressure for each bar, the pullout function gives the pullout resistance of the crimp at a given load for each bar and the displacement function gives the displacement of each crimp for a given load for each bar.

Function straight(barstraight, pressurestraight) If (pressurestraight < 0) Then straight = "Error" ElseIf (barstraight = "Bar 1") Then If (pressurestraight < 5) Then straight = 74.5 * pressurestraight / 5 Else straight = ((230 - 74.5) / (30 - 5)) * (pressurestraight - 5) + 74.5 End If ElseIf (barstraight = "Bar 2") Then If (pressurestraight < 5) Then sraight = 39.48 * pressurestraight / 5 Else straight = ((150 - 39.48) / (30 - 5)) * (pressurestraight - 5) + 39.48 End If ElseIf (barstraight = "Bar 3") Then If (pressurestraight < 5) Then straight = 10.44 * pressurestraight / 5 Else straight = ((36.96 - 10.44) / (30 - 5)) * (pressurestraight - 5) + 10.44 End If Else straight = "Error" End If End Function

Function pullout(bar, pressure, tension) 89

If (bar = "Bar 1") Then If (pressure < 0 Or tension < 0 Or tension > 8500) Then pullout = "Error" ElseIf (pressure >= 30) Then If (tension >= 6000) Then pullout = -(283.7 / 2500) * (tension - 6000) + 283.7 ElseIf (tension >= 946.3148) Then pullout = -0.1099 * tension + 943.1 Else pullout = 839.1 End If ElseIf (pressure = 25) Then If (tension >= 6000) Then pullout = -(248 / 2500) * (tension - 6000) + 248 ElseIf (tension >= 1032.258) Then pullout = -0.093 * tension + 806 Else pullout = 713 End If ElseIf (pressure < 30 And pressure > 25) Then pullout = (((pullout(bar, 30, tension) - pullout(bar, 25, tension)) * (5 - (30 - pressure))) / 5) + pullout(bar, 25, tension) ElseIf (pressure = 20) Then If (tension >= 6000) Then pullout = -(215.2 / 2500) * (tension - 6000) + 215.2 ElseIf (tension >= 1094.987) Then pullout = -0.0758 * tension + 670 Else pullout = 587 End If ElseIf (pressure = 15) Then If (tension >= 6000) Then pullout = -(193.08 / 2500) * (tension - 6000) + 193.08 Else pullout = -0.0504 * tension + 495.48 End If ElseIf (pressure < 25 And pressure > 20) Then pullout = (((pullout(bar, 25, tension) - pullout(bar, 20, tension)) * (5 - (25 - pressure))) / 5) + pullout(bar, 20, tension) ElseIf (pressure < 20 And pressure > 15) Then pullout = (((pullout(bar, 20, tension) - pullout(bar, 15, tension)) * (5 - (20 - pressure))) / 5) + pullout(bar, 15, tension) ElseIf (pressure = 10) Then If (tension >= 6000) Then 90

pullout = -(151.35 / 2500) * (tension - 6000) + 151.35 Else pullout = -0.0375 * tension + 376.35 End If ElseIf (pressure = 7.5) Then If (tension >= 6000) Then pullout = -(102.15 / 2500) * (tension - 6000) + 102.15 Else pullout = -0.0339 * tension + 305.55 End If ElseIf (pressure < 15 And pressure > 10) Then pullout = (((pullout(bar, 15, tension) - pullout(bar, 10, tension)) * (5 - (15 - pressure))) / 5) + pullout(bar, 10, tension) ElseIf (pressure < 10 And pressure > 7.5) Then pullout = (((pullout(bar, 10, tension) - pullout(bar, 7.5, tension)) * (2.5 - (10 - pressure))) / 2.5) + pullout(bar, 7.5, tension) ElseIf (pressure = 5) Then If (tension >= 6000) Then pullout = -(30.48 / 2500) * (tension - 6000) + 30.48 Else pullout = -0.0358 * tension + 245.28 End If ElseIf (pressure = 2.5) Then If (tension >= 6000) Then pullout = -(9.3 / 2500) * (tension - 6000) + 9.3 Else pullout = -0.0207 * tension + 133.5 End If ElseIf (pressure < 7.5 And pressure > 5) Then pullout = (((pullout(bar, 7.5, tension) - pullout(bar, 5, tension)) * (2.5 - (7.5 - pressure))) / 2.5) + pullout(bar, 5, tension) ElseIf (pressure < 5 And pressure > 2.5) Then pullout = (((pullout(bar, 5, tension) - pullout(bar, 2.5, tension)) * (2.5 - (5 - pressure))) / 2.5) + pullout(bar, 2.5, tension) ElseIf (pressure = 0) Then pullout = 0 Else pullout = (((pullout(bar, 2.5, tension) - pullout(bar, 0, tension)) * (2.5 - (2.5 - pressure))) / 2.5) + pullout(bar, 0, tension) End If ElseIf (bar = "Bar 2") Then If (pressure < 0 Or tension < 0 Or tension > 4781.25) Then pullout = "Error" ElseIf (pressure >= 30) Then 91

If (tension >= 3375) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) ElseIf (tension >= 532.3021) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) Else pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) End If ElseIf (pressure = 25) Then If (tension >= 3375) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) ElseIf (tension >= 580.6452) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) Else pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) End If ElseIf (pressure < 30 And pressure > 25) Then pullout = (((pullout(bar, 30, tension) - pullout(bar, 25, tension)) * (5 - (30 - pressure))) / 5) + pullout(bar, 25, tension) ElseIf (pressure = 20) Then If (tension >= 3375) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) ElseIf (tension >= 615.9301) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) Else pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) End If ElseIf (pressure = 15) Then If (tension >= 3375) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) Else pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) End If ElseIf (pressure < 25 And pressure > 20) Then pullout = (((pullout(bar, 25, tension) - pullout(bar, 20, tension)) * (5 - (25 - pressure))) / 5) + pullout(bar, 20, tension) ElseIf (pressure < 20 And pressure > 15) Then pullout = (((pullout(bar, 20, tension) - pullout(bar, 15, tension)) * (5 - (20 - pressure))) / 5) + pullout(bar, 15, tension) ElseIf (pressure = 10) Then If (tension >= 3375) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) Else pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) End If 92

ElseIf (pressure = 7.5) Then If (tension >= 3375) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) Else pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) End If ElseIf (pressure < 15 And pressure > 10) Then pullout = (((pullout(bar, 15, tension) - pullout(bar, 10, tension)) * (5 - (15 - pressure))) / 5) + pullout(bar, 10, tension) ElseIf (pressure < 10 And pressure > 7.5) Then pullout = (((pullout(bar, 10, tension) - pullout(bar, 7.5, tension)) * (2.5 - (10 - pressure))) / 2.5) + pullout(bar, 7.5, tension) ElseIf (pressure = 5) Then If (tension >= 3375) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) Else pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) End If ElseIf (pressure = 2.5) Then If (tension >= 3375) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) Else pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) End If ElseIf (pressure < 7.5 And pressure > 5) Then pullout = (((pullout(bar, 7.5, tension) - pullout(bar, 5, tension)) * (2.5 - (7.5 - pressure))) / 2.5) + pullout(bar, 5, tension) ElseIf (pressure < 5 And pressure > 2.5) Then pullout = (((pullout(bar, 5, tension) - pullout(bar, 2.5, tension)) * (2.5 - (5 - pressure))) / 2.5) + pullout(bar, 2.5, tension) ElseIf (pressure = 0) Then pullout = 0 Else pullout = (((pullout(bar, 2.5, tension) - pullout(bar, 0, tension)) * (2.5 - (2.5 - pressure))) / 2.5) + pullout(bar, 0, tension) End If ElseIf (bar = "Bar 3") Then If (pressure < 0 Or tension < 0 Or tension > 3000) Then pullout = "Error" ElseIf (pressure >= 30) Then If (tension >= 1500) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) ElseIf (tension >= 236.579) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) 93

Else pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) End If ElseIf (pressure = 25) Then If (tension >= 1500) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) ElseIf (tension >= 258.065) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) Else pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) End If ElseIf (pressure < 30 And pressure > 25) Then pullout = (((pullout(bar, 30, tension) - pullout(bar, 25, tension)) * (5 - (30 - pressure))) / 5) + pullout(bar, 25, tension) ElseIf (pressure = 20) Then If (tension >= 1500) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) ElseIf (tension >= 273.747) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) Else pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) End If ElseIf (pressure = 15) Then If (tension >= 1500) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) Else pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) End If ElseIf (pressure < 25 And pressure > 20) Then pullout = (((pullout(bar, 25, tension) - pullout(bar, 20, tension)) * (5 - (25 - pressure))) / 5) + pullout(bar, 20, tension) ElseIf (pressure < 20 And pressure > 15) Then pullout = (((pullout(bar, 20, tension) - pullout(bar, 15, tension)) * (5 - (20 - pressure))) / 5) + pullout(bar, 15, tension) ElseIf (pressure = 10) Then If (tension >= 1500) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) Else pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) End If ElseIf (pressure = 7.5) Then If (tension >= 1500) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) Else 94

pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) End If ElseIf (pressure < 15 And pressure > 10) Then pullout = (((pullout(bar, 15, tension) - pullout(bar, 10, tension)) * (5 - (15 - pressure))) / 5) + pullout(bar, 10, tension) ElseIf (pressure < 10 And pressure > 7.5) Then pullout = (((pullout(bar, 10, tension) - pullout(bar, 7.5, tension)) * (2.5 - (10 - pressure))) / 2.5) + pullout(bar, 7.5, tension) ElseIf (pressure = 5) Then If (tension >= 1500) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) Else pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) End If ElseIf (pressure = 2.5) Then If (tension >= 1500) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) Else pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) End If ElseIf (pressure < 7.5 And pressure > 5) Then pullout = (((pullout(bar, 7.5, tension) - pullout(bar, 5, tension)) * (2.5 - (7.5 - pressure))) / 2.5) + pullout(bar, 5, tension) ElseIf (pressure < 5 And pressure > 2.5) Then pullout = (((pullout(bar, 5, tension) - pullout(bar, 2.5, tension)) * (2.5 - (5 - pressure))) / 2.5) + pullout(bar, 2.5, tension) ElseIf (pressure = 0) Then pullout = 0 Else pullout = (((pullout(bar, 2.5, tension) - pullout(bar, 0, tension)) * (2.5 - (2.5 - pressure))) / 2.5) + pullout(bar, 0, tension) End If Else pullout = "Error" End If End Function

Function displacement(bar1, tension1) If (bar1 = "Bar 1") Then If (tension1 > 12200) Then displacement = "Error" ElseIf (tension1 >= 7620) Then displacement = (0.35 / 4580) * (tension1 - 7620) + 0.8 ElseIf (tension1 >= 4000) Then 95

displacement = (0.33 / 3620) * (tension1 - 4000) + 0.47 ElseIf (tension1 >= 1700) Then displacement = (0.39 / 2300) * (tension1 - 1700) + 0.08 ElseIf (tension1 >= 0) Then displacement = (0.08 / 1700) * tension1 End If ElseIf (bar1 = "Bar 2") Then If (tension1 > 6862.5) Then displacement = "Error" ElseIf (tension1 >= 1850) Then displacement = ((0.56 - 0.325) / (3200 - 1850)) * (tension1 - 1850) + 0.325 ElseIf (tension1 >= 760) Then displacement = ((0.325 - 0.045) / (1850 - 760)) * (tension1 - 760) + 0.045 ElseIf (tension1 >= 0) Then displacement = (0.045 / 760) * tension1 End If ElseIf (bar1 = "Bar 3") Then If (tension1 > 3050) Then displacement = "Error" ElseIf (tension1 >= 1905) Then displacement = 0.5 * displacement("Bar 1", tension1 * (0.5 ^ 2 / 0.25 ^ 2)) ElseIf (tension1 >= 1000) Then displacement = 0.5 * displacement("Bar 1", tension1 * (0.5 ^ 2 / 0.25 ^ 2)) ElseIf (tension1 >= 425) Then displacement = 0.5 * displacement("Bar 1", tension1 * (0.5 ^ 2 / 0.25 ^ 2)) ElseIf (tension1 >= 0) Then displacement = 0.5 * displacement("Bar 1", tension1 * (0.5 ^ 2 / 0.25 ^ 2)) End If Else displacement = "Error" End If End Function

A.2 Scripts for the properties of crimp 2

Bar 1 is referred to the 1/2'’’ diameter bar, Bar 2 is the 3/8’’ diameter bar and

