Structural Performance Analysis of Underground Stormwater Storage Chamber

A thesis presented to

the faculty of

the Russ College of Engineering and Technology of Ohio University

In partial fulfillment

of the requirements for the degree

Master of Science

Junqing Zhu

June 2012

This thesis titled

Structural Performance Analysis of Underground Stormwater Storage Chamber

JUNQING ZHU

has been approved for

the Department of Civil Engineering

and the Russ College of Engineering and Technology by

Teruhisa Masada

Professor of Civil Engineering

Dennis Irwin

Dean, Russ College of Engineering and Technology 3

ABSTRACT

ZHU, JUNQING, M.S., June 2012, Civil Engineering

Structural Performance Analysis of Underground Stormwater Storage Chamber

Director of Thesis: Teruhisa Masada

Within the last two decades, a new drainage product called stormwater chambers have emerged in the U. S. for managing storm water. These products are typically arch- shaped, light-weight, cost-effective, chemically stable, and easy to install. Despite the popularization of these products, currently there is a lack of research work on their structural performance and also a complete devoid of any rational analysis/design methods for these structures. In this thesis, a computer software package CANDE-2007 was used to run a number of sophisticated two-dimensional numerical simulations for both single and multiple chamber systems. Using the simulation results, discussions were made on several topics related to the buried chamber structure. Data from field loading tests was examined to confirm simulation results. Based on the results of computer simulations and field load test, a set of analytical methods were proposed. Key conclusions reached in the thesis work are that the arch-shaped chamber structures are capable of sustaining a relatively high level of external loading and they are able to distribute stress well in the soil. The foot region of the chamber appears to be critical.

Approved: ______

Teruhisa Masada

Professor of Civil Engineering 4

ACKNOWLEDGMENTS

First and foremost, I would like to show my greatest gratitude to my advisor Dr.

Teruhisa Masada for assisting me a lot to finish this thesis. I would also thank him for supporting me all the time through my two-year Master’s Program.

I would like to thank Dr. Shad M. Sargand, Sang-Soo Kim and Xiaoping Shen for being my committee member. I would also like to thank other faculties and colleagues in the Civil Engineering Department who supported me during the completion of this research.

Lastly, I would like to thank my father and my mother for supporting me to study abroad in the U. S. and encouraging me all the time. 5

TABLE OF CONTENTS

Page

Abstract ...... 3 Acknowledgments...... 4 List of Tables ...... 7 List of Figures ...... 8 Chapter 1 Introduction ...... 11 1.1 Background ...... 11 1.2 Objectives ...... 13 1.3 Outline of Thesis ...... 14 Chapter 2 Literature Review ...... 16 2.1 History of Stormwater Management ...... 16 2.2 Available Chamber Products ...... 17 2.3 Standards ...... 18 2.4 General Installation Guidelines ...... 21 2.5 Researches ...... 23 Chapter 3 Computer Simulations ...... 27 3.1 CANDE-2007 ...... 27 3.2 General Methodology for Single Chamber Structure ...... 29 3.2 General Methodology for Multi-Chamber Structures ...... 36 3.4 Results of CANDE-2007 Simulations ...... 37 3.4.1 Single Circular Pipe ...... 38 3.4.2 Single Semi-Circular Chamber ...... 43 3.4.3 Different Cross-Sectional Shape Single Chambers ...... 55 3.4.4 Multiple Semi-Circular Chambers ...... 63 Chapter 4 Field Load Testing ...... 83 4.1 Introduction ...... 83 4.2 Chamber Product ...... 84 4.3 Installation Procedures ...... 85 4.4 Chamber Instrumentations ...... 88 6

4.5 Loading Methods ...... 90 4.6 Field Load Test Results ...... 94 4.6.1 Soil Pressure Measured at Crown ...... 94 4.6.2 Deformation Behaviors of Buried Chambers...... 97 Chapter 5 Analysis of Buried Chamber Structure ...... 104 5.1 Introduction ...... 104 5.2 Basic Analysis of Loaded Chamber Product ...... 104 5.3 Assumptions for Buried Chamber Analysis ...... 107 5.4 Analysis of Buried Chamber Structure ...... 110 Chapter 6 Summary and Conclusions ...... 113 6.1 Literature Review ...... 113 6.2 Computer Simulations ...... 114 6.2.1 Chamber vs. Pipe ...... 114 6.2.2 External Loading Type...... 116 6.2.3 Chamber’s Cross-Sectional Geometry ...... 117 6.2.4 Chamber Spacing in Multi-Chamber Installation ...... 119 6.3 Field Load Tests ...... 120 6.4 Proposed Analytical Methods ...... 122 6.5 Recommendations ...... 123 References ...... 125 Appendix A: CANDE Results of Elliptical Chamber ...... 127 Appendix B: CANDE Results of Trapezoidal Chamber ...... 129 Appendix C: CANDE Results of Triangular Chamber...... 131 Appendix D: CANDE Results of Rectangular Chamber ...... 133 Appendix E: Comparison Table for Different Crosssectional Shape Chambers ...... 135

LIST OF TABLES

Page

Table 2.1: Dimension Requirements and Tolerances (ASTM F2418-05, 2005) ...... 19 Table 2.2: Inputs for CANDE ...... 24 Table 3.1: Summary of Key Inputs for CANDE 2007 Simulations ...... 34 Table 3.2: Sectional Properties of Chamber Wall ...... 35 Table 3.3: Interpretation of Structure Failure Mode ...... 37 Table 3.4: Recommended Plastic Properties for Short and Long-term Loading ...... 37 Table 3.5: Summary of Circular Pipe Responses at Structure Failed ...... 42 Table 3.6: Summary of Chamber and Pipe’s Responses at 70 psi Surface-Loading ...... 47 Table 3.7: Surface Loading Level at Structure and Soil Failure ...... 48 Table 3.8: Summary of Chamber Responses under Two Types of 60 psi Surface-Loading ...... 53 Table 3.9: Surface Loading Level at Structure and Soil Failure ...... 53 Table 3.10: Geometric Parameters of Different Cross-Sectional Shapes ...... 56 Table 3.11: Geometric Parameters of Different Shapes ...... 56 Table 3.12: Summary of Chamber Responses at 20 psi Surface-Loading ...... 59 Table 3.13: Surface Loading Level at Structure and Soil Failure ...... 59 Table 3.14: Summary of Multi-Chamber Responses at 40 psi Surface-Loading ...... 79 Table 3.15: Surface Loading Level at Structure and Soil Failure ...... 80 Table 4.1: Wheel and Axle Loads Measured in Field ...... 91 Table 4.2: Soil Pressure Readings under Level 1 (Empty Dump Truck) Loading ...... 94 Table 4.3: Soil Pressure Readings under Level 2 (144-kN; 32.4-kip) Loading ...... 95 Table 4.4: Soil Pressure Readings under Level 3 (180-kN; 40.4-kip) Loading ...... 95 Table 4.5: Soil Pressure Readings under Level 4 (214-kN; 48-kip) Loading ...... 95 Table 4.6: Dimensional Changes Experienced by Chamber A...... 97 Table 4.7: Dimensional Changes Experienced by Chamber B ...... 98 Table 4.8: Dimensional Changes Experienced by Chamber C ...... 98 Table E.1: Performance of different shapes under 50 psi ...... 135 Table E.2: Performance of different shapes under 60 psi ...... 136 8

LIST OF FIGURES

Page

Figure 1.1: Arch-Shaped Plastic chambers (Stormtech, 2012) ...... 12 Figure 2.1: Examples of Available Stormwater Collection Chamber Products ...... 17 Figure 2.2: General Illustration of Chamber Structure (ASTM F2418-05, 2005) ...... 18 Figure 2.3: Single Layer System (Triton, 2010) ...... 22 Figure 2.4: FEM Chamber Models (a. ABAQUS Model; b. CANDE Model) ...... 24 Figure 3.1: Typical Half Mesh Used for Single Chamber ...... 30 Figure 3.2: Determination of K and n (CANDE-89 Manual, 1989) ...... 32 Figure 3.3: Determination of Kb and m (CANDE-89 Manual, 1989) ...... 32 Figure 3.4: Design of Chamber Wall Section (CANDE Manual 2007) ...... 35 Figure 3.5: Typical Half Mesh Used for Multiple Chamber Analysis ...... 36 Figure 3.6: Half-Mesh Used for Single Circular Pipe ...... 39 Figure 3.7: Mesh Plot of Vertical Soil Pressure Distribution around Circular Pipe ...... 40 Figure 3.8: Node Numbering System Used for Circular Pipe ...... 40 Figure 3.9: Plot of X-direction Deflection for the Pipe ...... 40 Figure 3.10: Plot of Y-direction Deflection for the Pipe ...... 41 Figure 3.11: Plot of Bending Moment in Circular Pipe Wall ...... 41 Figure 3.12: Plot of Thrust Force in Circular Pipe Wall...... 41 Figure 3.13: Plot of Shear Force in Circular Pipe Wall ...... 42 Figure 3.14: Half-Mesh Used for Single Semi-Circular Chamber ...... 44 Figure 3.15: Mesh Plot of Vertical Soil Pressure Distribution around Semi-Circular Chamber ...... 45 Figure 3.16: Node Numbering System Used for Semi-Circular Chamber ...... 45 Figure 3.17: Plot of X-direction Deflection for Semicircular Chamber ...... 45 Figure 3.18: Plot of Y-direction Deflection for Semicircular Chamber ...... 46 Figure 3.19: Plot of Bending Moment in Semi-Circular Chamber Wall ...... 46 Figure 3.20: Plot of Thrust Force in Semi-Circular Chamber Wall ...... 46 Figure 3.21: Plot of Shear Force in Semi-Circular Chamber Wall ...... 47 Figure 3.22: Mesh Plot of Vertical Soil Pressure Distribution around Semi-Circular Chamber ...... 50 Figure 3.23: Plots of Semi-Circular Chamber Deflections ...... 51 Figure 3.24: Plot of Bending Moment in Semi-Circular Chamber Wall ...... 51 Figure 3.25: Plot of Thrust Force in Semi-Circular Chamber Wall ...... 52 Figure 3.26: Plot of Shear Force in Semi-Circular Chamber Wall ...... 52 Figure 3.27: Mesh Plot of Vertical Soil Pressure Distribution for Elliptical Chamber .... 57 Figure 3.28: Mesh Plot of Vertical Soil Pressure Distribution for Trapezoidal Chamber 57 Figure 3.29: Mesh Plot of Vertical Soil Pressure Distribution for Triangular Chamber .. 57 Figure 3.30: Mesh Plot of Vertical Soil Pressure Distribution for Rectangular Chamber 58 Figure 3.31: Nodes Placed on Each Different Chamber Shape ...... 58 Figure 3.32: Half-Mesh Used for Multiple Semi-Circular Chamber ...... 64 9