Function pullout(bar, pressure, tension) If (bar = "Bar 1") Then If (pressure < 0 Or tension < 0 Or tension > 9000) Then pullout = "Error" ElseIf (pressure >= 30) Then If (tension >= 3000) Then pullout = ((169.26 - 612.56) / (9000 - 3000)) * (tension - 3000) + 612.56 ElseIf (tension >= 1500) Then pullout = 612.56 Else pullout = ((612.56 - 767.7) / 1500) * tension + 767.7 End If ElseIf (pressure = 25) Then If (tension >= 3000) Then pullout = ((135 - 525) / (9000 - 3000)) * (tension - 3000) + 525 ElseIf (tension >= 1500) Then pullout = 525 Else pullout = ((525 - 650) / 1500) * tension + 965 End If ElseIf (pressure < 30 And pressure > 25) Then pullout = (((pullout(bar, 30, tension) - pullout(bar, 25, tension)) * (5 - (30 - pressure))) / 5) + pullout(bar, 25, tension) ElseIf (pressure = 20) Then If (tension >= 3000) Then pullout = ((102.5 - 437.5) / (9000 - 3000)) * (tension - 3000) + 437.5 ElseIf (tension >= 1500) Then pullout = 437.5 Else pullout = ((437.5 - 530) / 1500) * tension + 530 End If ElseIf (pressure = 15) Then If (tension >= 3000) Then pullout = ((60 - 350) / (9000 - 3000)) * (tension - 3000) + 350 ElseIf (tension >= 1500) Then pullout = 350 Else pullout = ((350 - 412) / (1500)) * tension + 412 End If ElseIf (pressure < 25 And pressure > 20) Then pullout = (((pullout(bar, 25, tension) - pullout(bar, 20, tension)) * (5 - (25 - pressure))) / 5) + pullout(bar, 20, tension) ElseIf (pressure < 20 And pressure > 15) Then 98

pullout = (((pullout(bar, 20, tension) - pullout(bar, 15, tension)) * (5 - (20 - pressure))) / 5) + pullout(bar, 15, tension) ElseIf (pressure = 10) Then If (tension >= 3000) Then pullout = ((26.05 - 264.95) / (9000 - 3000)) * (tension - 3000) + 264.95 ElseIf (tension >= 1500) Then pullout = 264.95 Else pullout = ((264.95 - 302.52) / 1500) * tension + 302.52 End If ElseIf (pressure = 7.5) Then If (tension >= 3000) Then pullout = ((26 - 230) / (9000 - 3000)) * (tension - 3000) + 230 ElseIf (tension >= 1500) Then pullout = 230 Else pullout = ((230 - 280) / (1500)) * (tension) + 280 End If ElseIf (pressure < 15 And pressure > 10) Then pullout = (((pullout(bar, 15, tension) - pullout(bar, 10, tension)) * (5 - (15 - pressure))) / 5) + pullout(bar, 10, tension) ElseIf (pressure < 10 And pressure > 7.5) Then pullout = (((pullout(bar, 10, tension) - pullout(bar, 7.5, tension)) * (2.5 - (10 - pressure))) / 2.5) + pullout(bar, 7.5, tension) ElseIf (pressure = 5) Then If (tension >= 3000) Then pullout = ((28.16 - 196.42) / (9000 - 3000)) * (tension - 3000) + 196.42 ElseIf (tension >= 1500) Then pullout = 196.42 Else pullout = ((196.42 - 265.33) / 1500) * tension + 265.33 End If ElseIf (pressure = 2.5) Then If (tension >= 3000) Then pullout = ((15 - 105) / (9000 - 3000)) * (tension - 3000) + 105 ElseIf (tension >= 1500) Then pullout = 105 Else pullout = ((105 - 150) / 1500) * tension + 150 End If ElseIf (pressure < 7.5 And pressure > 5) Then pullout = (((pullout(bar, 7.5, tension) - pullout(bar, 5, tension)) * (2.5 - (7.5 - pressure))) / 2.5) + pullout(bar, 5, tension) ElseIf (pressure < 5 And pressure > 2.5) Then 99

pullout = (((pullout(bar, 5, tension) - pullout(bar, 2.5, tension)) * (2.5 - (5 - pressure))) / 2.5) + pullout(bar, 2.5, tension) ElseIf (pressure = 0) Then pullout = 0 Else pullout = (((pullout(bar, 2.5, tension) - pullout(bar, 0, tension)) * (2.5 - (2.5 - pressure))) / 2.5) + pullout(bar, 0, tension) End If ElseIf (bar = "Bar 2") Then If (pressure < 0 Or tension < 0 Or tension > 5062.5) Then pullout = "Error" ElseIf (pressure >= 30) Then If (tension >= 1687.5) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) ElseIf (tension >= 843.75) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) Else pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) End If ElseIf (pressure = 25) Then If (tension >= 1687.5) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) ElseIf (tension >= 843.75) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) Else pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) End If ElseIf (pressure < 30 And pressure > 25) Then pullout = (((pullout(bar, 30, tension) - pullout(bar, 25, tension)) * (5 - (30 - pressure))) / 5) + pullout(bar, 25, tension) ElseIf (pressure = 20) Then If (tension >= 1687.5) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) ElseIf (tension >= 843.75) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) Else pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) End If ElseIf (pressure = 15) Then If (tension >= 1687.5) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) ElseIf (tension >= 843.75) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) Else 100

pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) End If ElseIf (pressure < 25 And pressure > 20) Then pullout = (((pullout(bar, 25, tension) - pullout(bar, 20, tension)) * (5 - (25 - pressure))) / 5) + pullout(bar, 20, tension) ElseIf (pressure < 20 And pressure > 15) Then pullout = (((pullout(bar, 20, tension) - pullout(bar, 15, tension)) * (5 - (20 - pressure))) / 5) + pullout(bar, 15, tension) ElseIf (pressure = 10) Then If (tension >= 1687.5) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) ElseIf (tension >= 843.75) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) Else pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) End If ElseIf (pressure = 7.5) Then If (tension >= 1687.5) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) ElseIf (tension >= 843.75) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) Else pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) End If ElseIf (pressure < 15 And pressure > 10) Then pullout = (((pullout(bar, 15, tension) - pullout(bar, 10, tension)) * (5 - (15 - pressure))) / 5) + pullout(bar, 10, tension) ElseIf (pressure < 10 And pressure > 7.5) Then pullout = (((pullout(bar, 10, tension) - pullout(bar, 7.5, tension)) * (2.5 - (10 - pressure))) / 2.5) + pullout(bar, 7.5, tension) ElseIf (pressure = 5) Then If (tension >= 1687.5) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) ElseIf (tension >= 843.75) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) Else pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) End If ElseIf (pressure = 2.5) Then If (tension >= 3375) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) ElseIf (tension >= 1687.5) Then pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) ElseIf (tension >= 843.75) Then 101

pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) Else pullout = 0.75 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.375 ^ 2)) End If ElseIf (pressure < 7.5 And pressure > 5) Then pullout = (((pullout(bar, 7.5, tension) - pullout(bar, 5, tension)) * (2.5 - (7.5 - pressure))) / 2.5) + pullout(bar, 5, tension) ElseIf (pressure < 5 And pressure > 2.5) Then pullout = (((pullout(bar, 5, tension) - pullout(bar, 2.5, tension)) * (2.5 - (5 - pressure))) / 2.5) + pullout(bar, 2.5, tension) ElseIf (pressure = 0) Then pullout = 0 Else pullout = (((pullout(bar, 2.5, tension) - pullout(bar, 0, tension)) * (2.5 - (2.5 - pressure))) / 2.5) + pullout(bar, 0, tension) End If ElseIf (bar = "Bar 3") Then If (pressure < 0 Or tension < 0 Or tension > 3000) Then pullout = "Error" ElseIf (pressure >= 30) Then If (tension >= 750) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) ElseIf (tension >= 375) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) Else pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) End If ElseIf (pressure = 25) Then If (tension >= 750) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) ElseIf (tension >= 375) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) Else pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) End If ElseIf (pressure < 30 And pressure > 25) Then pullout = (((pullout(bar, 30, tension) - pullout(bar, 25, tension)) * (5 - (30 - pressure))) / 5) + pullout(bar, 25, tension) ElseIf (pressure = 20) Then If (tension >= 750) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) ElseIf (tension >= 375) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) Else 102

pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) End If ElseIf (pressure = 15) Then If (tension >= 750) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) ElseIf (tension >= 375) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) Else pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) End If ElseIf (pressure < 25 And pressure > 20) Then pullout = (((pullout(bar, 25, tension) - pullout(bar, 20, tension)) * (5 - (25 - pressure))) / 5) + pullout(bar, 20, tension) ElseIf (pressure < 20 And pressure > 15) Then pullout = (((pullout(bar, 20, tension) - pullout(bar, 15, tension)) * (5 - (20 - pressure))) / 5) + pullout(bar, 15, tension) ElseIf (pressure = 10) Then If (tension >= 750) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) ElseIf (tension >= 375) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) Else pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) End If ElseIf (pressure = 7.5) Then If (tension >= 750) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) ElseIf (tension >= 375) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) Else pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) End If ElseIf (pressure < 15 And pressure > 10) Then pullout = (((pullout(bar, 15, tension) - pullout(bar, 10, tension)) * (5 - (15 - pressure))) / 5) + pullout(bar, 10, tension) ElseIf (pressure < 10 And pressure > 7.5) Then pullout = (((pullout(bar, 10, tension) - pullout(bar, 7.5, tension)) * (2.5 - (10 - pressure))) / 2.5) + pullout(bar, 7.5, tension) ElseIf (pressure = 5) Then If (tension >= 750) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) ElseIf (tension >= 375) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) Else 103

pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) End If ElseIf (pressure = 2.5) Then If (tension >= 1500) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) ElseIf (tension >= 750) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) ElseIf (tension >= 375) Then pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) Else pullout = 0.5 * pullout("Bar 1", pressure, tension * (0.5 ^ 2 / 0.25 ^ 2)) End If ElseIf (pressure < 7.5 And pressure > 5) Then pullout = (((pullout(bar, 7.5, tension) - pullout(bar, 5, tension)) * (2.5 - (7.5 - pressure))) / 2.5) + pullout(bar, 5, tension) ElseIf (pressure < 5 And pressure > 2.5) Then pullout = (((pullout(bar, 5, tension) - pullout(bar, 2.5, tension)) * (2.5 - (5 - pressure))) / 2.5) + pullout(bar, 2.5, tension) ElseIf (pressure = 0) Then pullout = 0 Else pullout = (((pullout(bar, 2.5, tension) - pullout(bar, 0, tension)) * (2.5 - (2.5 - pressure))) / 2.5) + pullout(bar, 0, tension) End If Else pullout = "Error" End If End Function

Function displacement(bar1, tension1) If (bar1 = "Bar 1") Then If (tension1 > 9000) Then displacement = "Error" ElseIf (tension1 >= 3036) Then displacement = (0.315064897 / 5309) * (tension1 - 3036) + 0.101449872 ElseIf (tension1 >= 0) Then displacement = (0.101449872 / 3036) * tension1 End If ElseIf (bar1 = "Bar 2") Then If (tension1 > 6862.5) Then displacement = "Error" ElseIf (tension1 >= 1363) Then displacement = ((0.27 - 0.045) / (3265 - 1363)) * (tension1 - 1363) + 0.045 ElseIf (tension1 >= 0) Then 104

displacement = (0.045 / 1363) * tension1 End If ElseIf (bar1 = "Bar 3") Then If (tension1 > 2250) Then displacement = "Error" ElseIf (tension1 >= 759) Then displacement = 0.5 * displacement("Bar 1", tension1 * (0.5 ^ 2 / 0.25 ^ 2)) ElseIf (tension1 >= 0) Then displacement = 0.5 * displacement("Bar 1", tension1 * (0.5 ^ 2 / 0.25 ^ 2)) End If Else displacement = "Error" End If End Function

105

APPENDIX B. MSE Walls Complete Designs

B.1 Soil and Bars properties

Table B.1 Properties of the select fill for the MSE wall.

Soil Information  130 pcf

 38 deg ka 0.237883078 Ko 0.384338525

Table B.2 Corrosion considerations.

Corrosion Time 75 Rate 0.00047 Ec 0.03525

Table B.3 Reinforcement information.

Bar 1 Information Bar 2 Information Bar 3 Information Diameter 0.50'' Diameter 0.38'' Diameter 0.25''

An 0.196 inc2 An 0.110 inc2 An 0.049 inc2

Ac 0.144882596 Ac 0.072822314 Ac 0.025305725

y 60 ksi y 60 ksi y 60 ksi

Tal 4.35 kips Tal 2.18 kips Tal 0.76 kips

B.2 Wall Designed with Crimp 1 and Sc = 2.00 ft.

Table B.4 General information of the wall designed with crimp 1 and Sc = 2.00 ft.

Layer Depth S T v h h hcalculated max La Le Lt kr/ka kr Bar (ft) (Ksf) (ksf) (ksf) (ft) (Kips) (ft) (ft) (ft) 1 1.25 1.00 0.24 0.16 0.00 0.04 Bar 3 1.00 0.10 18.90 10.00 28.90 2 3.75 1.00 0.24 0.49 0.00 0.12 Bar 3 1.00 0.29 17.68 10.00 27.68 3 6.25 1.00 0.24 0.81 0.00 0.19 Bar 2 1.80 0.87 16.46 10.94 27.40 4 8.75 1.00 0.24 1.14 0.00 0.27 Bar 2 1.80 1.22 15.24 12.85 28.09 5 11.25 1.00 0.24 1.46 0.00 0.35 Bar 2 1.90 1.65 14.02 14.00 28.02 6 13.75 1.00 0.24 1.79 0.00 0.43 Bar 2 1.90 2.02 12.80 16.00 28.80 7 16.25 1.00 0.24 2.11 0.00 0.50 Bar 2 1.74 2.18 11.58 16.00 27.58 8 18.75 1.00 0.24 2.44 0.00 0.58 Bar 2 1.51 2.18 10.36 14.00 24.36 9 21.25 1.00 0.24 2.76 0.00 0.66 Bar 2 1.33 2.18 9.14 14.57 23.71 10 23.75 1.00 0.24 3.09 0.00 0.73 Bar 2 1.19 2.18 7.93 12.68 20.61 11 26.25 1.00 0.24 3.41 0.00 0.81 Bar 2 1.08 2.18 6.71 12.14 18.84 12 28.75 1.00 0.24 3.74 0.00 0.89 Bar 2 0.98 2.18 5.49 11.18 16.66 13 31.25 1.00 0.24 4.06 0.00 0.97 Bar 2 0.90 2.18 4.27 10.00 14.27 14 33.75 1.00 0.24 4.39 0.00 1.04 Bar 2 0.84 2.18 3.05 10.00 13.05 15 36.25 1.00 0.24 4.71 0.00 1.12 Bar 2 0.78 2.18 1.83 10.00 11.83 16 38.75 1.00 0.24 5.04 0.00 1.20 Bar 2 0.73 2.18 0.61 8.83 9.44 106

Table B.5 Pullout resistance calculations of the wall designed with crimp 1 and Sc = 2.00 ft.

Straigt Crimp Crimp Crimp Crimp Crimp Crimp Crimp Crimp Strai h Tensi Tensi Tensi Tensi Tensi Tensi Tensi Tensi Tensi 1 2 3 4 5 6 7 8 T gth 1 Pullout on In on In on In on In on In on In on In on In on In Lay max Pullout Pullout Pullout Pullout Pullout Pullout Pullout Pullout (Kip Lengt Unit Crim Crim Crim Crim Crim Crim Crim Crim Crim er Resista Resista Resista Resista Resista Resista Resista Resista s) h Resista p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8 p 9 nce nce nce nce nce nce nce nce (ft) nce (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lb/in) 0.1 136.5 104.2 1 4 1.10 0.20 7 27.58 8 28.18 71.38 28.80 37.88 29.42 3.74 3.74 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.4 415.2 336.1 253.0 165.5 2 2 0.32 0.59 2 64.91 7 69.03 1 73.36 0 77.92 73.44 73.44 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.2 1187. 963.0 728.1 482.2 224.7 3 5 1.54 3.53 32 139.67 1 150.23 4 161.29 1 172.87 0 185.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.7 1713. 1450. 1174. 886.5 585.0 269.6 4 5 0.76 4.36 78 158.87 31 170.98 74 183.64 0 196.89 1 210.75 7 225.25 0.00 0.00 0.00 0.00 0.00 2.3 2256. 1960. 1650. 1324. 981.5 621.5 243. 5 8 1.98 5.19 50 171.02 94 185.95 43 201.65 24 218.13 6 235.45 6 253.64 37 243.37 0.00 0.00 0.00 2.9 2821. 2516. 2193. 1851. 1489. 1106. 701. 272. 6 1 1.20 6.02 99 160.86 63 178.66 46 197.50 45 217.44 50 238.54 46 260.88 07 284.51 06 272.06 0.00 3.1 3111. 2787. 2441. 2072. 1678. 1259. 812. 336. 7 5 0.42 6.85 69 160.14 09 181.59 04 204.45 13 228.82 86 254.80 59 282.50 64 312.03 15 336.15 0.00 3.1 2995. 2629. 2233. 1806. 1344. 846.2 307. 8 5 1.64 7.68 10 181.69 00 211.07 51 242.81 28 277.10 77 314.14 2 354.15 66 307.66 0.00 0.00 0.00 3.1 3058. 2665. 2234. 1762. 1245. 678.6 58.0 9 5 0.86 8.52 55 188.93 26 226.50 39 267.67 35 312.76 22 362.17 8 416.30 1 58.01 0.00 0.00 0.00 3.1 3137. 2719. 2255. 1742. 1173. 544.0 10 5 0.07 9.35 59 194.05 21 239.10 78 289.00 45 344.28 85 405.50 3 467.48 0.00 0.00 0.00 0.00 0.00 3.1 2987. 2518. 1993. 1406. 750.2 11 5 1.29 10.18 91 225.28 35 280.70 37 342.66 43 411.94 1 489.39 16.54 16.54 0.00 0.00 0.00 0.00 0.00 3.1 3078. 2584. 2027. 1399. 691.0 12 5 0.51 11.01 15 229.20 71 292.51 97 363.94 79 444.54 2 535.48 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.1 2899. 2346. 1716. 999.7 183.4 13 5 1.73 11.84 77 269.01 57 345.61 77 432.82 6 532.11 6 183.46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.1 3001. 2429. 1774. 1022. 160.8 14 5 0.95 12.67 20 267.55 51 351.32 04 447.37 53 557.49 9 160.89 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.1 3118. 2543. 1885. 1129. 263.9 15 5 0.17 13.50 21 250.40 71 334.59 02 431.11 82 541.77 5 263.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.1 2906. 2281. 1564. 742.0 16

5 1.39 14.34 75 281.39 30 373.04 21 478.12 4 598.59 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 107

Table B.6 Calculations of the tension in the connections of the wall designed with crimp 1 and Sc = 2.00 ft.

Straigth Crimp - Crimp - Crimp - Crimp - Crimp - Crimp - Crimp - Straig Tensi Tensi Tensi Tensi Tensi Tensi Tensi Tensi Pullout 1 2 3 4 5 6 7 T th -1 on In on In on In on In on In on In on In on In Lay max Unit Pullout Pullout Pullout Pullout Pullout Pullout Pullout Tc (Kip Lengt Crimp Crimp Crimp Crimp Crimp Crimp Crimp Crimp er Resista Resista Resista Resista Resista Resista Resista Resista (lbs) s) h -1 -2 -3 -4 -5 -6 -7 -8 nce nce nce nce nce nce nce nce (ft) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lb/in) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) 0.1 137.0 104.7 1 4 0.90 0.20 4 27.57 6 28.17 71.88 28.79 38.38 29.41 4.25 4.25 0.00 0.00 0.00 0.00 0.00 0.00 0.4 405.6 326.0 242.3 154.3 2 2 1.68 0.59 1 65.41 6 69.56 6 73.92 0 78.51 61.66 61.66 0.00 0.00 0.00 0.00 0.00 0.00 1.2 1232. 1010. 778.1 534.5 279.5 3 5 0.46 3.53 95 137.52 78 147.98 6 158.94 8 170.41 4 182.41 12.48 12.48 0.00 0.00 0.00 0.00 1.7 1688. 1423. 1147. 857.5 554.7 238.0 4 5 1.24 4.36 50 160.03 88 172.19 09 184.92 8 198.22 6 212.14 2 226.70 0.00 0.00 0.00 0.00 2.3 2378. 2088. 1784. 1465. 1129. 777.3 407.0 142.5 5 8 0.02 5.19 27 164.86 86 179.49 82 194.85 42 211.00 87 227.95 7 245.77 5 264.48 0.00 7 2.9 2850. 2546. 2225. 1885. 1525. 1144. 885.5 6 1 0.80 6.02 46 159.20 76 176.91 35 195.64 20 215.48 22 236.46 25 258.67 0.00 0.00 0.00 8 3.1 3015. 2684. 2331. 1955. 1554. 1291. 7 5 1.58 6.85 70 166.48 76 188.35 95 211.65 84 236.50 88 262.99 0.00 0.00 0.00 0.00 0.00 89 3.1 3112. 2755. 2370. 1954. 1504. 1203. 8 5 0.36 7.68 33 172.28 63 200.91 31 231.83 06 265.24 41 301.32 0.00 0.00 0.00 0.00 0.00 08 3.1 3028. 2632. 2198. 1723. 1406. 9 5 1.14 8.52 92 191.76 80 229.60 83 271.06 39 316.49 0.00 0.00 0.00 0.00 0.00 0.00 0.00 91 3.1 2929. 2489. 2001. 1684. 10 5 1.93 9.35 94 216.41 20 263.87 01 316.44 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 57 3.1 3059. 2598. 2083. 1750. 11 5 0.71 10.18 65 216.81 56 271.24 05 332.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 97 3.1 2949. 2439. 2128. 12 5 1.49 11.01 47 245.71 52 311.14 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 38 3.1 3107. 2583. 2270. 13 5 0.27 11.84 89 240.19 51 312.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 71 3.1 2986. 2716. 14 5 1.05 12.67 50 269.70 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 80 3.1 2849. 15 5 1.83 13.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 54 3.1 3041. 16 5 0.61 14.34 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 04

108

Table B.7 Calculations of the deflections of the wall designed with crimp 1 and Sc = 2.00 ft.

δ T δ T δ T δ T δ T δ T δ T δ T δ T δ T δ T Layer -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 1 1 2 2 3 3 4 4 5 5 (in (lbs) (in) (lbs) (in) (lbs) (in) (lbs) (in) (lbs) (in) (lbs) (in) (lbs) (in) (lbs) (in) (lbs) (in) (lbs) (in) )

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 1 0.00 00 0.00 00 27.75 26 61.44 58 94.52 89 94.05 89 60.96 57 27.26 26 0.00 00 0.00 00 3 0.00 0.00 101.1 0.00 191.8 0.01 278.0 0.02 287.6 0.02 201.9 0.01 111.8 0.01 16.9 0.00 0.00 0.1 2 0.00 00 5.75 05 6 95 5 81 4 62 6 71 6 90 0 05 5 16 0.00 00 1 0.00 95.2 0.00 358.5 0.02 610.0 0.03 850.2 0.06 804.6 0.05 562.3 0.03 308.5 0.01 42.8 0.00 0.00 0.2 3 0.00 00 5 56 8 12 7 61 5 82 3 65 0 33 6 83 7 25 0.00 00 4 0.00 244. 0.01 560.9 0.03 863.4 0.07 1152. 0.14 1178. 0.15 889.9 0.07 588.5 0.03 273. 0.01 0.00 0.5 4 0.00 00 48 45 3 32 8 16 73 59 00 24 1 84 8 49 40 62 0.00 00 5 244. 0.01 622. 0.03 982.3 0.10 1325. 0.19 1651. 0.27 1529. 0.24 1197. 0.15 847.9 0.06 481. 0.02 95.9 0.00 1.1 5 25 45 40 69 5 21 00 01 15 39 38 26 07 73 6 76 21 85 3 57 2 410. 0.02 831. 0.06 1230. 0.16 1606. 0.26 1961. 0.34 1933. 0.33 1576. 0.25 1198. 0.15 798. 0.05 374. 0.02 1.6 6 43 43 82 34 00 57 24 24 76 45 29 95 11 46 11 75 07 48 71 22 9 313. 0.01 791. 0.05 1239. 0.16 1660. 0.27 2054. 0.36 2150. 0.37 1762. 0.30 1348. 0.19 907. 0.08 437. 0.02 1.8 7 30 86 20 30 49 82 00 62 45 06 43 73 33 25 58 62 50 29 28 59 6 195. 0.01 742. 0.04 1248. 0.17 1717. 0.29 2151. 0.37 2033. 0.35 1590. 0.25 1111. 0.13 594. 0.03 36.6 0.00 1.6 8 41 16 31 40 58 05 23 09 08 74 85 70 60 84 78 54 53 52 0 22 8 0.00 459. 0.02 1045. 0.11 1579. 0.25 2067. 0.36 2097. 0.36 1612. 0.26 1080. 0.12 498. 0.02 0.00 1.5 9 0.00 00 46 72 12 82 71 56 67 29 30 80 17 39 68 74 42 95 0.00 00 5 0.00 0.00 821.6 0.06 1424. 0.21 1968. 0.34 2176. 0.38 1654. 0.27 1076. 0.12 436. 0.02 0.00 1.4 10 0.00 00 0.00 00 0 08 44 57 68 57 33 18 45 48 37 63 05 58 0.00 00 3 0.00 0.00 881.4 0.07 1523. 0.24 2098. 0.36 2026. 0.35 1443. 0.22 791.8 0.05 63.0 0.00 0.00 1.3 11 0.00 00 0.00 00 9 62 85 12 40 82 66 58 65 06 2 32 6 37 0.00 00 2 0.00 0.00 0.00 1354. 0.19 1988. 0.34 2116. 0.37 1500. 0.23 804.2 0.05 19.0 0.00 0.00 1.2 12 0.00 00 0.00 00 0.00 00 94 78 21 91 89 15 13 51 2 64 4 11 0.00 00 1 0.00 0.00 0.00 1489. 0.23 2146. 0.37 1938. 0.34 1252. 0.17 470.8 0.02 0.00 0.00 1.1 13 0.00 00 0.00 00 0.00 00 15 23 64 66 51 04 21 14 7 79 0.00 00 0.00 00 5 0.00 0.00 0.00 0.00 2025. 0.35 2039. 0.35 1327. 0.19 510.4 0.03 0.00 0.00 0.9 14 0.00 00 0.00 00 0.00 00 0.00 00 25 55 95 81 40 08 4 02 0.00 00 0.00 00 3 0.00 0.00 0.00 0.00 0.00 2156. 0.37 1441. 0.22 621.4 0.03 0.00 0.00 0.6 15 0.00 00 0.00 00 0.00 00 0.00 00 0.00 00 96 84 60 01 2 68 0.00 00 0.00 00 4 0.00 0.00 0.00 0.00 0.00 1945. 0.34 1179. 0.15 300.6 0.01 0.00 0.00 0.5 16 0.00 00 0.00 00 0.00 00 0.00 00 0.00 00 49 16 19 27 1 78 0.00 00 0.00 00 1