Figure 3.33: Mesh Plot of Vertical Soil Pressure Distribution around Circular Chamber 64 Figure 3.34: Plots of X-direction Deflection in Chamber Group 1 ...... 65 Figure 3.35: Plots of Y-direction Deflection in Chamber Group 1 ...... 65 Figure 3.36: Plots of X-direction Deflection in Chamber Group 2 ...... 65 Figure 3.37: Plots of Y-direction Deflection in Chamber Group 2 ...... 66 Figure 3.38: Plot of Bending Moment in Semi-Circular Chamber Wall of Group 1&2 .. 66 Figure 3.39: Plots of Thrust Force in Semi-Circular Chamber Wall of Group 1&2 ...... 67 Figure 3.40: Plot of Shear Force in Chamber Wall of Group 1 ...... 67 Figure 3.41: Plot of Shear Force in Chamber Wall of Group 2 ...... 68 Figure 3.42: Half-Mesh Used for Multiple Semi-Circular Chambers ...... 69 Figure 3.43: Mesh Plot of Vertical Soil Pressure Distribution around Circular Chambers ...... 69 Figure 3.44: Plot of X-direction Deflection in Chamber Group 1 ...... 69 Figure 3.45: Plot of Y-direction Deflection in Chamber Group 1 ...... 70 Figure 3.46: Plot of X-direction Deflection in Chamber Group 2 ...... 70 Figure 3.47: Plot of Y-direction Deflection in Chamber Group 2 ...... 70 Figure 3.48: Plot of Bending Moment in Semi-Circular Chamber Wall ...... 71 Figure 3.49: Plot of Thrust Force in Chamber Wall of Group 1...... 71 Figure 3.50: Plot of Thrust Force in Chamber Wall of Group 2...... 72 Figure 3.51: Plot of Shear Force in Semi-Circular Chamber Wall ...... 72 Figure 3.52: Half-Mesh Used for Multiple Semi-Circular Chambers ...... 73 Figure 3.53: Mesh Plot of Vertical Soil Pressure Distribution around Circular Pipe ...... 74 Figure 3.54: Plots of Deflections in Semi-circular Chamber Group 1 ...... 74 Figure 3.55: Plots of Deflections in Semi-circular Chamber Group 2 ...... 75 Figure 3.56: Plot of Bending Moment in Chamber Wall of Group 1 ...... 75 Figure 3.57: Plot of Bending Moment in Chamber Wall of Group 2 ...... 76 Figure 3.58: Plot of Thrust Force in Semi-Circular Chamber Wall ...... 76 Figure 3.59: Plot of Shear Force in Semi-Circular Chamber Wall ...... 77 Figure 3.60: Node Numbering System Applied to Multiple Chambers ...... 78 Figure 4.1: General Appearance of Chamber Product Tested ...... 85 Figure 4.2: Chambers Installation Plan ...... 87 Figure 4.3: A Photograph Taken During Field Installation of Chamber Structures ...... 87 Figure 4.4: A Soil Pressure Cell Placed Over a Buried Chamber Structure ...... 88 Figure 4.5: Four Linear Wire Potentiometers Installed Inside Each Chamber ...... 89 Figure 4.6: Axle Configurations of Dump Truck Used in Field Testing ...... 90 Figure 4.7: Actual Photograph of Dump Truck ...... 90 Figure 4.8: Schematics for Live Load Application Plan (Drawing 1) ...... 92 Figure 4.9: Schematics for Live Load Application Plan (Drawing 2) ...... 93 Figure 4.10: Transverse Loading – Axle 3 over Chamber C ...... 93 Figure 4.11: Longitudinal Loading – Axle 3 over Chambers A & B ...... 94 Figure 4.12: Vertical Soil Pressure Measured at Chamber Crown for Chamber A ...... 96 Figure 4.13: Vertical Soil Pressure Measured at Chamber Crown for Chamber B ...... 97 Figure 4.14: Dimensional Changes Experienced by Chamber Structures ...... 100 10

Figure 4.15: Deformation Characteristics of Buried Circular Pipe and Arch Chamber . 102 Figure 5.1: Loading of Idealized Chamber Product...... 105 Figure 5.2: Illustration for Analysis of Buried Chamber Structure ...... 108 Figure A.1: Half Mesh Plot of Elliptical Chamber ...... 127 Figure A.2: Plots of Displacement in Elliptical Chamber Wall ...... 127 Figure A.3: Plot of Bending Moment in Elliptical Chamber Wall ...... 128 Figure A.4: Plot of Thrust Force in Elliptical Chamber Wall...... 128 Figure A.5: Plot of Shear Force in Elliptical Chamber Wall ...... 128 Figure B.1: Half-Mesh Used for Trapezoidal Chamber ...... 129 Figure B.2: Plots of Trapezoidal Chamber Deflections ...... 129 Figure B.3: Plot of Bending Moment in Trapezoidal Chamber Wall ...... 130 Figure B.4: Plot of Thrust Force in Trapezoidal Chamber Wall ...... 130 Figure B.5: Plot of Shear Force in Trapezoidal Chamber Wall ...... 130 Figure C.1: Half-Mesh Used for Triangular Chamber...... 131 Figure C.2: Plots of Triangular Chamber Deflections ...... 131 Figure C.3: Plot of Bending Moment in Triangular Chamber Wall ...... 132 Figure C.4: Plot of Thrust Force in Triangular Chamber Wall ...... 132 Figure C.5: Plot of Shear Force in Triangular Chamber Wall ...... 132 Figure D.1: Half-Mesh Used for Rectangular Chamber ...... 133 Figure D.2: Plots of Rectangular Chamber Deflections ...... 133 Figure D.3: Plot of Bending Moment in Rectangular Chamber Wall ...... 134 Figure D.4: Plot of Thrust Force in Rectangular Chamber Wall ...... 134 Figure D.5: Plot of Shear Force in Rectangular Chamber Wall ...... 134

CHAPTER 1 INTRODUCTION

1.1 Background

In areas where buildings, roads, and parking lots are constructed, a large volume of runoff water is often generated rapidly during each major storm event due to relatively short time of concentration and a lack of infiltration into subsoil. If this runoff water is not temporarily stored and then released in a controlled manner, the storm runoff water could begin to build up and cause flooding problems in some areas. For this reason, a network of stormwater drainage structures is installed, along with catch basins and manholes, to handle the storm water runoff volumes. Traditionally, the network system consisted largely of circular drain pipes made of concrete, steel, and/or plastics (e.g.,

PVC, HDPE). Some of these pipeline structures are very heavy, not cost-effective, and susceptible to damages due to differential settlement and durability issues (Cultec, 2007).

In addition, these pipe structures cannot temporarily store the runoff water. They simply convey the stormwater flow to the next element in the network system downstream.

In recent years quality of storm runoff water is becoming a critical issue in many water management districts. In 1999, the United States Environmental Protection Agency published the National Pollutant Discharge Elimination System Phase II (NPDES II) stormwater program. Under the Clean Water Act, the runoff water is required to be treated with best management practices (BMPs). Within the last two decades, a new drainage product called stormwater storage chamber has emerged in the U.S. for managing storm water. It appears to be a good solution to the problem, as it can be 12

installed at shallow depth and does not take up a large surface area like a sediment detention ponds does. Moreover, it holds some advantages over traditional stormwater drainage products, as it is usually made from thermoplastic resin material such as high density polyethylene (HDPE) and poly vinyl chloride (PVC). The stormwater chamber is typically an arch-shaped and open-bottom structural element, as seen in Figure 1. It is installed below the ground surface to serve as an underground structure, which is mainly used for subsurface retention, detention, conveyance and reuse of storm water or groundwater. The stormwater chambers are light weight, cost effective, chemically stable, and easier to install than the conventional concrete/metal counterparts. Also, these chambers can be stock-piled in a bulk quantity and shipped easily because of their open- ended geometries.

Figure 1.1: Arch-Shaped Plastic chambers (Stormtech, 2012)

The underground chamber structures are becoming increasingly more popular nowadays due to the above noted advantages. However, no design/analysis guidelines have been established for the storm water retention chambers by the engineering community. Some engineers assume conveniently that the arch-shaped chambers must behave like circular pipes underground. With more chamber products are installed in the ground every week, there is an urgent need to study the structural behavior of buried chambers and develop a set of analysis methods for the buried chambers. In this thesis, the author has made a modest step toward fulfilling the need.

1.2 Objectives

In this thesis, the author would make use of FEM (Finite Element Method) to look into the structural behavior of buried plastic chambers under loadings. An effort would also be made to investigate soil-chamber interaction mode and to propose an analytical method. Detailed objectives of the current thesis are as follows:

1) To conduct a thorough literature review to obtain the current state-of-the-

knowledge on the buried chamber structures;

2) To perform single-structure computer simulations to identify key differences in

structural performance between a semi-circular chamber and a circular pipe;

3) To perform single-structure computer simulations to investigate the optimum

cross-sectional shape for the buried chamber structure; 14

4) To perform computer simulations of the buried multi-chamber problems to gain

insights into how chambers interact with each other and the surrounding soil to

resist the loads;

5) To perform computer simulations to gain insights into potential failure modes of

underground chamber-soil composite system;

6) To examine in detail the full-scale field load test data obtained by the Ohio

University research team;

7) To propose a set of analytical methods for the buried chambers based on the

results of the literature review, computer simulations, and field test data.

1.3 Outline of Thesis

Chapter 2 provides the current state-of-practice knowledge on the buried storm water storage chamber technology, which covers topics ranging from historical perspectives to government/ industry standards on the chambers and any major research work done on the stormwater chamber structures in the past. Chapter 3 is devoted to computer simulations. After providing the features of the computer software CANDE-

2007, the general methodologies applied for single-chamber and multi-chamber simulation problems are described in detail. The remaining sections of this chapter present the results of the computer simulations. Chapter 4 examines in detail the full- scale field load testing of buried chambers that were carried out by Ohio University researchers a few years ago. First, all details of the test program are provided. Then, the test results are presented to point out how chambers responded to the applied loads in the 15

field. Comments are made to compare the results of the field load tests and the computer simulations. Chapter 5 builds on top of the previous three chapters and attempts to develop a set of relatively comprehensive analytical methods applicable to the buried chamber structures. Chapter 6 concludes the main section of the thesis by offering a summary of and conclusions reached in each major stage of the thesis work. This final chapter also provides a few recommendations for any future research work.

CHAPTER 2 LITERATURE REVIEW

2.1 History of Stormwater Management

The management of stormwater is subject to government regulations in the U.S.

The history of regulations can be traced backed to the Refuse Act in 1899. The act prohibited discharging any refuse matter into navigable water (EPA 1973). The main shortcoming of this act was that it was applicable only to navigable water, leaving out the majority of waterways in the United States (EPA, 1973). In 1948, the Federal Water

Pollution Control Act (FWPA) was enacted to provide a mechanism for funding so that states can build treatment works of pollution. This act was amended and extended several times. In 1972, the Clean Water Act (CWA) was established, derived from the

FWPA. This act mainly focused on dealing with chemical pollutants (EPA, 1973). In

1999, the United States Environmental Protection Agency (EPA) established the National

Pollutant Discharge Elimination System Phase II (NPDES II) stormwater program.

NPDES II focuses on controlling water pollution by regulating point sources that discharge pollutants into waters of the United States (EPA, 2012).

The CWA 1972 and NPDES 2002 are the current governmental regulations that require the application of best management of practices (BMPs) to control stormwater.

BMPs are divided into nonstructural and structural BMP. According to Filshill (2010), definition of structural BMP is “any BMP that involves manmade structure or alteration that would improve the quality of the stormwater” (p. 11). One of the most widely used structural BMPs is underground storage system. The underground storage systems 17

include steel or plastic pipes, concrete culverts, stone beds wrapped in filter fabrics, and arch-shaped plastic chambers. This introduces stormwater chamber as a structural BMP.

2.2 Available Chamber Products

Currently, various types of chamber products are available in the market.

Typically they are made of PP (Polypropylene) or HDPE (High density polyethylene) material. Some chamber products are made of soy-based resin. The most distinguished advantage of these materials is that chambers made of thermoplastic resins are resistant to chemicals typically found in stormwater run-off, such as acids and hydrocarbons. The chambers made from plastics tend to be light-weight and low-cost. They may be also resistant to abrasion actions caused by sediment-laden fast hydraulic flow. In addition, they can maintain adequate stiffness through higher temperatures experienced during installation and service (Stormtech, 2009).

With no industry standards in place, the chamber products come in several shapes.

Figure 2.1 below shows some examples.

Figure 2.1: Examples of Available Stormwater Collection Chamber Products

2.3 Standards

The American Society for Testing and Materials (ASTM) International established standard specification F-2418 for polypropylene corrugated wall stormwater collection chambers in 2005. This standard covers dimensional and material requirements as well as a simple load test method for the chamber structures. Table 2.1 below shows dimension requirements and tolerances from the standard dimensions. Figure 2.1 below gives a brief illustration of the terminology used in the standard.

Figure 2.2: General Illustration of Chamber Structure (ASTM F2418-05, 2005)

Table 2.1: Dimension Requirements and Tolerances (ASTM F2418-05, 2005)

Chamber Nominal Nominal Rise Span Min. Min. Wall Min. Arch Stiffness Size Height Width Foot Width Thickness Constant in. in. Average Tolerance Average in. Tolerance in. in. in. lb./ft.% (mm) (mm) in. (mm) in. (mm) (mm) (mm) (mm) (mm) 16 33 16(406) 33(838) 13.1(333) 0.4(10) 24.3(617) 0.4(10) 4.0(100) 0.125(3.18) 300 30 51 30(762) 51(1295) 26.7(678) 0.4(10) 42.6(1082) 0.4(10) 4.0(100) 0.175(4.45) 300

ASTM F-2418 describes a load test procedure for chamber products, which is very similar to the parallel-plate load test often performed on circular pipe products per

ASTM D-2412. Each chamber specimen is first conditioned for at least 4 hours in the standard room temperature/humidity conditions. Then, the chamber specimen is placed upright in the loading area with its feet fixed to the level platform. The vertical load is then applied slowly from the top via a flat plate at a constant-displacement rate matching

2% rise dimension per minute. The arch stiffness constant (ASC) is calculated by the following equation when the vertical deflection is equal to 2%:

Where ASC = arch stiffness constant (lb. /ft. / %); F = vertical load applied (lb.);

y = vertical deflection (= 2%); and L = specimen length (ft.).

The chamber is loaded up to 8% vertical deflection to observe any signs of structural distress and/or failure.

The American Association of State Highway & Transportation Officials

(AASHTO) has been setting national and international standards for the design of bridges and buried culverts since 1931. Section 12 of the AASHTO LRFD Bridge Design

Specifications (2009) provides the specifications for buried culvert structures, based on the load resistance factor design (LRFD) approach. A portion of Section 12 is devoted to culvert structures made from various materials. However, the current AASHTO LRFD specifications present nothing on the arch-shaped stormwater collection chamber structures. 21

2.4 General Installation Guidelines

Although several different manufacturers distribute their own stormwater chamber products, basic installation steps appear to be nearly identical among them. The following is a summary of typical installation guidelines for stormwater chambers provided by a few companies (Stormtech 2012; Triton 2010):

1) Prepare necessary materials and equipment. These include crushed stone,

chambers and chamber caps, excavator, filter fabric, fill material, vibratory roller

and other required material.

2) Excavate and level the designated installation area. The excavated area should be

a little larger than its designed size, so that chambers could be installed properly.

Standing water should be kept off the excavated area. Necessary measures should

be done to drain the water.

3) Prepare the subgrade soil and lay the filter fabric over the subgrade soil and

around the perimeter of the excavation area as needed.

4) Place clean, crushed, angular stone over the entire bottom surface of the

excavation area. Nominal size of the crushed stone should be 0.75 to 2.00 inches

(19 to 51 mm). Then, compact the whole are with vibratory roller to make the

surface flat. Place a nonwoven geotextile sheet over the crushed stone as needed.

5) Place and assemble the chambers in rows. One issue that worth mentioning here is

that the spacing between adjacent chamber rows. If the spacing is too narrow, the

fill material between the two rows would not be sufficient enough to form a

sizable column to support the load coming from the top. If the spacing is too 22

wide, the excavated area would not be used efficiently. Generally, according to

each chamber company’s installation manual, the minimum spacing between

adjacent rows is 6 inches (152 mm).

6) Place crushed stone over the chambers. The same stone material is used here as

previously used. The stone can be placed by an excavator, a dozer or a telescoping

conveyer boom.

7) The very last step is backfilling. Place non-woven fabric filter over the whole

area, with a height of at least 2 inches (51 mm). Then distribute the fill with a

construction vehicle that meets the maximum wheel loads or ground pressure

limits. Compact each lift of backfill. The minimum cover height is generally 18

inches (457 mm).