109

B.3 Wall Designed with Crimp 1 and Sc = 1.50 ft.

Table B.8 General information of the wall designed with crimp 1 and Sc = 1.50 ft.

Depth S T v h h hcalculated max La Le Lt Layer kr/ka kr Bar (ft) (Ksf) (ksf) (ksf) (ft) (Kips) (ft) (ft) (ft) 1 1.25 1.00 0.24 0.16 0.00 0.04 Bar 3 1.30 0.13 18.90 9.00 27.90 2 3.75 1.00 0.24 0.49 0.00 0.12 Bar 3 1.30 0.38 17.68 10.50 28.18 3 6.25 1.00 0.24 0.81 0.00 0.19 Bar 2 2.30 1.11 16.46 12.00 28.46 4 8.75 1.00 0.24 1.14 0.00 0.27 Bar 2 2.40 1.62 15.24 13.06 28.30 5 11.25 1.00 0.24 1.46 0.00 0.35 Bar 2 2.10 1.83 14.02 13.50 27.52 6 13.75 1.00 0.24 1.79 0.00 0.43 Bar 2 2.06 2.18 12.80 15.00 27.80 7 16.25 1.00 0.24 2.11 0.00 0.50 Bar 2 1.74 2.18 11.58 13.50 25.08 8 18.75 1.00 0.24 2.44 0.00 0.58 Bar 2 1.51 2.18 10.36 12.00 22.36 9 21.25 1.00 0.24 2.76 0.00 0.66 Bar 2 1.33 2.18 9.14 10.50 19.64 10 23.75 1.00 0.24 3.09 0.00 0.73 Bar 2 1.19 2.18 7.93 10.50 18.43 11 26.25 1.00 0.24 3.41 0.00 0.81 Bar 2 1.08 2.18 6.71 9.00 15.71 12 28.75 1.00 0.24 3.74 0.00 0.89 Bar 2 0.98 2.18 5.49 9.00 14.49 13 31.25 1.00 0.24 4.06 0.00 0.97 Bar 2 0.90 2.18 4.27 9.91 14.18 14 33.75 1.00 0.24 4.39 0.00 1.04 Bar 2 0.84 2.18 3.05 7.50 10.55 15 36.25 1.00 0.24 4.71 0.00 1.12 Bar 2 0.78 2.18 1.83 7.50 9.33 16 38.75 1.00 0.24 5.04 0.00 1.20 Bar 2 0.73 2.18 0.61 7.50 8.11

110

Table B.9 Pullout resistance calculations of the wall designed with crimp 1 and Sc = 1.50 ft.

Straig th Ten Crimp Ten Crimp Ten Crimp Ten Crimp Ten Crimp Ten Crimp Ten Crimp Ten Crimp Ten Crimp Ten Crimp Stra Pullo sion 1 sion 2 sion 3 sion 4 sion 5 sion 6 sion 7 sion 8 sion 9 sion 10 T igth La ma ut In Pullo In Pullo In Pullo In Pullo In Pullo In Pullo In Pullo In Pullo In Pullo In Pullo 1 ye x Unit Cri ut Cri ut Cri ut Cri ut Cri ut Cri ut Cri ut Cri ut Cri ut Cri ut (Ki Len r Resist mp Resist mp Resist mp Resist mp Resist mp Resist mp Resist mp Resist mp Resist mp Resist mp Resist ps) gth ance 1 ance 2 ance 3 ance 4 ance 5 ance 6 ance 7 ance 8 ance 9 ance 10 ance (ft) (lb/in (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) ) 1 0.1 0.60 0.20 179. 26.78 149 27.34 118 27.92 86.8 28.51 54.8 29.11 22.1 22.17 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.5 540. 471. 398. 322. 242. 157. 68.7 2 4 0.32 0.59 4 58.39 48 61.98 89 65.76 53 69.74 1 73.93 65 78.33 2 68.72 0.00 0.00 0.00 0.00 0.00 0.00 1.6 159 120.3 141 128.9 122 138.0 102 147.5 810. 157.4 589. 167.8 357. 178.7 115. 115.5 3 0 0.04 3.53 8 0 4.9 6 2.4 2 0.9 0 0 4 09 4 7 3 5 6 0.00 0.00 0.00 0.00 2.3 227 133.2 206 142.9 183 153.1 160 163.7 136 174.8 111 186.5 847. 198.7 569. 211.4 279. 224.7 4 4 1.26 4.36 2 0 0.4 3 9.0 1 7.5 5 5.3 8 2.0 3 0 1 8 5 98 7 0.00 0.00 2.6 256 155.2 232 167.7 205 180.9 178 194.8 149 209.4 119 224.7 875. 240.7 541. 257.6 190. 190.5 5 3 0.98 5.19 9 1 0.6 7 9.4 7 5.0 4 6. 1 4.0 1 8 9 6 8 58 8 0.00 0.00 3.1 309 144.9 284 159.6 257 175.3 229 191.8 199 209.3 167 227.8 133 247.4 980. 268.2 603. 290.1 205. 205.3 6 5 0.70 6.02 5 1 2.2 8 4.2 0 0.5 4 0. 5 2.5 7 6.3 7 4 2 89 8 3 3 3.1 311 160.1 282 178.8 252 198.8 220 220.1 186 242.8 149 267.0 110 292.7 687. 320.2 244. 244.0 7 5 0.42 6.85 1 4 8 7 5.9 4 3.8 2 0.3 1 4.1 0 3.8 9 7 8 08 8 0.00 0.00 3.1 313 170.5 282 195.3 249 222.1 213 251.0 174 282.3 132 316.1 865. 352.5 375. 375.0 8 5 0.14 7.68 3 9 4 8 0.8 6 0.3 9 0.9 4 0.2 0 8 7 0 0 0.00 0.00 0.00 0.00 3.1 300 193.8 266 226.9 228 263.3 186 303.1 140 346.7 907. 394.4 359. 359.4 9 5 1.36 8.52 7 1 0 7 0.1 0 3.5 0 7.1 0 21 6 4 7 0.00 0.00 0.00 0.00 0.00 0.00 3.1 302 206.1 265 246.4 223 291.0 177 340.5 126 395.3 704. 456.0 80.3 10 5 1.07 9.35 5 3 1 4 6.3 9 7.0 5 8.2 4 65 2 8 80.38 0.00 0.00 0.00 0.00 0.00 0.00 3.1 304 218.0 264 265.4 219 318.3 169 377.5 113 443.7 509. 509.6 11 5 0.79 10.18 8 7 7 4 9.0 9 7.4 9 6.6 8 67 7 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.1 307 229.2 265 284.0 216 345.9 162 415.7 101 494.4 317. 317.9 12 5 0.51 11.01 8 0 0 3 8.5 0 4.4 1 0.5 7 94 4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.1 311 239.4 266 302.1 214 373.5 155 454.7 890. 547.2 129. 129.9 13 5 0.23 11.84 2 9 0 7 4.9 3 8.2 7 3 6 99 9 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.1 292 278.6 241 352.9 183 438.1 117 535.7 407. 407.2 14 5 1.45 12.67 5 9 8 5 7.3 0 1.1 2 2 7 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.1 295 243 184 116 15 5 1.17 13.50 6 274.1 8 349.9 5. 436.8 6.0 536.4 386. 386.4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.1 299 268.7 246 345.9 186 434.4 116 535.9 375. 375.3 111 16 5 0.89 14.34 2 9 5 8 1.9 9 9.3 7 3 6 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Table B.10 Calculations of the tension in the connections of the wall designed with crimp 1 and Sc = 1.50 ft.

Strai Ten Ten Ten gth Ten Crim Ten Crim Ten Crim Ten Crim Ten Crim Ten Crim Ten Crim Crim Crim Crim Stra sion sion sion T Pullo sion p -1 sion p -2 sion p -3 sion p -4 sion p -5 sion p -6 sion p -7 p -8 p -9 p -10 m igth In In In La ut In Pullo In Pullo In Pullo In Pullo In Pullo In Pullo In Pullo Pullo Pullo Pullo ax -1 Cri Cri Cri Tc ye (Ki Unit Cri ut Cri ut Cri ut Cri ut Cri ut Cri ut Cri ut ut ut ut Len mp mp mp (lbs) r ps Resis mp Resis mp Resis mp Resis mp Resis mp Resis mp Resis mp Resis Resis Resis Resis gth -8 -9 -10 ) tance -1 tance -2 tance -3 tance -4 tance -5 tance -6 tance -7 tance tance tance tance (ft) (lbs (lbs (lbs (lb/in (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) ) ) ) ) 0. 0.9 178 148 117 86. 54. 21. 0.0 0.0 0.0 0.0 0.0 1 18 0 0.20 .79 26.79 .47 27.36 .58 27.93 11 28.52 05 29.12 40 21.40 0 0.00 0 0.00 0 0.00 0 0.00 0 0. 1.1 534 465 392 315 234 149 60. 0.0 0.0 0.0 0.0 2 54 8 0.59 .39 58.71 .08 62.32 .16 66.11 .44 70.11 .73 74.32 .81 78.74 47 60.47 0 0.00 0 0.00 0 0.00 0 153 135 115 1. 1.4 8.5 123.1 1.9 131.9 6.5 141.1 951 150.7 737 160.8 513 171.4 278 182.4 32. 0.0 0.0 0.0 3 60 6 3.53 3 4 1 2 1 2 .91 6 .67 4 .35 0 .47 6 52 32.52 0 0.00 0 0.00 0 232 211 189 166 142 117 2. 0.2 5.2 130.7 6.0 140.3 7.2 150.4 8.3 160.9 8.9 171.9 8.5 183.4 916 195.5 642 208.1 356 221.2 56. 0.0 4 34 4 4.36 8 6 7 7 5 3 7 5 7 6 7 7 .65 1 .70 0 .15 7 43 56.43 0 259 235 209 181 153 123 2. 0.5 7.6 153.7 0.4 166.2 0.7 179.3 7.9 193.1 1.3 207.6 0.2 222.8 913 238.8 581 255.6 232 232.6 0.0 0.0 5 63 2 5.19 3 8 4 7 6 9 5 8 6 6 8 8 .99 6 .72 6 .65 5 0 0.00 0 308 283 256 228 198 166 132 3. 0.8 7.9 145.3 4.1 160.1 5.6 175.8 1.4 192.3 0.7 209.9 2.4 228.4 5.5 248.1 969 268.8 0.0 0.0 700 6 15 0 6.02 1 6 7 5 5 0 6 7 1 1 3 6 8 0 .10 8 0 0.00 0 0.00 .22 305 276 246 213 178 141 102 3. 1.0 6.8 163.7 9.7 182.7 3.6 202.9 7.3 224.5 9.4 247.4 8.6 271.9 3.2 298.1 0.0 0.0 0.0 725 7 15 8 6.85 2 7 0 3 3 6 3 1 7 9 3 9 9 1 0 0.00 0 0.00 0 0.00 .18 302 270 235 198 158 115 3. 1.3 0.1 179.6 2.1 205.2 8.6 232.7 7.5 262.5 6.6 294.7 3.6 329.4 0.0 0.0 0.0 0.0 824 8 15 6 7.68 2 8 3 0 1 7 3 5 7 2 4 7 0 0.00 0 0.00 0 0.00 0 0.00 .16 313 279 242 202 158 110 3. 0.1 1.1 181.9 5.8 214.0 8.5 249.1 6.1 287.5 5.3 329.6 2.3 375.8 0.0 0.0 0.0 0.0 726 9 15 4 8.52 1 9 4 3 3 2 4 6 0 8 4 2 0 0.00 0 0.00 0 0.00 0 0.00 .52 309 273 232 187 137 3. 0.4 8.1 198.3 1.6 237.7 5.6 281.4 5.9 329.9 7.7 383.5 0.0 0.0 0.0 0.0 0.0 994 10 15 3 9.35 8 0 4 6 3 8 1 1 6 4 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 .22 305 265 221 171 133 3. 0.7 9.6 216.8 9.6 264.0 2.3 316.8 2.3 375.8 0.0 0.0 0.0 0.0 0.0 0.0 6.5 11 15 1 10.18 5 1 3 3 9 1 7 3 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 4 112