Figure 2.3: Single Layer System (Triton, 2010) 23

Above is a brief introduction of installation process and requirements. Readers may want to refer to each company’s installation manuals and consult experienced engineers for detailed instructions. Figure 2.3 illustrates the installation conditions.

2.5 Researches

There are a limited number of literatures available on this subject, since the stromwater chamber is quite a new underground structure and not too many researchers have studied its structural performance aspects on this structure.

Beaver et al. (2003) tested and analyzed structural performance of buried stormwater chamber. They conducted computer modeling of stormwater chamber with

CANDE-89 and ABAQUS. Figure 2.4 shows the Finite Element models they used. They also conducted field load tests to evaluate the computer simulation results. Dimensions of the structure were: rise 760 mm (30 in) and span 1270 mm (50 in).

CANDE-89 was used to model an arch-shaped chamber installed under a cover height of 2,440 mm (8 ft.). The model consisted of a 1/2 –chamber section with symmetric boundary conditions that imply adjacent chamber spacing of 150 mm (6 in).

Some of the CANDE simulation inputs are shown in Table 1. Polypropylene material was chosen for the chamber, and the soil material surrounding the chamber was coarse grained with the density equal to 95% of maximum dry density per the standard Proctor test (SW95, per AASHTO). The model incorporated the Mohr-Coulomb failure criterion.

The soil located more than 150 mm (6 in.) below the chamber was considered undisturbed and linear-elastic. 24

Table 2.2: Inputs for CANDE

Depth No. Elements Soil Model Structure Material Load

2440mm (8 ft.) 18 Duncan/Selig(SW95) PP/PP2 18.8kN/m3 (120 lb/ft3)

(a) ABAQUS Model (b) CANDE Model Figure 2.4: FEM Chamber Models (a. ABAQUS Model; b. CANDE Model)

The results of this model showed that bending moments in the chamber wall are low for all conditions tested due to the combination of stiff soil and the low bending stiffness of the chamber, as well as the chamber geometry. Thrust forces in the chamber wall section decreased from mid-term to long-term, which indicates that the load is transferred from the leg to the surrounding soil. The vertical arching factor (VAF) values were similar with thermoplastic pipe and culverts under similar circumstances, which indicates that the simplified AASHTO design approach for VAF due to service dead loads is acceptable for chamber design under moderate cover (Beaver et al., 2003). VAF is defined as the ratio of load carried by chamber to soil prism load. Shortcoming of this 25

study is that the foot of the chamber was not modeled very well, which could be critical in realistic simulation of buried chamber behaviors.

Beaver et al. (2003) conducted similar chamber analyses using ABAQUS for shallow burial condition of 450 mm cover with three adjacent chambers. The model was similar to that used in the CANDE-89 analysis. Results of this model showed that axial thrust and bending moment in the chamber wall are higher for shallow covers. According to Beaver et al. (2003), this is because of that ratio of chamber stiffness to soil stiffness is high, and the elliptical arch-shape of chambers performs better under uniform loadings than the concentrated loadings from vehicle wheels. Stiffness of chamber reduced with the soil stiffness held constant, because of the load transfer from the chamber to the surrounding soils. Field testing results conducted by Beaver et al. in 2001 are consistent with finite element method predictions.

In 2007, a research team at Ohio University conducted a series of field load tests on stormwater chambers. A group of chambers were buried in an excavated area side by side. The area then was backfilled with coarse granular soil. The depth of the crown of the chambers was 0.46 m (18 inches). Four sensors were set up inside each chamber to measure deformations in the rise, base-level span, span in the shoulder level and diagonal distance from the foot to the shoulder. Also, a soil pressure cell was installed above each chamber to record vertical pressure at the crown during the testing. Different levels of live loading were applied on top of the soil by positioning a dump truck.

Results of this field testing show that the chamber under the minimum soil cover can support a wheel load of 52.3 kN (11.8 kips) and an axle load of 109.0 kN (24.5 kips) 26

in both transverse and longitudinal directions (Masada, 2011). Deflections and vertical pressure induced were within the AASHTO LRFD specifications. The author concluded that the chamber structure behaves not exactly same with flexible pipes, and this calls for a need to gain more insights into performance of chamber structure under loading. More details of this unique field load testing program are presented in Chapter 4 of this thesis. 27

CHAPTER 3 COMPUTER SIMULATIONS

3.1 CANDE-2007

CANDE is an acronym for Culvert ANalysis and DEsign. It is a two-dimensional finite element computer code specifically developed for buried structure analysis and design. CANDE models buried structure and soil within a combined two-dimensional slice called “mesh”. The underground structure may be loaded gravitationally under the dead weight of soil fill placed above it. The structure may be also subjected to an incremental loading applied at the top of the mesh, due to live loads or construction activities for example. Buried structure could be of any shape (circular, box, arch …), of any material (steel, aluminum, concrete, thermoplastic …), and of any size. An important advantage CANDE has over other finite element package is that CANDE has a set of built-in constitutive models for soils and gives a detailed output containing evaluation of the buried structure in terms of safety factor against all failure modes (ex. excessive deflection, wall crushing, and wall buckling).

The first version of CANDE was released in 1976, with its development sponsored by Federal Highway Administration (FHWA). The original package contained analysis and design execution modes. Pipe types contained corrugated aluminum, basic, reinforced concrete, plastic, and corrugated steel, and soil models contained linear elastic, overburden dependent, and nonlinear hyperbolic model by Hardin. There were three solution levels available in the original CANDE already. Level 1 allowed a direct access to the full-field elastic solutions established by Burns and Richard (1964). Levels 2 and 3 28

provided more sophisticated numerical analysis, including linear and nonlinear modeling features. Level 2 had some limitations on the shape of the structure and the number of soils specified but could generate the half-mesh automatically. At level 3, every aspect of the computer modeling, including the buried structure, surrounding soils, external loading, and boundary conditions could be defined flexibly by the users. Interface element types included in the original CANDE were bonded, frictionless, and frictional.

In 1987, an upgrading project on CANDE was sponsored by FHWA. The second version of CANDE, known as “CANDE-89”, was released in 1989. This upgrade brought many improvements to the software and made CANDE executable on personal computers. This generation of CANDE was very popular and it lasted for almost 20 years. In 2005, a new upgrading project was sponsored by AASHTO to make CANDE suitable to modern computing technology. The primary purpose of this upgrade was to make the third version compatible to the latest Windows Operating System. The third version of CANDE, known as “CANDE 2007”, was officially released in 2007. This generation of CANDE increased pre- and post-processing speed with modern computer technology. More culvert types, more material choices, large deformation theory, and new capabilities (including an ability to handle multiple structures placed side by side) were incorporated in it. Also, design criteria were updated in CANDE 2007 to embrace the AASHTO load resistance factor design (LRFD) specifications for buried structures.

One of the features added in this upgrade, which worth being mentioned is that convergence algorithms for the Duncan/Selig hyperbolic soil model have become much faster. This is helpful because in CANDE 2007, Duncan/Selig soil model did not 29

converge very well. The calculations always exceeded the iteration limit in each step, even though the iteration limit was set to be 100. With this latest update, the convergence problem was somewhat eliminated. Therefore, in the current thesis work CANDE 2007

(with 2011 update) was employed exclusively to perform all computer simulations of buried structure problems. In the current study, all the modeling was performed at level 3.

3.2 General Methodology for Single Chamber Structure

In each modeling of single chamber structure problems, a two-dimensional half- mesh was prepared to have the chamber structure being installed in soil and being subjected to the gravitational loading (coming from the soil fill placed above the chamber) as well as the external loading (positioned along the top boundary of the mesh).

CANDE 2007 analyzed stress-strain responses of the chamber and the surrounding soil mass under each increment of the loading. The single structure analysis had the following two main purposes:

1) Delineate fundamental differences in the structural performance between a circular pipe and a semi-circular chamber both installed and loaded under identical conditions; and

2) Compare structural performances among single chamber structures having different cross-sectional shapes such as semi-circular, rectangular, triangular, and trapezoidal.

Figure 3.1 shows a typical half-mesh used to examine mechanical behaviors of a buried single chamber. 30

Figure 3.1: Typical Half Mesh Used for Single Chamber

In this model, only right half of the chamber is modeled, since it is exactly symmetric along the vertical centerline. The mesh has an overall mesh height of 120 inches (3.05 m) and a soil cover of 72 inches (1.83 m) over the structure. The shape of the chamber is semi-circular with a radius of 24 inches (0.61 m). The foot of the chamber is 4 inches (102 mm) in width.

The first step in modeling this half-mesh was to create nodes in the Cartesian coordinate system by inputting x, y-coordinate values of each node. The mesh shown above has a total of 313 nodes. The second step was to connect these separate nodes to build elements. There are four types of elements available in CANDE 2007, which are rectangular, triangular, beam and interface elements. A series of two-node beam elements were used to erect the chamber structure. Rectangular and triangular elements were used to model the soils that exist below, next to, and above the chamber. Unit weights were specified for the soil elements to induce gravitational self-loading. 31

Several constitutive laws can govern stress-strain behavior of soils. In the current study, the Duncan/Selig hyperbolic model was utilized to describe nonlinear stress-strain behaviors of soils realistically. In the old version of CANDE, soil models only contained linear elastic, incremental elastic (elastic moduli are dependent upon current fill height) and variable modulus model using a modified version of the Hardin soil model. Duncan and others developed a formulation for finite element analysis of stresses in soils based on tangent Young’s modulus and bulk modulus (Duncan, 1980). Selig and his students furthered extended Duncan’s formulation by modifying the mathematical relationship of the tangent bulk modulus. The form and inputs in Selig’s formulation are very similar to those in Duncan’s model. The only difference is the mathematical relationship of the tangent bulk modulus. Below are the improved formulations for the tangent and bulk moduli, included in the so-called Duncan/Selig model (CANDE-89 Manual):

Young’s modulus Et:

Eq. 3.1

where Rf = failure ratio ; = internal friction angle; C = cohesion; Pa = atmospheric pressure (which is used only to non-dimensionalize the parameters K and n);

K, n = parameter (determined from Figure 3.2 using triaxial test data); σ1, σ3 = normal stresses.

Bulk modulus B:

Eq. 3.2 32

where Pa = atmospheric pressure; Kb and m are determined as shown in Figure 3.3

(using triaxial test data). The line in Figure 3.4 is the logarithmic form of Eq. 3.2.

Figure 3.2: Determination of K and n (CANDE-89 Manual, 1989)

Figure 3.3: Determination of Kb and m (CANDE-89 Manual, 1989)

Interface elements could be placed between the chamber wall surface and the adjacent soil to simulate the realistic frictional sliding between the two parts. If no interface elements are specified, the chamber wall will be fully bonded to the surrounding soil.

In the mesh shown in Figure 3.1, a total of 291 elements were created, with 20 of them being beam elements (for the chamber structure) and the rest made up of rectangular and triangular elements (for the soils). No interface elements were added to avoid any convergence problems. To simulate the actual field installation process, the construction sequence steps were specified for the mesh. The in situ soil (soil below the chamber) and the chamber structure itself were assigned in the first construction step. The rest of the soil layers were accumulated vertically upward through subsequent ten construction steps.

After all the nodes and elements were created, applicable boundary conditions were specified along each boundary of the mesh. In the example mesh shown in

Figure3.1, all the nodes along the bottom boundary were fixed. All the nodes along the vertical boundary on each side of the mesh were placed on vertical rollers to allow them to move only in the vertical direction. Also, along these side nodes no rotations were allowed to prevent premature formations of plastic hinges. External loading was simulated along the top boundary by placing a uniformly distributed surcharge loading.

The surcharging loading was increased in 10-psi (69-kPa) increments to a maximum intensity of 100 psi (690-kPa).

Table 3.1: Summary of Key Inputs for CANDE 2007 Simulations

Type of Plastic PVC Load Duration Short-term Young’s Modulus(psi) 160,000 Poisson’s Ratio 0.4 Analysis Mode Small Deformation Soil Model Type Duncan/Selig Density of soil (lb/ft3) 110 Soil Material Name SW 95 Soil Cover (in) 24

Once the basic mesh construction is taken care of by going through the above steps, a few more inputs are needed to define the problem. First, the material constituting the chamber structure needs to be characterized. This is typically done by selecting one of the raw materials listed in the CANDE library. In the example mesh, the chamber was considered to be made of PVC material, which assigned a Young’s modulus value of 160 ksi (1.10 GPa) and a Poisson’s ratio of 0.40. These inputs are shown in Table 3.1, which were applied to all models in this thesis. The chamber wall is often corrugated to provide added stiffness while being less bulky. Figure 3.4 illustrates the hypothetical chamber wall geometry design. Here, the wall’s sectional property was defined by the following parameters: the length of the wall profile period, the height of the wall profile, the web angle with the horizontal, the web thickness, the length of the corrugation valley, the thickness of the corrugation valley, the length of the corrugation valley, and the thickness of the crest. With these details entered, the program can compute the area and moment of inertia of the wall section per unit length. Table 3.2 below lists the inputs for chamber wall’s sectional properties, which were applied to all models in this thesis. 35

Figure 3.4: Design of Chamber Wall Section (CANDE Manual 2007)

Table 3.2: Sectional Properties of Chamber Wall

Length of Profile Period (in) 6.00 (152 mm) Total Height of Profile Section (in) 2.0 (51 mm) Web Angle with the Horizontal (degrees) 90 Web Thickness (in) 0.125 (3.00 mm) Web Edge Support Coefficient 4 Number of Horizontal Elements in Profile 2 Length of Valley (in) 2.0 (51 mm) Length of Crest (in) 4.0 (102 mm) Valley & Crest Thickness (in) 0.125 (3.0 mm) Valley & Crest Edge Support Coefficient 4

Next, each soil material in the mesh needs to be defined. In the example mesh shown in Figure 3.1, the chamber was embedded in a uniform soil material described by

SW95 under the Duncan/Selig hyperbolic model library. This material is a clean granular soil (compacted to 95% of the standard Proctor maximum dry unit weight) and has a typical unit weight of 110 pcf (17.3 kN/m3).

3.2 General Methodology for Multi-Chamber Structures

After completing the single chamber structure modeling, CANDE 2007’s ability to have multiple structures side by side was utilized to study the effect of chamber spacing on the structural performance of buried chamber structures. The semi-circular chamber type was selected for this second modeling phase. Figure 3.5 illustrates a typical half mesh employed in the study. Here, the interactions among three chambers are being modeled. The mesh generation process is essentially the same as that described previously for the single chamber analysis. The main difference here is the sheer number of nodes and elements due to the presence of additional chambers and the expanded mesh size. With more nodes and elements, it is easier to make mistakes while entering all the level-3 input data. The sample mesh shown in the figure contains 1,011 nodes, 989 elements, and 20 loading steps.

Figure 3.5: Typical Half Mesh Used for Multiple Chamber Analysis

3.4 Results of CANDE-2007 Simulations

Table 3.3: Interpretation of Structure Failure Mode

Demand Capacity

Thrust stress (psi) fu=ultimate strength

Global Buckling (psi) fu=buckling capacity

Combined Strain (in/in) εmax=bending + thrust εult=ultimate strain Allowable =5% Allowable Deflection (%) Δ =computed deflect% max (recommended)

The above design criteria are equally applicable to working stress or LRFD design methodologies. For the working stress approach, the demand and the capacity quantities are un-factored, and the design evaluation is given by safety factors defined as capacity divided by demand (CANDE Manual 2007). Detailed discussion is provided below.

Table 3.4: Recommended Plastic Properties for Short and Long-term Loading

Type of plastic Effective Young’s Modulus Ultimate strength Short-term Long-term Short-term Long-term (ksi) (ksi) (ksi) (ksi) HDPE 110.0 22.0 3.00 0.90 PVC 400.0 140.0 6.00 2.60 PP 135.0 27.0 3.10 1.00

1. Thrust stress: Thrust stress demand is computed by the dividing the maximum

thrust force in the culvert by the cross-sectional area. The ultimate strength for

thrust stress is dependent on the type plastic and the load duration. Nominal

values, taken from the ASSHTO LRFD specifications and elsewhere, are shown

in the table below. 38

2. Global Buckling: The thrust stress level that causes global buckling may be

conservatively approximated from the simplified AASHTO LRFD equations

12.7.2.4-1-2. A more accurate alternative is to utilize the new large deformation

formulation with buckling capacity prediction available in CANDE 2007.

3. Combined Strain: Combined strain means the maximum outer-fiber strain from

thrust and bending and the demand is the largest combined strain anywhere in the

culvert. The combined strain limit value (or capacity) as recommended by

AASHTO LRFD specifications is equal to 1.5 times the long-term strength

divided by the long-term modulus. Accordingly, HDPE=0.06 in/in, PVC=0.028

in/in, and PP=0.045 in/in.

4. Allowable Deflection: Computed deflection is the relative vertical movement

between the top and bottom of the culvert structure, and the percent deflection is

relative the vertical distance. The service load value for allowable deflection is

generally taken as 5% of the diameter for all plastic pipes; however, the deflection

limit is not directly specified in the AASHTO LRFD design specifications.

3.4.1 Single Circular Pipe

Prior to examining structural behaviors of buried chamber structures, a buried single 24-inch (61-cm) radius circular pipe problem was studied for the purpose of establishing baseline for evaluating the underground chamber structures. This exercise was also needed to verify the CANDE 2007 performance. Specifications contained in the input data file (such as the pipe material properties, pipe’s profile-wall design, type of 39

backfill material used, boundary conditions applied, construction steps simulated, and uniform surface loading , and the cover height) for this run were made basically identical to those embedded in the input data file used subsequently to analyze chamber structures.

Figure 3.6 shows the half-mesh used to study the structural behavior of the single circular pipe structure. Figures 3.7 through 3.12 and Tables 3.5 present the CANDE-2007 results.

Steps 11, 20 and 21 are presented in the plots of structural performance to show the development as loading increases. Step 11 is at the end of mesh construction and no load is applied. Step 20 is under the loading of 90 psi (621kPa), at which the structure failed.

Step 21 is under the loading of 100 psi (689 kPa). No interface elements were incorporated into the mesh, due to convergence problems. CANDE calculates the factor of safety against over-deflection using a vertical deflection limit of -5%. This is very conservative. In reality, the vertical deflection limit may be set at -20%. Thus, as long as the factor of safety for over-deflection is above 0.25, the deflection should not be a concern.