Table B.10 Continued

301 258 208 173 3. 0.9 5.5 237.2 0.1 293.1 8.8 356.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.7 12 15 9 11.01 3 4 1 0 4 3 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 1 296 249 216 3. 1.2 5.8 259.8 2.7 325.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7.4 13 15 7 11.84 0 6 9 6 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 3 313 266 234 3. 0.0 8.5 247.4 3.0 317.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5.9 14 15 5 12.67 7 2 5 0 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 5 309 283 3. 0.3 2.6 254.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 8.4 15 15 3 13.50 1 5 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 6 304 3. 0.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 16 15 1 14.34 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 4

Table B.11 Calculations of the deflections of the wall designed with crimp 1 and Sc = 1.50 ft.

Ten Ten Ten Ten Ten Ten Ten Ten Ten Ten Ten Ten sio Defl sio Defl sio Defl sio Defl sio Defl sio Defl sio Defl sio Defl sio Defl sio Defl sio Defl sio De n In ectio n In ectio n In ectio n In ectio n In ectio n In ectio n In ectio n In ectio n In ectio n In ectio n In ectio n In Tota Layer pt Cri n Cri n Cri n Cri n Cri n Cri n Cri n Cri n Cri n Cri n Cri n Cri l Numb h mp in mp in mp in mp in mp in mp in mp in mp in mp in mp in mp in mp Defl er (ft -6 Crim -5 Crim -4 Crim -3 Crim -2 Crim -1 Crim 1 Crim 2 Crim 3 Crim 4 Crim 5 Crim 6 ectio ) (lbs p -6 (lbs p -5 (lbs p -4 (lbs p -3 (lbs p -2 (lbs p -1 (lbs p 1 (lbs p 2 (lbs p 3 (lbs p 4 (lbs p 5 (lbs n ) (in) ) (in) ) (in) ) (in) ) (in) ) (in) ) (in) ) (in) ) (in) ) (in) ) (in) ) (in) 1. 0.0 0.0 27. 60. 92. 123 124 92. 60. 28. 0.0 0.0 1 25 0 0.00 0 0.00 67 0.00 21 0.01 16 0.01 .51 0.01 .22 0.01 87 0.01 95 0.01 42 0.00 0 0.00 0 0.06 3. 0.0 31. 122 208 290 368 374 297 215 129 39. 0.0 2 75 0 0.00 54 0.00 .32 0.01 .60 0.02 .61 0.03 .55 0.03 .64 0.04 .01 0.03 .33 0.02 .40 0.01 00 0.00 0 0.20 104 110 6. 0.0 149 390 620 839 9.5 9.7 902 686 459 222 0.0 3 25 0 0.00 .87 0.01 .54 0.02 .38 0.04 .89 0.07 3 0.12 1 0.13 .90 0.08 .36 0.04 .62 0.03 .21 0.01 0 0.55 111 136 161 155 131 105 8. 284 573 850 5.7 8.8 0.9 7.7 3.2 7.5 790 510 217 4 75 .22 0.02 .93 0.03 .90 0.07 1 0.14 7 0.20 1 0.26 4 0.25 6 0.19 3 0.12 .06 0.05 .28 0.03 .65 1.37

11 201 552 886 120 150 179 176 147 117 853 517 165 113 5 .2 .96 0.01 .51 0.03 .19 0.08 3.8 0.16 6.7 0.24 3.9 0.31 5.6 0.30 6.3 0.23 2.5 0.15 .31 0.07 .97 0.03 .68 1.62

Table B.11 Continued

13 386 774 114 148 181 212 213 182 149 115 784 396 6 .7 .32 0.02 .91 0.05 2.0 0.14 9.0 0.23 6.8 0.32 6.6 0.37 4.3 0.37 4.9 0.32 7.6 0.23 1.1 0.15 .51 0.05 .49 2.28 16 137 174 209 215 180 143 103 .2 95. 547 972 1.1 4.9 5.5 0.4 3.4 3.5 9.1 618 170 7 5 03 0.01 .89 0.03 .69 0.10 6 0.20 4 0.30 6 0.37 3 0.38 4 0.31 3 0.22 7 0.12 .77 0.04 .58 2.08 18 123 166 205 217 178 136 .7 0.0 277 775 6.8 3.7 8.8 2.1 6.1 9.0 918 431 0.0 8 5 0 0.00 .67 0.02 .78 0.05 8 0.17 3 0.28 7 0.36 6 0.38 1 0.31 8 0.20 .59 0.09 .94 0.03 0 1.87 21 127 174 216 204 160 112 .2 0.0 200 762 4.8 2.7 9.8 6.2 7.2 6.4 599 23. 0.0 9 5 0 0.00 .62 0.01 .21 0.05 3 0.18 4 0.30 5 0.38 1 0.36 9 0.26 3 0.14 .63 0.04 88 0.00 0 1.71 23 114 166 213 206 158 105 .7 0.0 0.0 569 6.2 6.8 6.9 4.1 6.2 6.9 470 0.0 0.0 10 5 0 0.00 0 0.00 .51 0.03 3 0.14 8 0.28 3 0.37 7 0.36 9 0.26 6 0.12 .63 0.03 0 0.00 0 1.60 26 101 158 209 208 157 .2 0.0 0.0 369 0.8 4.9 8.4 7.7 2.9 997 354 0.0 0.0 11 5 0 0.00 0 0.00 .00 0.02 4 0.11 2 0.26 0 0.37 3 0.37 9 0.25 .50 0.11 .09 0.02 0 0.00 0 1.50 28 149 205 211 156 .7 0.0 0.0 0.0 865 5.5 4.2 6.8 6.1 944 243 0.0 0.0 12 5 0 0.00 0 0.00 0 0.00 .10 0.07 3 0.23 7 0.36 9 0.37 8 0.25 .82 0.09 .73 0.01 0 0.00 0 1.40 31 139 200 215 156 .2 0.0 0.0 0.0 0.0 8.4 4.5 1.6 5.9 899 139 0.0 0.0 13 5 0 0.00 0 0.00 0 0.00 0 0.00 3 0.21 4 0.35 6 0.38 1 0.25 .06 0.08 .86 0.01 0 0.00 0 1.28 33 156 217 196 131 .7 0.0 0.0 0.0 0.0 0.9 7.3 3.9 6.2 573 0.0 0.0 0.0 14 5 0 0.00 0 0.00 0 0.00 0 0.00 4 0.25 2 0.38 1 0.34 6 0.19 .70 0.03 0 0.00 0 0.00 0 1.20 36 213 199 133 .2 0.0 0.0 0.0 0.0 0.0 1.3 4.9 6.8 582 0.0 0.0 0.0 15 5 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 6 0.37 1 0.35 3 0.19 .32 0.03 0 0.00 0 0.00 0 0.95 38 203 136 .7 0.0 0.0 0.0 0.0 0.0 0.0 1.5 3.8 598 0.0 0.0 0.0 16 5 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 1 0.36 3 0.20 .31 0.04 0 0.00 0 0.00 0 0.59

114

B.4 Wall Designed with Crimp 2 and Sc = 2.00 ft.

Table B.12 General information of the wall designed with crimp 2 and Sc = 2.00 ft.

Depth S T v h h hcalculated max La Le Lt Layer kr/ka kr Bar (ft) (Ksf) (ksf) (ksf) (ft) (Kips) (ft) (ft) (ft) 1 1.25 1 0.24 0.16 0.00 0.04 Bar 3 1.20 0.12 18.29 10.00 28.29 2 3.75 1 0.24 0.49 0.00 0.12 Bar 3 1.00 0.29 17.07 10.00 27.07 3 6.25 1 0.24 0.81 0.00 0.19 Bar 2 2.10 1.01 15.85 13.15 29.00 4 8.75 1 0.24 1.14 0.00 0.27 Bar 2 2.00 1.35 14.63 14.00 28.63 5 11.25 1 0.24 1.46 0.00 0.35 Bar 2 1.80 1.57 13.41 15.30 28.71 6 13.75 1 0.24 1.79 0.00 0.43 Bar 2 1.80 1.91 12.19 16.00 28.19 7 16.25 1 0.24 2.11 0.00 0.50 Bar 2 1.74 2.18 10.97 16.32 27.30 8 18.75 1 0.24 2.44 0.00 0.58 Bar 2 1.51 2.18 9.75 18.00 27.75 9 21.25 1 0.24 2.76 0.00 0.66 Bar 2 1.33 2.18 8.54 14.00 22.54 10 23.75 1 0.24 3.09 0.00 0.73 Bar 2 1.19 2.18 7.32 12.00 19.32 11 26.25 1 0.24 3.41 0.00 0.81 Bar 2 1.08 2.18 6.10 10.22 16.32 12 28.75 1 0.24 3.74 0.00 0.89 Bar 2 0.98 2.18 4.88 10.00 14.88 13 31.25 1 0.24 4.06 0.00 0.97 Bar 2 0.90 2.18 3.66 10.00 13.66 14 33.75 1 0.24 4.39 0.00 1.04 Bar 2 0.84 2.18 2.44 10.00 12.44 15 36.25 1 0.24 4.71 0.00 1.12 Bar 2 0.78 2.18 1.22 10.00 11.22 16 38.75 1 0.24 5.04 0.00 1.20 Bar 2 0.73 2.18 0.00 8.24 8.24

115

Table B.13 Pullout resistance calculations of the wall designed with crimp 2 and Sc = 2.00 ft.