Figure 3.6: Half-Mesh Used for Single Circular Pipe 40

Figure 3.7: Mesh Plot of Vertical Soil Pressure Distribution around Circular Pipe

Figure 3.8: Node Numbering System Used for Circular Pipe

Figure 3.9: Plot of X-direction Deflection for the Pipe 41

Figure 3.10: Plot of Y-direction Deflection for the Pipe

Figure 3.11: Plot of Bending Moment in Circular Pipe Wall

Figure 3.12: Plot of Thrust Force in Circular Pipe Wall

Figure 3.13: Plot of Shear Force in Circular Pipe Wall

Table 3.5: Summary of Circular Pipe Responses at Structure Failed

Surface Pressure at Structural Failure 90 psi (Node 14; shoulder) Max. Vertical Displacement Experienced by Pipe (in) -2.07 (Node 1; crown) Max. Horizontal Displacement Experienced by Pipe (in) 0.103 (Node 21; spring-line) Max. Bending Moment in Pipe Wall (in-lb/in) 89.6 (Node 5; near crown) Max. Thrust Force in Pipe Wall (lb/in) -738 (Nodes 14; shoulder) Max. Shear Force in Pipe Wall (lb/in) 15.7 (Node 6; upper shoulder) Vertical Soil Pressure at Pipe Crown (psi) -22 Vertical Soil Pressure at Pipe Spring-line (psi) -164 Horizontal Soil Pressure at Pipe Spring-line (psi) -39.2 Factor of Safety Fs Against Over-Deflection 1.159 (> 0.25) Factor of Safety Fs Against Wall Crushing 0.959 Factor of Safety Fs Against Combined Strain 0.955 Factor of Safety Fs Against Wall Buckling (Global) 3.527 Surface Pressure at Soil Failure 20 psi (Elements 301-303; against shoulder) Shear Failure

Based on the CANDE 2007 outputs, the following comments can be made regarding the structural performance/behavior of the single circular pipe:

The pipe responses were very minor to the loads/stresses induced during the

initial installation steps. 43

Under the uniform surface loading, the soil located against the pipe’s spring-line

was most stressed vertically.

The pipe deformed into a slight horizontal ellipse, with vertical deflection of -

4.3% and horizontal deflection of +0.4% at 90psi.

The pipe was able to promote a notable degree of positive arching. This is

evidenced by the fact that the crown soil pressure was 22 psi (152 kPa) under the

maximum surface loading of 90 psi (621 kPa).

The shear failure of the soil against the pipe’s shoulder region remained localized

and did not spread into other soil regions under increasing surface loading.

Ultimately the pipe failed in the shoulder area under the surface loading of 90 psi

(621 kPa). This means that the pipe-soil system was able to carry a relatively high

level of surface loading. The failure was a combination of wall crushing and over-

straining. Wall buckling was not a factor in the pipe’s performance limitation.

In terms of the bending moment, thrust force, and shear force development, the

upper shoulder region of the pipe’s cross-section appears to be more critical than

any other regions.

3.4.2 Single Semi-Circular Chamber

Next, a single 24-inch (61-cm) radius semi-circular chamber case was studied using CANDE 2007. Specifications contained in the input data file (such as the chamber material properties, chamber’s profile-wall design, type of backfill material used, 44

boundary conditions applied, construction steps simulated, and uniform surface loading , and the cover height) for this run were made basically identical to those used previously in the input data file for the single circular pipe structure. For an added feature, structural performance of the chamber was examined under two surface-loading types – widely distributed loading and narrowly distributed central loading. Figure 3.13 shows the half- mesh used to study the structural behavior of the single semi-circular chamber structure.

Figure 3.14: Half-Mesh Used for Single Semi-Circular Chamber

3.4.2.1 Widely Distributed Loading

Figures 3.14 through 3.19 and Table 3.6 through Table 3.7 present the CANDE-

2007 results under the wide distributed surface loading. Steps 11, 23 and 26 are presented in the plots of structural performance to show the development as loading increases. Step

11 is at the end of mesh construction and no load is applied. Step 23 is under the loading of 70 psi (483 kPa), at which the structure failed. Step 26 is under the loading of 100 psi

(689 kPa). No interface elements were incorporated into the mesh, due to convergence problems. 45

Figure 3.15: Mesh Plot of Vertical Soil Pressure Distribution around Semi-Circular Chamber

Figure 3.16: Node Numbering System Used for Semi-Circular Chamber

Figure 3.17: Plot of X-direction Deflection for Semicircular Chamber 46

Figure 3.18: Plot of Y-direction Deflection for Semicircular Chamber

Figure 3.19: Plot of Bending Moment in Semi-Circular Chamber Wall

Figure 3.20: Plot of Thrust Force in Semi-Circular Chamber Wall

Figure 3.21: Plot of Shear Force in Semi-Circular Chamber Wall

Table 3.6: Summary of Chamber and Pipe’s Responses at 70 psi Surface-Loading

Chamber Pipe Max. Vertical Displacement (in) -1.58 (Node 1; crown) -1.84 (Node 1; crown) Max. Horizontal Displacement (in) -0.068 (Node 7; 0.129 (Node 21; spring- shoulder region) line) Max. Bending Moment (in-lb/in) 293 (Node 20; leg/feet 81.0 (Node 5; near junction) crown) Max. Thrust Force in the Wall (lb/in) -623 (Node 17; leg) -640 (Nodes 14; shoulder) Max. Shear Force in Chamber Wall 135 (Node 21; 13.5 (Node 6; upper (lb/in) edge of feet) shoulder) Vertical Soil Pressure at Crown (psi) -21.2 -18 Vertical Soil Pressure at Feet/Springline -168 -134 (psi) Horizontal Soil Pressure at Feet (psi) -42.0 -33.3 Factor of Safety Against Over- 0.759 1.305 Deflection Factor of Safety Against Combined 0.966 1.132 Strain Factor of Safety Against Wall Crushing 1.231 1.180 Factor of Safety Against Wall Buckling 3.460 3.530 (Global)

Table 3.7: Surface Loading Level at Structure and Soil Failure

Chamber Pipe Surface Loading Level at 70 (Node 19; lower leg) 90 (Node 14; shoulder) Structure Failure (psi) Surface Loading Level at Soil 5 (Element 94; near the 20 (Elements 301-303; against Failure (psi) feet); Shear Failure shoulder); Shear Failure

Based on the CANDE 2007 outputs, the following comments can be made regarding the structural performance/behavior of the single semi-circular chamber structure:

The chamber responses were insignificant to the loads/stresses induced during the

initial installation steps.

The chamber was able to promote a notable degree of positive arching. This is

evidenced by the fact that the crown soil pressure was 21 psi (145 kPa) under the

maximum surface loading of 70 psi (483 kPa).

Under the uniform surface loading, the soil underneath the chamber feet was most

stressed vertically. Comparing with pipe, the soil stress was distributed around the

spring-line. This means that pipe performs better to avoid stress concentration.

The chamber deformed into a slight horizontal half-ellipse, with vertical

deflection of -6.6% and horizontal deflection of -0.28% at 70 psi.

The amount of vertical displacement of the crown was very comparable between

the chamber and the pipe.

The side wall of the chamber moved inward, while the side wall of the circular

pipe moved outward when structure failed. 49

The maximum horizontal displacement occurred in the lower leg region as well as in the upper shoulder region for the chamber, while that occurred at the spring- line for the pipe.

The degree of positive arching was very similar between the two shapes, with the maximum crown soil pressure registered at 21 psi (145 kPa) for the chamber and

18 psi (124kPa) for the pipe.

The premature shear failure of the soil initiating near the chamber’s leg region remained localized and did not spread into other soil regions under increasing surface loading.

Ultimately the chamber failed in the lower leg region under the surface loading of

70 psi (483 kPa) (20 psi or 138 kPa less than the maximum surface loading intensity supported by the pipe-soil system). This means that the chamber-soil system was able to carry a relatively high level of surface loading. The failure due to over-straining. Wall buckling was not a factor in the chamber’s performance limitation.

In terms of the bending moment, thrust force, and shear force development, they were generally more pronounced in the chamber wall than in the pipe wall. And, the leg region appears to be more critical than any other regions within the chamber’s cross-section.

In terms of shear force development, the feet section of the chamber’s cross- section appears to be most critical. 50

Overall, the structural performance of the semi-circular chamber was slightly inferior to that of the circular pipe. This is probably due to the fact that the chamber structure cannot deflect outward in the horizontal direction (due to its feet somewhat anchored under vertical soil pressure) to mobilize the backfill soil’s passive pressure support as efficiently as the pipe structure is capable of.

3.4.2.2 Narrow Central loading

Figures 3.20 through 3.24 and Table 3.8 through Table 3.9 present the CANDE-

2007 results under the narrow central surface loading. Steps 11, 17 and 21 are presented in the plots of structural performance to show the development as loading increases. Step

11 is at the end of mesh construction and no load is applied. Step 17 is under the loading of 60 psi, at which the structure failed. Step 21 is under the loading of 100 psi. No interface elements were incorporated into the mesh, due to convergence problems. Figure

3.20 presents not only the vertical stress distributions but also the chamber’s deformed shape under the maximum surface loading.