Straigt Crimp Crimp Crimp Crimp Crimp Crimp Crimp Crimp Strai h Tensi Tensi Tensi Tensi Tensi Tensi Tensi Tensi Tensi 1 2 3 4 5 6 7 8 T gth 1 Pullout on In on In on In on In on In on In on In on In on In Lay max Pullout Pullout Pullout Pullout Pullout Pullout Pullout Pullout (Kip Lengt Unit Crim Crim Crim Crim Crim Crim Crim Crim Crim er Resista Resista Resista Resista Resista Resista Resista Resista s) h Resista p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8 p 9 nce nce nce nce nce nce nce nce (ft) nce (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lb/in) 0.1 162.9 128.8 1 7 1.71 0.20 6 29.44 1 30.37 93.73 31.32 57.71 32.29 20.70 20.70 0.00 0.00 0.00 0.00 0.00 0.00 0 0.4 410.9 328.0 241.9 149.6 2 2 0.93 0.59 2 68.69 9 72.03 2 78.18 0 84.76 50.71 50.71 0.00 0.00 0.00 0.00 0.00 0.00 0 1.4 1454. 1216. 978.0 739.6 495.2 237.0 3 6 0.15 3.53 90 153.79 48 153.79 5 153.79 3 159.71 7 173.63 1 188.33 0.00 0.00 0.00 0.00 0 1.9 1876. 1604. 1322. 1041. 760.4 475.5 178. 4 5 1.37 4.36 72 167.87 25 176.69 97 176.69 69 176.69 1 180.24 7 192.40 57 178.57 0.00 0.00 0 2.2 2217. 1920. 1608. 1282. 957.6 632.3 299. 5 5 0.59 5.19 84 172.36 93 188.23 15 200.71 89 200.71 4 200.71 8 207.91 92 219.24 0.00 0.00 0 2.7 2624. 2305. 1967. 1610. 1236. 862.3 488. 98.7 6 6 1.81 6.02 86 174.60 76 193.29 97 213.07 39 229.50 39 229.50 8 229.50 38 245.09 9 98.79 0 3.1 3061. 2726. 2369. 1990. 1586. 1164. 741. 313. 7 5 1.03 6.85 55 170.77 32 192.12 74 214.84 45 239.00 99 258.29 24 258.29 49 263.78 25 286.77 0 3.1 3123. 2749. 2349. 1922. 1466. 994.1 521. 28.5 8 5 0.25 7.68 30 189.73 16 215.28 46 242.58 46 271.75 30 287.79 0 287.79 89 308.89 8 28.58 0 3.1 2996. 2569. 2112. 1621. 1099. 577.7 35.3 9 5 1.46 8.52 26 222.12 76 253.18 22 286.49 36 317.42 58 317.42 9 338.11 1 35.31 0.00 0.00 0 3.1 3069. 2605. 2105. 1567. 995.6 424.3 10 5 0.68 9.35 20 239.31 57 275.46 79 314.43 04 347.04 7 347.04 1 424.31 0.00 0.00 0.00 0.00 0 3.1 2913. 2394. 1832. 1224. 603.2 11 5 1.90 10.18 45 274.31 86 317.61 97 364.52 18 376.66 4 576.30 0.00 0.00 0.00 0.00 0.00 0.00 0 3.1 2997. 2443. 1840. 1183. 512.8 12 5 1.12 11.01 60 289.79 58 339.05 29 392.70 35 406.29 3 512.83 0.00 0.00 0.00 0.00 0.00 0.00 0 3.1 3097. 2510. 1867. 1164. 444.2 13 5 0.34 11.84 33 303.02 11 358.38 54 418.96 39 435.93 7 444.27 0.00 0.00 0.00 0.00 0.00 0.00 0 3.1 2908. 2265. 1558. 794.9 14 5 1.56 12.67 49 339.14 20 402.51 55 459.42 9 466.14 24.70 24.70 0.00 0.00 0.00 0.00 0.00 0.00 0 3.1 3019. 2367. 1650. 867.0 15 5 0.78 13.50 42 328.21 11 392.47 54 459.42 2 459.42 83.50 83.50 0.00 0.00 0.00 0.00 0.00 0.00 0 3.1 2801. 2108. 1346. 542.6 16

5 2.00 14.34 87 349.64 17 417.98 14 459.42 6 500.94 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 116

Table B.14 Calculations of the tension in the connections of the wall designed with crimp 2 and Sc = 2.00 ft.

Straigth Crimp - Crimp - Crimp - Crimp - Crimp - Crimp - Crimp - Straig Tensi Tensi Tensi Tensi Tensi Tensi Tensi Tensi Pullout 1 2 3 4 5 6 7 T th -1 on In on In on In on In on In on In on In on In Lay max Unit Pullout Pullout Pullout Pullout Pullout Pullout Pullout Tc (Kip Lengt Crimp Crimp Crimp Crimp Crimp Crimp Crimp Crimp er Resista Resista Resista Resista Resista Resista Resista Resista (lbs) s) h -1 -2 -3 -4 -5 -6 -7 -8 nce nce nce nce nce nce nce nce (ft) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lb/in) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) 0.1 166.3 132.2 1 7 0.29 0.20 1 29.35 5 30.27 97.26 31.22 61.33 32.19 24.43 24.43 0.00 0.00 0.00 0.00 0.00 0.00 0.4 409.9 327.0 240.8 148.4 2 2 1.07 0.59 2 68.69 9 72.10 5 78.25 6 84.84 49.48 49.48 0.00 0.00 0.00 0.00 0.00 0.00 1.4 1382. 1144. 906.0 667.5 419.1 156.5 3 6 1.85 3.53 85 153.79 42 153.79 0 153.79 7 163.82 2 177.96 1 156.51 0.00 0.00 0.00 0.00 1.9 1915. 1644. 1363. 1081. 800.6 517.5 222.3 4 5 0.63 4.36 21 166.08 54 176.69 25 176.69 97 176.69 9 178.52 7 190.61 7 203.21 0.00 19.16 2.2 2166. 1866. 1551. 1225. 900.6 575.3 365.5 5 5 1.41 5.19 45 175.11 79 191.12 11 200.71 86 200.71 0 200.71 5 209.85 0.00 0.00 0.00 0 2.7 2741. 2429. 2098. 1748. 1378. 1004. 774.7 6 6 0.19 6.02 43 167.77 16 186.06 59 205.42 67 225.92 25 229.50 24 229.50 0.00 0.00 0.00 4 3.1 3065. 2730. 2374. 1995. 1592. 1334. 7 5 0.97 6.85 83 170.50 88 191.83 58 214.53 60 238.67 47 258.29 0.00 0.00 0.00 0.00 0.00 18 3.1 2984. 2600. 2190. 1752. 1469. 8 5 1.75 7.68 13 199.23 48 225.44 63 253.43 79 283.33 0.00 0.00 0.00 0.00 0.00 0.00 0.00 45 3.1 3091. 2671. 2221. 1738. 1424. 9 5 0.54 8.52 22 215.21 65 245.76 52 278.53 62 313.69 0.00 0.00 0.00 0.00 0.00 0.00 0.00 92 3.1 2998. 2529. 2023. 1702. 10 5 1.32 9.35 32 244.84 16 281.42 42 320.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 57 3.1 3134. 2633. 2092. 1749. 11 5 0.10 10.18 12 255.89 95 297.65 02 342.89 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 13 3.1 3030. 2478. 2142. 12 5 0.88 11.01 01 286.90 88 335.92 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 96 3.1 2910. 2589. 13 5 1.66 11.84 33 320.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 68 3.1 3079. 2756. 14 5 0.44 12.67 22 322.32 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 89 3.1 2948. 15 5 1.22 13.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 33 3.1 3145. 16 5 0.00 14.34 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 92

117

Table B.15 Calculations of the deflections of the wall designed with crimp 2 and Sc = 2.00 ft.

T T δ Lay -6 δ T δ T δ T δ T δ T δ T δ T δ T δ T δ T δ 6 T (lbs -6 -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 1 1 2 2 3 3 4 4 5 5 (lb (in er (in) (lbs) (in) (lbs) (in) (lbs) (in) (lbs) (in) (lbs) (in) (lbs) (in) (lbs) (in) (lbs) (in) (lbs) (in) (lbs) (in) ) s) )

0.0 0.00 0.00 0.00 0.00 0.00 115.2 0.00 111.9 0.00 0.00 0.00 0.00 0.00 0. 1 0 00 0.00 00 6.05 04 43.44 29 79.84 53 8 77 4 75 76.40 51 39.91 27 2.42 02 0.00 00 0 03 0.0 0.00 0.00 0.00 0.00 192.9 0.01 282.3 0.01 283.3 0.01 193.9 0.01 0.00 0.00 0.00 0. 2 0 00 0.00 00 0.00 00 97.11 65 2 29 5 89 5 89 9 30 98.26 66 0.00 00 0.00 00 0 08 0.0 0.00 0.00 190. 0.00 451.2 0.01 697.9 0.02 936.3 0.03 1008. 0.03 770.0 0.02 527.3 0.01 270. 0.00 0.00 0. 3 0 00 0.00 00 45 63 2 49 5 30 7 09 43 33 0 54 8 74 94 89 0.00 00 0 16 0.0 0.00 175. 0.00 472. 0.01 757.3 0.02 1038. 0.03 1319. 0.04 1281. 0.04 1000. 0.03 718.8 0.02 432. 0.01 133. 0.00 0. 4 0 00 25 58 38 56 5 50 63 43 91 36 42 23 13 30 5 37 24 43 40 44 0 24 0.0 0.00 164. 0.00 501. 0.01 827.0 0.02 1152. 0.03 1477. 0.05 1528. 0.06 1203. 0.03 878.4 0.02 553. 0.01 218. 0.00 0. 5 0 00 34 54 26 65 9 73 34 80 60 86 99 46 74 97 8 90 22 83 07 72 0 30 20. 0.00 413. 0.01 789. 0.02 1163. 0.03 1537. 0.06 1899. 0.10 1782. 0.09 1414. 0.05 1040. 0.03 666. 0.02 284. 0.00 0. 6 67 07 55 37 91 61 91 84 92 57 50 85 93 47 52 11 52 44 51 20 73 94 0 46 0.0 0.00 441. 0.01 864. 0.02 1286. 0.04 1708. 0.08 2104. 0.13 2100. 0.13 1703. 0.08 1282. 0.04 859. 0.02 436. 0.01 0. 7 0 00 47 46 22 85 97 25 39 59 58 27 30 22 84 53 13 23 38 84 63 44 0 61 0.0 0.00 0.00 629. 0.02 1101. 0.03 1573. 0.06 2022. 0.12 2162. 0.13 1722. 0.08 1252. 0.04 780. 0.02 303. 0.01 0. 8 0 00 0.00 00 16 08 37 64 58 99 88 31 05 95 25 75 42 13 21 58 84 00 0 55 0.0 0.00 0.00 596. 0.01 1118. 0.03 1640. 0.07 2129. 0.13 2035. 0.12 1538. 0.06 1016. 0.03 494. 0.01 0.00 0. 9 0 00 0.00 00 83 97 62 69 40 78 97 57 00 45 52 58 73 36 95 63 0.00 00 0 51 0.0 0.00 0.00 0.00 921.6 0.03 1492. 0.06 2037. 0.12 2107. 0.13 1569. 0.06 998.0 0.03 426. 0.01 0.00 0. 10 0 00 0.00 00 0.00 00 0 04 96 04 07 47 95 31 37 94 1 29 64 41 0.00 00 0 47 0.0 0.00 0.00 0.00 971.5 0.03 1592. 0.07 2172. 0.14 1952. 0.11 1353. 0.04 732.4 0.02 0.00 0.00 0. 11 0 00 0.00 00 0.00 00 0 21 44 21 86 08 20 47 35 47 1 42 0.00 00 0.00 00 0 43 0.0 0.00 0.00 0.00 0.00 1432. 0.05 2068. 0.12 2036. 0.12 1396. 0.04 726.3 0.02 0.00 0.00 0. 12 0 00 0.00 00 0.00 00 0.00 00 14 32 76 85 34 47 84 90 2 40 0.00 00 0.00 00 0 38 0.0 0.00 0.00 0.00 0.00 0.00 1949. 0.11 2136. 0.13 1458. 0.05 738.1 0.02 0.00 0.00 0. 13 0 00 0.00 00 0.00 00 0.00 00 0.00 00 08 43 07 65 24 63 1 44 0.00 00 0.00 00 0 33 0.0 0.00 0.00 0.00 0.00 0.00 2117. 0.13 1947. 0.11 1209. 0.03 445.6 0.01 0.00 0.00 0. 14 0 00 0.00 00 0.00 00 0.00 00 0.00 00 96 43 23 41 26 99 9 47 0.00 00 0.00 00 0 30 0.0 0.00 0.00 0.00 0.00 0.00 0.00 2058. 0.12 1311. 0.04 527.6 0.01 0.00 0.00 0. 15 0 00 0.00 00 0.00 00 0.00 00 0.00 00 0.00 00 16 72 16 33 4 74 0.00 00 0.00 00 0 19 0.0 0.00 0.00 0.00 0.00 0.00 0.00 1840. 0.10 1052. 0.03 248.7 0.00 0.00 0.00 0. 16 0 00 0.00 00 0.00 00 0.00 00 0.00 00 0.00 00 61 15 22 47 5 82 0.00 00 0.00 00 0 14

118

B.5 Wall Designed with Crimp 2 and Sc = 1.50 ft.

Table B.16 General information of the wall designed with crimp 2 and Sc = 1.50 ft.

Depth S T v h h hcalculated max La Le Lt Layer kr/ka kr Bar (ft) (Ksf) (ksf) (ksf) (ft) (Kips) (ft) (ft) (ft) 1 1.25 1 0.24 0.16 0.00 0.04 Bar 3 1.60 0.15 18.29 10.50 28.79 2 3.75 1 0.24 0.49 0.00 0.12 Bar 3 1.40 0.41 17.07 10.50 27.57 3 6.25 1 0.24 0.81 0.00 0.19 Bar 2 2.60 1.26 15.85 13.10 28.96 4 8.75 1 0.24 1.14 0.00 0.27 Bar 2 2.30 1.56 14.63 13.50 28.13 5 11.25 1 0.24 1.46 0.00 0.35 Bar 2 2.20 1.91 13.41 15.35 28.76 6 13.75 1 0.24 1.79 0.00 0.43 Bar 2 2.06 2.18 12.19 15.00 27.19 7 16.25 1 0.24 2.11 0.00 0.50 Bar 2 1.74 2.18 10.97 13.50 24.47 8 18.75 1 0.24 2.44 0.00 0.58 Bar 2 1.51 2.18 9.75 12.05 21.81 9 21.25 1 0.24 2.76 0.00 0.66 Bar 2 1.33 2.18 8.54 12.00 20.54 10 23.75 1 0.24 3.09 0.00 0.73 Bar 2 1.19 2.18 7.32 10.50 17.82 11 26.25 1 0.24 3.41 0.00 0.81 Bar 2 1.08 2.18 6.10 9.00 15.10 12 28.75 1 0.24 3.74 0.00 0.89 Bar 2 0.98 2.18 4.88 8.95 13.83 13 31.25 1 0.24 4.06 0.00 0.97 Bar 2 0.90 2.18 3.66 8.29 11.94 14 33.75 1 0.24 4.39 0.00 1.04 Bar 2 0.84 2.18 2.44 7.81 10.25 15 36.25 1 0.24 4.71 0.00 1.12 Bar 2 0.78 2.18 1.22 7.71 8.93 16 38.75 1 0.24 5.04 0.00 1.20 Bar 2 0.73 2.18 0.00 7.50 7.50

119

Table B.17 Pullout resistance calculations of the wall designed with crimp 2 and Sc = 1.50 ft.

Straig th Ten Crimp Ten Crimp Ten Crimp Ten Crimp Ten Crimp Ten Crimp Ten Crimp Ten Crimp Ten Crimp Ten Crimp Stra Pullo sion 1 sion 2 sion 3 sion 4 sion 5 sion 6 sion 7 sion 8 sion 9 sion 10 T igth La ma ut In Pullo In Pullo In Pullo In Pullo In Pullo In Pullo In Pullo In Pullo In Pullo In Pullo 1 ye x Unit Cri ut Cri ut Cri ut Cri ut Cri ut Cri ut Cri ut Cri ut Cri ut Cri ut (Ki Len r Resist mp Resist mp Resist mp Resist mp Resist mp Resist mp Resist mp Resist mp Resist mp Resist mp Resist ps) gth ance 1 ance 2 ance 3 ance 4 ance 5 ance 6 ance 7 ance 8 ance 9 ance 10 ance (ft) (lb/in (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) ) 0.2 219. 188. 156. 122. 88.8 53.8 17.9 1 2 1.21 0.20 81 27.90 37 28.75 09 29.63 92 30.52 6 31.45 8 32.39 5 17.95 0.00 0.00 0.00 0.00 0.00 0.00 2 0.5 0.93 0.59 577 68.69 498 68.69 419 68.69 340 71.18 258 77.01 170 83.26 76.7 76.77 0.00 0.00 0.00 0.00 0.00 0.00 1.8 178 150.0 156 153.7 135 153.7 113 153.7 916. 153.7 699. 162.0 473. 174.8 235. 188.4 3 1 0.65 3.53 1.65 7 8.10 9 0.83 9 3.56 9 30 9 03 3 53 6 18 3 0.00 0.00 0.00 0.00 2.2 222 151.8 199 162.5 174 173.7 149 176.6 124 176.6 987. 176.6 732. 181.4 472. 192.5 201. 201.5 4 4 0.37 4.36 1.26 3 0.98 5 9.98 8 7.76 9 2.63 9 49 9 36 4 47 3 50 0 0.00 0.00 2.7 274 143.9 251 156.6 226 169.9 199 184.0 172 198.8 142 200.7 113 200.7 841. 200.7 547. 210.8 242. 221.1 5 6 0.09 5.19 9.96 2 2.62 1 2.60 7 9.22 5 1.76 7 9.48 1 5.36 1 24 9 04 2 81 8 3.1 305 149.6 279 164.7 252 180.7 223 197.6 192 215.5 160 229.5 126 229.5 925. 229.5 587. 240.7 238. 238.6 6 5 1.31 6.02 1.51 1 3.53 2 0.43 1 1.33 5 5.31 7 1.36 0 3.48 0 61 0 73 3 62 2 3.1 306 170.7 276 189.5 245 209.4 212 230.6 176 253.1 139 258.2 100 258.2 628. 269.8 234. 234.8 7 5 1.03 6.85 1.55 7 7.44 0 4.59 3 1.81 3 7.84 7 1.32 9 9.69 9 05 7 83 3 0.00 0.00 3.1 307 192.8 274 215.5 239 239.6 201 265.4 161 287.7 118 287.7 758. 293.4 326. 321.7 8 5 0.75 7.68 7.20 8 6.01 0 2.20 6 4.22 8 0.44 9 4.33 9 23 0 52 0 0.00 0.00 0.00 0.00 3.1 309 214.6 273 241.4 233 270.2 191 301.0 145 317.4 987. 317.4 516. 342.8 20.3 9 5 0.46 8.52 8.44 8 0.48 7 5.73 2 2.24 5 7.91 2 22 2 53 7 8 20.38 0.00 0.00 0.00 0.00 3.1 312 234.9 272 266.3 228 300.2 181 336.7 131 347.0 798. 419.2 211. 211.2 10 5 0.18 9.35 5.28 4 2.10 7 7.49 6 8.98 9 3.96 4 67 1 23 3 0.00 0.00 0.00 0.00 0.00 0.00 3.1 297 269.2 252 306.9 203 347.9 150 376.6 940. 376.6 381. 381.0 11 5 1.40 10.18 4.52 1 2.10 8 1.90 1 0.78 6 91 6 04 4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.1 299 289.7 250 333.1 197 380.4 139 406.2 795. 603.0 12 5 1.12 11.01 7.60 9 9.64 8 8.28 3 9.67 9 21 7 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.1 302 309.7 250 359.0 193 412.9 130 435.9 656. 544.5 13 5 0.84 11.84 6.28 2 3.42 1 1.26 5 5.17 3 09 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.1 306 324.1 250 378.5 190 438.3 123 459.4 547. 500.2 14 5 0.56 12.67 0.56 6 8.29 6 1.62 3 5.19 2 66 5 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.1 310 320.2 253 375.7 191 436.6 123 459.4 536. 501.8 15 5 0.28 13.50 0.44 3 7.14 2 8.34 8 8.59 2 09 5 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.1 288 341.1 228 400.2 163 459.4 912. 459.4 195. 195.5 120 16 5 1.50 14.34 7.88 7 8.67 0 0.43 2 97 2 51 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Table B.18 Calculations of the tension in the connections of the wall designed with crimp 2 and Sc = 1.50 ft.

Straig Crimp Crimp Crimp Crimp Crimp Crimp Crimp Crimp Crimp Strai Tens Tens Tens Tens Tens Tens Tens Tens Tens th -1 -2 -3 -4 -5 -6 -7 -8 -9 T gth - ion ion ion ion ion ion ion ion ion ma Pullou Pullou Pullou Pullou Pullou Pullou Pullou Pullou Pullou Pullou Lay 1 In In In In In In In In In Tc x t Unit t t t t t t t t t er (Ki Leng Crim Crim Crim Crim Crim Crim Crim Crim Crim (lbs) Resist Resist Resist Resist Resist Resist Resist Resist Resist Resist ps) th p -1 p -2 p -3 p -4 p -5 p -6 p -7 p -8 p -9 ance ance ance ance ance ance ance ance ance ance (ft) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lb/in) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) (lbs) 0.2 221. 190. 158. 125. 91.2 56.3 20.5 1 2 0.29 0.20 98 27.84 60 28.69 37 29.56 27 30.46 8 31.38 6 32.33 0 20.50 0.00 0.00 0.00 0.00 0.00 0.5 580. 501. 421. 342. 260. 173. 79.8 2 8 0.57 0.59 45 68.69 15 68.69 86 68.69 57 71.00 96 76.82 54 83.05 9 79.89 0.00 0.00 0.00 0.00 0.00 1.8 177 150.4 155 153.7 134 153.7 112 153.7 907. 153.7 690. 162.5 464. 175.4 225. 189.0 3 1 0.85 3.53 3.07 1 9.18 9 1.92 9 4.65 9 38 9 12 3 11 0 23 0 0.00 0.00 0.00 2.2 218 153.6 194 164.5 170 175.8 145 176.6 119 176.6 941. 176.6 686. 183.4 424. 194.5 151. 151.7 4 4 1.13 4.36 1.30 9 9.17 0 6.22 1 1.96 9 6.83 9 70 9 56 0 72 7 70 0 0.00 2.7 266 148.3 242 161.2 217 174.8 190 189.2 162 200.7 132 200.7 103 200.7 737. 204.3 533. 5 6 1.41 5.19 7.43 3 5.68 5 1.01 7 2.74 0 0.12 1 6.00 1 1.89 1 77 2 0.00 0.00 45 3.1 313 144.9 287 159.7 261 175.4 232 192.0 202 209.6 170 228.2 137 229.5 103 229.5 804. 6 5 0.19 6.02 1.96 0 8.68 3 0.57 4 6.76 6 6.32 5 8.29 8 1.63 0 3.75 0 0.00 0.00 25 3.1 310 167.8 281 186.4 250 206.1 217 227.1 182 249.4 145 258.2 107 258.2 813. 7 5 0.47 6.85 6.95 8 5.72 3 5.95 6 6.45 5 5.95 7 3.13 9 1.50 9 0.00 0.00 0.00 0.00 21 3.1 307 192.9 274 215.5 239 239.7 201 265.5 160 287.7 118 287.7 895. 8 5 0.75 7.68 6.34 4 5.09 6 1.22 3 3.18 5 9.32 9 3.21 9 0.00 0.00 0.00 0.00 0.00 0.00 42 3.1 304 218.9 266 246.0 226 275.1 184 306.2 138 317.4 106 9 5 1.04 8.52 0.13 3 7.93 3 8.62 0 0.24 9 0.67 2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.25 3.1 299 244.8 258 277.0 213 311.7 165 347.0 131 10 5 1.32 9.35 8.32 4 5.24 4 9.95 6 9.95 4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.91 3.1 313 255.8 269 292.5 221 332.2 170 375.3 132 11 5 0.10 10.18 4.12 9 5.02 5 9.26 7 3.78 0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 8.48 3.1 309 281.0 261 323.6 209 370.0 172 12 5 0.38 11.01 6.07 3 6.87 4 5.05 5 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 5.00 3.1 305 307.2 253 356.3 217 13 5 0.66 11.84 2.43 6 2.03 2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 5.71 3.1 300 329.8 267 14 5 0.94 12.67 3.18 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.37 3.1 294 15 5 1.22 13.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 8.33 3.1 314

16 5 0.00 14.34 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 5.92 121

Table B.19 Calculations of the deflections of the wall designed with crimp 2 and Sc = 1.50 ft.