Figure 3.22: Mesh Plot of Vertical Soil Pressure Distribution around Semi-Circular Chamber 51

Figure 3.23: Plots of Semi-Circular Chamber Deflections

Figure 3.24: Plot of Bending Moment in Semi-Circular Chamber Wall

Figure 3.25: Plot of Thrust Force in Semi-Circular Chamber Wall

Figure 3.26: Plot of Shear Force in Semi-Circular Chamber Wall

Table 3.8: Summary of Chamber Responses under Two Types of 60 psi Surface-Loading

Central Load Wide Distributed Load Max. Vertical Displacement (in) -2.14 (Node 1; crown) -1.46 (Node 1; crown) Max. Horizontal Displacement (in) 0.377 (Node 12; -0.058 (Node 6; shoulder) shoulder region) Max. Bending Moment (in-lb/in) 429 (Node 2; near 279 (Node 20; leg/feet crown) junction) Max. Thrust Force (lb/in) -500 (Node 8; upper -559 (Node 17; leg) shoulder) Max. Shear Force (lb/in) 140 (Node 21; edge of 131 (Node 21; edge of feet) feet) Vertical Soil Pressure at Chamber -31.8 -17.6 Crown (psi) Vertical Soil Pressure at Chamber Feet -41.6 -146 (psi) Horizontal Soil Pressure at Chamber -16.2 -35 Feet (psi) Factor of Safety Against Over- 0.561 (> 0.25) 0.822 (> 0.25) Deflection Factor of Safety Against Combined 0.843 1.082 Strain Factor of Safety Against Wall Crushing 1.808 1.438 Factor of Safety Against Wall Buckling 2.147 3.592 (Global)

Table 3.9: Surface Loading Level at Structure and Soil Failure

Central Load Wide Distributed Load Surface Loading Level at 60 psi (Node 2; crown); 70 psi (Node 19; lower leg); Structure Failure (psi) Surface Loading Level at Soil 10 psi (Element 94; near feet); 5 psi (Element 94; near feet); Failure (psi) Shear failure Shear failure

Based on the CANDE 2007 outputs, the following comments can be made regarding from the structural performance/behavior of the single semi-circular chamber structure:

Under the narrow distributing loading, the cover soil layer became over stressed

(see Figure 3.20). 54

Under the narrow loading, the chamber deformed more (-8.9%) at 60 psi vertically compared to the previous case with the wide uniform surface loading (-

6.1%) at 60 psi. This maximum vertical deflection was enough to induce a slight reversed curvature in the crown region.

Under the narrow loading, the chamber’s side moved outward by as much as

1.6% at 60 psi. Under the widely distributed loading, the chamber’s side moved inward by 0.24% at 60 psi.

The maximum horizontal displacement (outward) occurred in the shoulder region of the chamber under the narrow surface loading. The maximum horizontal movement (inward) occurred in the lower leg and shoulder regions of the chamber under the wide uniform surface loading.

The degree of positive arching was much less under the narrowly focused loading, with the maximum crown soil pressure registered at 32 psi (221 kPa) under the narrow surface loading of 60 psi (414 kPa) and 18 psi (124 kPa) under the wide surface loading of 60 psi (414 kPa).

The premature shear failure of the soil occurred near the chamber’s leg region regardless of the type of surface loading being applied. The failure in that region stayed localized throughout the loading steps. On the other hand, soil failure going on within the cover soil above the chamber crown got progressively worst.

Eventually, the narrow surface loading caused the chamber’s crown region to fail under the surface loading intensity of 60 psi (414 kPa). This was triggered by the bearing capacity failure of the soil cover over the chamber crown. The previous 55

wide surface loading caused the chamber’s leg region to fail under the surface

loading intensity of 70 psi (483 kPa). The failure was due to over-straining in both

cases. Wall buckling was not a factor in the chamber’s performance limitation.

In terms of the bending moment, thrust force, and shear force development, they

became more magnified under the narrow surface loading. The crown region

appears to be critical for the bending action, the upper shoulder region for the

thrust action, and the edge of feet for the shearing action.

During construction stages prior to paving, cautions are needed to make sure that

this type of loading is not going to be applied to the buried chamber structure.

Overall, the narrowly distributed central loading proved to be much harsher than the widely distributed loading to the chamber-soil composite. This is because under the widely distributed loading, the surrounding soil is consolidated and became denser and stiffer, so that it provides more passive pressure.

3.4.3 Different Cross-Sectional Shape Single Chambers

In order to identify the best possible cross-sectional geometry for the chamber structure, various sectional shapes (other than the semi-circular shape) were also considered. Table 3.10 lists five options, which reflects to some degree a range of commercial products that are currently available in the market. Four of the shapes

(triangular, elliptical, rectangular, and trapezoidal) listed here are new. The vertical ellipse shape was created by following an equation for a vertical ellipse. Although these cross-sections are each unique, they did share the same characteristics when being 56

analyzed by CANDE 2007 – overall mesh width of 120 inches (3.05 m), overall mesh depth of 96 inches (2.44 m), soil cover thickness of 24 inches (0.61 m), the corrugated profile-wall design (specified in Figure 3.4 and Table 3.2), the raw material (PVC), the installation in a SW-95 backfill material, and the wide uniformly distributed loading.

Table 3.10 compares the half mesh prepared for each chamber geometry. Figure 3.25 to

Figure 3.28 display vertical soil pressure responses among the four new shapes and each chamber’s deformed shape under the maximum surface loading (100 psi). Figure 3.29 shows how the nodes on each chamber geometry were numbered. Table 3.12 and Table

3.13 summarize and compare the structural performances of the four chambers.

Additional graphical plots produced by CANDE 2007 can be found in the appendix section.

Table 3.10: Geometric Parameters of Different Cross-Sectional Shapes

Shape Rise (in) Top Span Bottom Span Side Slope Cross- (in) (in) sectional Area (in2) Semi-Circular 24 --- 48 Curved 904 Triangular 24 0 48 1H:1V 576 Elliptical 36 --- 48 Curved 1356 Rectangular 24 48 48 Vertical 1,152 Trapezoidal 24 28 48 1H: 2.4V 912

Table 3.11: Geometric Parameters of Different Shapes

No. No. Max. No. No. No. Nodes Elements Boundary Conditions Load Steps Beam Elements Semicircular 313 291 500 26 20 Triangular 329 303 500 22 9 Elliptical 313 291 500 26 20 Rectangular 267 241 500 22 13 Trapezoidal 310 284 800 22 11 57

Figure 3.27: Mesh Plot of Vertical Soil Pressure Distribution for Elliptical Chamber

Figure 3.28: Mesh Plot of Vertical Soil Pressure Distribution for Trapezoidal Chamber

Figure 3.29: Mesh Plot of Vertical Soil Pressure Distribution for Triangular Chamber 58

Rectangular

Figure 3.30: Mesh Plot of Vertical Soil Pressure Distribution for Rectangular Chamber

Nodes on Elliptical Chamber Nodes on Trapezoidal Chamber

Nodes on Rectangular Chamber Nodes on Triangular Chamber

Figure 3.31: Nodes Placed on Each Different Chamber Shape 59

Table 3.12: Summary of Chamber Responses at 20 psi Surface-Loading

Elliptical Trapezoidal Triangular Rectangular Max. Vertical -0.758 -0.91 -0.865 -2.18 Displacement (in) (Node 1; (Node 1; top (Node 3; near (Node 1; top slab crown) center) apex) center) Max. Horizontal -0.038 -0.102 -0.123 -0.105 Displacement (in) (Node 18; leg) (Node 8; lower (Node 5; (Node 11; middle of side) middle of side) side) Max. Bending Moment in 132.1 -210 65 -554 Chamber Wall (in-lb/in) (Node 20; (Node 5; top (Node 7; side) (Node 7; top corner) bottom of leg) corner) Max. Thrust Force in -274.3 -253 -245 -284 Chamber Wall (lb/in) (Node 14;side) (Node 10; (Node 8; (Node 9; side) lower side) bottom of side) Max. Shear Force in 59.9 41.9 -24 83 Chamber Wall (lb/in) (Node 21; (Node 4; edge (Node 1; apex) (Node 6; close to top edge of feet) of top) slab’s edge) Vertical Soil Pressure at -12.64 1.10 -24 3.15 Crown (psi) Vertical Soil Pressure at -61 -57 -55 -53.7 Chamber Foot (psi) Horizontal Soil Pressure at -17 -19 -39 -11.0 Chamber Foot (psi) Factor of Safety Over- 2.381 1.319 1.389 0.550 Deflection Factor of Safety Against 2.549 1.823 2.914 0.741 Combined Strain Factor of Safety Against 3.720 3.881 4.051 3.504 Wall Crushing Factor of Safety Against 5.592 5.458 5.779 4.662 Wall Buckling (Global)

Table 3.13: Surface Loading Level at Structure and Soil Failure

Elliptical Trapezoidal Triangular Rectangular Surface Loading 60 psi (Node 19; 50 psi (Node 5; 60 psi (Node 7; 20 psi (Node 7; top Level at Structure leg) top corner) lower side) corner) Failure (psi) Surface Loading 10 psi 10 psi (Elems 87; 10 psi (Elems 70, 10 psi (Elems 156, 157, Level at Soil (Elems 60, 77, under feet); Shear under feet); Shear 170-173, …; above Failure (psi) 94; under feet); failure failure chamber); Shear failure Shear failure

Based on the CANDE 2007 outputs, the following comments can be made regarding the structural performance/behavior of the single semi-circular chamber structure:

According to Figure 3.28, Table 3.12 and Table 3.13, the rectangular chamber

deformed excessively and ended up with the most spectacular failure. The top

slab acted as a flexible beam and deflected significantly under the external

loading. As the top slab deformed downward, the side experienced slight inward

movements. Relatively high vertical soil pressures were detected near the top

corner and under the chamber feet. In terms of the internal moment, thrust, and

shear responses, the upper corner where the top slab and the vertical side meets is

the most critical region. This chamber started failing due to over-straining that is

taking place at the upper corner, when the intensity of the surface loading was

only 20 psi (138 kPa). Wall buckling was not a factor in the chamber’s

performance limitation.