Te Te Te Te Te Te Te Te Te Te Te Te Te Te nsi nsi nsi nsi nsi nsi nsi nsi nsi nsi nsi nsi nsi nsi D on Def on Def on Def on Def on Def on Def on Def on Def on Def on Def on Def on Def on Def on Laye e In lect In lect In lect In lect In lect In lect In lect In lect In lect In lect In lect In lect In lect In r pt Cri ion Cri ion Cri ion Cri ion Cri ion Cri ion Cri ion Cri ion Cri ion Cri ion Cri ion Cri ion Cri ion Cri Tot Num h m in m in m in m in m in m in m in m in m in m in m in m in m in m al ber (f p - Cri p - Cri p - Cri p - Cri p - Cri p - Cri p - Cri p Cri p Cri p Cri p Cri p Cri p Cri p Def t) 7 mp 6 mp 5 mp 4 mp 3 mp 2 mp 1 mp 1 mp 2 mp 3 mp 4 mp 5 mp 6 mp 7 lect (lb -7 (lb -6 (lb -5 (lb -4 (lb -3 (lb -2 (lb -1 (lb 1 (lb 2 (lb 3 (lb 4 (lb 5 (lb 6 (lb ion s) (in) s) (in) s) (in) s) (in) s) (in) s) (in) s) (in) s) (in) s) (in) s) (in) s) (in) s) (in) s) (in) s) (in) 1. 15 51 86 12 15 15 11 84 49 13 2 0. 0.0 0. 0.0 .5 0.0 .5 0.0 .6 0.0 0. 0.0 3. 0.0 1. 0.0 8. 0.0 .3 0.0 .2 0.0 .1 0.0 0. 0.0 0. 0.0 1 5 00 0 00 0 7 0 6 0 0 1 72 1 94 1 77 1 49 1 2 1 1 0 5 0 00 0 00 6 3. 55 15 23 32 40 39 32 23 14 52 7 0. 0.0 0. 0.0 .2 0.0 0. 0.0 9. 0.0 2. 0.0 1. 0.0 9. 0.0 0. 0.0 6. 0.0 7. 0.0 .1 0.0 0. 0.0 0. 0.1 2 5 00 0 00 0 9 0 58 1 53 2 56 2 85 3 32 3 03 2 82 2 67 1 7 0 00 0 00 6 10 12 12 10 6. 85 33 56 78 03 20 28 11 79 57 34 95 2 0. 0.0 .6 0.0 2. 0.0 5. 0.0 5. 0.0 .0 0.0 .2 0.0 .8 0.0 .6 0.0 4. 0.0 4. 0.0 1. 0.0 .8 0.0 0. 0.2 3 5 00 0 7 0 07 1 19 2 76 3 3 3 9 4 7 4 0 3 34 3 26 2 65 1 0 0 00 7 12 14 15 12 10 8. 20 47 73 98 41 96 36 81 26 77 51 24 7 0. 0.0 0. 0.0 1. 0.0 1. 0.0 6. 0.0 .5 0.0 .7 0.0 .6 0.0 .5 0.0 .3 0.0 1. 0.0 3. 0.0 3. 0.0 0. 0.3 4 5 00 0 35 1 38 2 31 2 44 3 7 4 0 6 6 7 2 4 9 3 26 3 03 2 79 1 00 7 1 12 15 18 19 16 13 10 1. 45 35 65 95 44 38 25 08 25 31 37 74 44 13 2 .1 0.0 5. 0.0 6. 0.0 0. 0.0 .6 0.0 .7 0.0 .5 0.1 .0 0.1 .7 0.0 .5 0.0 .4 0.0 3. 0.0 5. 0.0 8. 0.5 5 5 6 0 90 1 40 2 52 3 4 4 6 7 0 0 3 1 0 8 8 4 6 3 35 2 81 1 13 8 1 11 15 18 21 20 17 14 11 3. 16 51 85 95 33 61 70 90 75 43 05 76 42 70 7 7. 0.0 9. 0.0 7. 0.0 .5 0.0 .4 0.0 .1 0.1 .7 0.1 .2 0.1 .9 0.0 .2 0.0 .4 0.0 7. 0.0 6. 0.0 .1 0.7 6 5 69 1 79 2 66 3 4 4 2 7 3 0 0 4 6 3 7 9 8 5 0 4 52 3 30 1 1 6 1 10 14 17 21 21 17 13 6. 26 65 36 18 93 45 00 44 66 98 60 20 2 0. 0.0 3. 0.0 5. 0.0 .7 0.0 .3 0.0 .2 0.1 .6 0.1 .3 0.1 .9 0.0 .9 0.0 5. 0.0 3. 0.0 9. 0.0 0. 0.6 7 5 00 0 30 1 07 2 0 3 4 5 4 0 9 4 0 3 6 9 8 5 34 3 71 2 19 1 00 8 1 12 17 21 21 17 12 8. 44 86 94 18 15 15 19 95 86 44 7 0. 0.0 0. 0.0 1. 0.0 8. 0.0 .1 0.0 .1 0.0 .0 0.1 .9 0.1 .1 0.0 .1 0.0 9. 0.0 2. 0.0 0. 0.0 0. 0.6 8 5 00 0 00 0 97 1 07 3 8 4 8 9 9 3 4 3 0 9 6 4 05 3 95 1 00 0 00 1 122

Table B.19 Continued

2 11 16 20 21 16 12 1. 21 69 65 36 78 37 99 29 75 28 2 0. 0.0 0. 0.0 3. 0.0 5. 0.0 .9 0.0 .6 0.0 .8 0.1 .1 0.1 .2 0.0 .4 0.0 8. 0.0 1. 0.0 0. 0.0 0. 0.5 9 5 00 0 00 0 05 1 30 2 9 4 8 8 8 3 9 4 4 8 0 4 71 3 40 1 00 0 00 7 2 10 15 20 21 16 11 3. 51 33 49 37 64 85 70 65 54 7 0. 0.0 0. 0.0 0. 0.0 8. 0.0 .7 0.0 .0 0.0 .0 0.1 .0 0.1 .9 0.0 .6 0.0 5. 0.0 .9 0.0 0. 0.0 0. 0.5 10 5 00 0 00 0 00 0 48 2 6 3 4 7 7 2 3 4 0 8 2 4 34 2 1 0 00 0 00 3 2 10 16 21 20 14 6. 53 93 53 72 13 80 92 36 2 0. 0.0 0. 0.0 0. 0.0 3. 0.0 .6 0.0 .5 0.0 .8 0.1 .2 0.1 .5 0.0 0. 0.0 0. 0.0 0. 0.0 0. 0.0 0. 0.5 11 5 00 0 00 0 00 0 77 2 4 4 1 8 6 4 7 2 9 6 72 3 85 1 00 0 00 0 00 0 2 15 21 20 14 8. 96 70 34 36 62 85 25 7 0. 0.0 0. 0.0 0. 0.0 0. 0.0 5. 0.0 .1 0.0 .8 0.1 .3 0.1 .9 0.0 8. 0.0 3. 0.0 0. 0.0 0. 0.0 0. 0.4 12 5 00 0 00 0 00 0 00 0 66 3 3 7 2 4 4 2 0 6 43 3 97 1 00 0 00 0 00 6 3 14 20 20 14 1. 80 91 65 51 80 63 2 0. 0.0 0. 0.0 0. 0.0 0. 0.0 0. 0.0 .1 0.0 .1 0.1 .0 0.1 .5 0.0 2. 0.0 .6 0.0 0. 0.0 0. 0.0 0. 0.4 13 5 00 0 00 0 00 0 00 0 00 0 5 6 7 3 2 3 4 6 46 3 0 0 00 0 00 0 00 0 3 20 20 14 3. 41 99 52 76 66 7 0. 0.0 0. 0.0 0. 0.0 0. 0.0 0. 0.0 0. 0.0 .9 0.1 .3 0.1 .3 0.0 4. 0.0 .4 0.0 0. 0.0 0. 0.0 0. 0.3 14 5 00 0 00 0 00 0 00 0 00 0 00 0 2 3 1 3 4 6 82 3 0 0 00 0 00 0 00 4 3 21 14 6. 39 81 77 67 2 0. 0.0 0. 0.0 0. 0.0 0. 0.0 0. 0.0 0. 0.0 0. 0.0 .1 0.1 .1 0.0 8. 0.0 .2 0.0 0. 0.0 0. 0.0 0. 0.2 15 5 00 0 00 0 00 0 00 0 00 0 00 0 00 0 9 4 9 6 69 3 3 0 00 0 00 0 00 2 3 19 12 8. 26 32 51 7 0. 0.0 0. 0.0 0. 0.0 0. 0.0 0. 0.0 0. 0.0 0. 0.0 .6 0.1 .7 0.0 5. 0.0 0. 0.0 0. 0.0 0. 0.0 0. 0.1 16 5 00 0 00 0 00 0 00 0 00 0 00 0 00 0 3 1 2 4 26 2 00 0 00 0 00 0 00 7

123

B.6 Wall Designed with AASHTO approach.

Table B.20 General information of the wall designed with AASHTO approach.

Depth    Tmax Sh Tmaxcal Le La Lt Ltdesign Layer Number k /k k v h h R F* (ft) r a r (Ksf) (ksf) (ksf) (Kips/ft) c (ft) (Kips) (ft) (ft) (ft) (ft) 1 1.25 1.67 0.40 0.16 0.00 0.07 0.18 0.03 6.25 1.13 1.74 13.38 11.63 25.01 28.00 2 3.75 1.61 0.38 0.49 0.00 0.21 0.52 0.03 6.25 3.27 1.61 13.90 11.63 25.53 28.00 3 6.25 1.54 0.37 0.81 0.00 0.34 0.84 0.04 4.32 3.62 1.48 10.02 11.63 21.65 28.00 4 8.75 1.48 0.35 1.14 0.00 0.45 1.13 0.05 3.21 3.62 1.36 7.83 11.63 19.46 28.00 5 11.25 1.42 0.34 1.46 0.00 0.56 1.39 0.06 2.61 3.62 1.23 6.73 11.63 18.35 28.00 6 13.75 1.36 0.32 1.79 0.00 0.65 1.62 0.07 2.23 3.62 1.10 6.14 11.63 17.77 28.00 7 16.25 1.29 0.31 2.11 0.00 0.73 1.83 0.08 1.98 3.62 0.97 5.88 11.63 17.50 28.00 8 18.75 1.23 0.29 2.44 0.00 0.80 2.01 0.09 1.80 3.62 0.85 5.86 11.63 17.49 28.00 9 21.25 1.20 0.29 2.76 0.00 0.89 2.22 0.10 1.63 3.62 0.78 5.60 10.50 16.10 28.00 10 23.75 1.20 0.29 3.09 0.00 0.99 2.48 0.11 1.46 3.62 0.78 5.01 9.00 14.01 28.00 11 26.25 1.20 0.29 3.41 0.00 1.10 2.74 0.13 1.32 3.62 0.78 4.53 7.50 12.03 28.00 12 28.75 1.20 0.29 3.74 0.00 1.20 3.00 0.14 1.21 3.62 0.78 4.14 6.00 10.14 28.00 13 31.25 1.20 0.29 4.06 0.00 1.30 3.26 0.15 1.11 3.62 0.78 3.81 4.50 8.31 28.00 14 33.75 1.20 0.29 4.39 0.00 1.41 3.52 0.16 1.03 3.62 0.78 3.52 3.00 6.52 28.00 15 36.25 1.20 0.29 4.71 0.00 1.51 3.78 0.17 0.96 3.62 0.78 3.28 1.50 4.78 28.00 16 38.75 1.20 0.29 5.04 0.00 1.62 4.04 0.19 0.90 3.62 0.78 3.07 0.00 3.07 28.00

124

B.7 Wall Designed with K-Stiffness approach using RECO straps.

Table B.21 General information of the wall designed with K-Stiffness approach using RECO straps.

Depth Sh Ji Slocal v Tmaxcalc Tmaxcalc x Sh Le La Lt Ltdesign Layer Number 2 local Dtmax F* (ft) (ft) (Kips/ft) (Kips/ft ) (Ksf) (Kips/ft) (Kips) (ft) (ft) (ft) (ft)

1 1.25 6.25 1440.00 576.00 1.00 0.05 0.25 0.01 0.07 1.74 0.39 11.63 12.02 28.00 2 3.75 6.25 1440.00 576.00 1.00 0.16 0.76 0.08 0.61 1.61 1.27 11.63 12.90 28.00 3 6.25 6.25 1440.00 576.00 1.00 0.27 1.26 0.23 1.68 1.48 2.30 11.63 13.92 28.00 4 8.75 6.25 1440.00 576.00 1.00 0.38 1.76 0.45 3.30 1.36 3.52 11.63 15.15 28.00 5 11.25 6.25 1440.00 576.00 1.00 0.48 2.27 0.74 5.46 1.23 5.00 11.63 16.62 28.00 6 13.75 4.20 2143.61 857.45 1.00 0.59 2.77 1.11 5.48 1.10 4.58 11.63 16.21 28.00 7 16.25 3.01 2993.97 1197.59 1.00 0.70 3.27 1.55 5.48 0.97 4.38 11.63 16.01 28.00 8 18.75 2.26 3986.06 1594.42 1.00 0.81 3.78 2.06 5.48 0.85 4.37 11.63 16.00 28.00 9 21.25 1.76 5119.87 2047.95 1.00 0.91 4.28 2.65 5.48 0.78 4.17 10.50 14.67 28.00 10 23.75 1.44 6260.77 2504.31 1.00 1.00 4.79 3.24 5.48 0.78 3.73 9.00 12.73 28.00 11 26.25 1.30 6919.80 2767.92 1.00 1.00 5.29 3.58 5.48 0.78 3.38 7.50 10.88 28.00 12 28.75 1.19 7578.82 3031.53 1.00 1.00 5.79 3.92 5.48 0.78 3.09 6.00 9.09 28.00 13 31.25 1.09 8237.85 3295.14 1.00 1.00 6.30 4.26 5.48 0.78 2.84 4.50 7.34 28.00 14 33.75 1.01 8896.88 3558.75 1.00 1.00 6.80 4.60 5.48 0.78 2.63 3.00 5.63 28.00 15 36.25 0.94 9555.91 3822.36 1.00 1.00 7.30 4.94 5.48 0.78 2.45 1.50 3.95 28.00 16 38.75 0.88 10214.94 4085.97 1.00 1.00 7.81 5.28 5.48 0.78 2.29 0.00 2.29 28.00

125