According to Figure 3.27, Table 3.12 and Table 3.13, the triangular chamber also

ended up experiencing a good amount of deformations. As the apex of the

chamber moved downward, the middle of the slanted side deflected inward like a

flexible beam. This structure did not do well in terms of promoting a positive soil

arching, as its pointed tip acted as a vertical stress magnet. Under the maximum

surface loading, vertical soil pressure right above the apex shot up to 300 psi (2.07

MPa). Relatively high vertical soil pressure was also detected under the chamber

feet. Bending and shearing actions were pronounced near the tip, while the thrust 61

action was elevated in the bottom of the side. This chamber started failing due to over-straining that is taking place in the lower side, when the intensity of the surface loading was 60 psi (414 kPa). Wall buckling was not a factor in the chamber’s performance limitation.

The trapezoidal shape was a hybrid of the rectangular and triangle shapes.

According to Figure 3.26, Table 3.12 and Table 3.13, as expected the structural performance of this geometry chamber reflected those of both triangular and rectangular chambers. This chamber’s maximum vertical displacement was somewhat less than what the other two shapes experienced (before failure). The top slab acted as a flexible beam but did not deflected significantly due to its shorter span. As the top moved downward, the side experienced slight inward movements. This structure did not promote a positive soil arching very well, as its top corner region acted as a vertical stress magnet. Under the maximum surface loading, vertical soil pressure went up to 120 psi (827 kPa) next to the top corner.

Relatively high vertical soil pressure also existed under the chamber feet. Bending action was pronounced at the top corner (where the top slab and the side meet).

The thrust action was elevated in the bottom of the side. This chamber started failing due to over-straining that is taking place in the upper corner, when the intensity of the surface loading was 50 psi (345 kPa). Wall buckling was not a factor in the chamber’s performance limitation.

Finally, according to Figure 3.25, Table 3.12 and Table 3.13, the elliptical shape chamber performed very well compared to any other chamber shapes (although 62

this chamber started failing under the surface loading of 60 psi (414 kPa). The

maximum vertical deflection experienced by this chamber was a lot less than

those experienced by other three geometry chambers. As the crown moved

downward, the arched side experienced slight inward movements. A side-by-side

comparison between Tables 3.6 and 3.12 shows that this vertical ellipse shape

chamber behaved very similar to the semi-circular chamber under the wide

distributed surface loading. This chamber was able to promote a mild degree of

positive arching. This is evidenced by the fact that the crown soil pressure was 29

psi (200 kPa) under the maximum surface loading of 60 psi (414 kPa). The leg

region appears to be more critical than any other regions within the chamber’s

cross-section. Wall buckling was not a factor in the chamber’s performance

limitation. The fact that the elliptical chamber began failing under the surface

pressure of 60 psi or 414 kPa (compared to 70 psi or 483 kPa for the semi-circular

chamber) indicates that by making the chamber taller the leg region of the

chamber becomes more vulnerable to bending/thrust/shear actions.

Generally, the semicircular and elliptical shape turns out to be the best shape comparing with other shapes. Basically they are arch-shaped. They performed better in avoiding soil stress concentration and can sustain larger loading levels. Also, arch-shape is the typical shape in the market.

3.4.4 Multiple Semi-Circular Chambers

Now that we have gained insights into many issues related to a buried single chamber structure, we can shift our attention to the multiple chamber installation problems. For simplicity, a case where three semi-circular chamber structures are installed side by side will be analyzed by CANDE 2007. The semi-circular shape is selected for the chamber, as this cross-section proved to be the most effective. According to Section 2.4, the industry guideline states that minimum spacing between adjacent rows is 6 inches (152 mm). In this final segment of Chapter 3, effects of the chamber spacing are examined by setting the spacing (from the edge of feet of one chamber to the edge of feet of another chamber) at 1, 6, and 12 inches (25, 152, and 305 mm). The half mesh shown in Figure 3.30 was utilized in this study. No interface elements were incorporated into the mesh, due to convergence problems. On the following pages, CANDE 2007 simulation results are provided in the order of increasing chamber spacing.

3.4.4.1 Chamber Spacing of 1 inch (25 mm)

Figure 3.30 below shows the half mesh used in the computer analysis. The chamber spacing is set at 1 inch (25 mm). Figure 3.31 displays the vertical soil pressure responses as well as the deformations experienced by the multi-chamber/soil composite system. Figure 3.32 through 3.35 present deflections, bending moment, thrust force, and shear force responses for the two chambers addressed in the mesh. Steps 10, 15 and 20 are presented in the plots of structural performance of Group 1 to show the development as loading increases. Step 10 is at the end of mesh construction and no load is applied.

Step 15 is under the loading of 50 psi, at which Group 1failed. Step 20 is under the 64

loading of 100 psi. Steps 10, 14 and 20 are presented in the plots of structural performance of Group 2. Step 14 is under the loading of 40 psi, at which the Group 2 failed. No interface elements were incorporated into the mesh, due to convergence problems.

Figure 3.32: Half-Mesh Used for Multiple Semi-Circular Chamber

Figure 3.33: Mesh Plot of Vertical Soil Pressure Distribution around Circular Chamber

Figure 3.34: Plots of X-direction Deflection in Chamber Group 1

Figure 3.35: Plots of Y-direction Deflection in Chamber Group 1

Figure 3.36: Plots of X-direction Deflection in Chamber Group 2 66

Figure 3.37: Plots of Y-direction Deflection in Chamber Group 2

Figure 3.38: Plot of Bending Moment in Semi-Circular Chamber Wall of Group 1&2 67

Figure 3.39: Plots of Thrust Force in Semi-Circular Chamber Wall of Group 1&2

Figure 3.40: Plot of Shear Force in Chamber Wall of Group 1 68

Figure 3.41: Plot of Shear Force in Chamber Wall of Group 2

3.4.4.2 Chamber Spacing of 6 inches (152 mm)

Figure 3.37 shows the half mesh used in the computer analysis. The chamber spacing is set at the industry minimum standard of 6 inches (152 mm). Figure 3.38 displays the vertical soil pressure responses as well as the deformations experienced by the multi-chamber/soil composite system. Figure 3.39 through 3.43 present the bending moment, thrust force, and shear force responses for the two chambers addressed in the mesh. Steps 10, 15 and 20 are presented in the plots of structural performance of both

Group 1&2 to show the development as loading increases. Step 10 is at the end of mesh construction and no load is applied. Step 15 is under the loading of 50 psi, at which both

Group 1&2 failed. Step 20 is under the loading of 100 psi. No interface elements were incorporated into the mesh, due to convergence problems.

Figure 3.42: Half-Mesh Used for Multiple Semi-Circular Chambers

Figure 3.43: Mesh Plot of Vertical Soil Pressure Distribution around Circular Chambers

Figure 3.44: Plot of X-direction Deflection in Chamber Group 1 70

Figure 3.45: Plot of Y-direction Deflection in Chamber Group 1

Figure 3.46: Plot of X-direction Deflection in Chamber Group 2

Figure 3.47: Plot of Y-direction Deflection in Chamber Group 2

Figure 3.48: Plot of Bending Moment in Semi-Circular Chamber Wall

Figure 3.49: Plot of Thrust Force in Chamber Wall of Group 1 72

Figure 3.50: Plot of Thrust Force in Chamber Wall of Group 2

Figure 3.51: Plot of Shear Force in Semi-Circular Chamber Wall

3.4.4.3 Chamber Spacing of 12 inches (305 mm)

Figure 3.44 below shows the half mesh used in the computer analysis. The chamber spacing is set at 12 inches (305 mm). Figure 3.45 displays the vertical soil pressure responses as well as the deformations experienced by the multi-chamber/soil composite system. Figure 3.46 through 3.50 present deflections, bending moment, thrust force, and shear force responses for the two chambers addressed in the mesh. Steps 10, 17 and 20 are presented in the plots of structural performance of both Group 1&2 to show the development as loading increases. Step 10 is at the end of mesh construction and no load is applied. Step 17 is under the loading of 70 psi, at which both Group 1&2 failed.

Step 20 is under the loading of 100 psi. No interface elements were incorporated into the mesh, due to convergence problems.

Figure 3.52: Half-Mesh Used for Multiple Semi-Circular Chambers

Figure 3.53: Mesh Plot of Vertical Soil Pressure Distribution around Circular Pipe

Figure 3.54: Plots of Deflections in Semi-circular Chamber Group 1 75

Figure 3.55: Plots of Deflections in Semi-circular Chamber Group 2

Figure 3.56: Plot of Bending Moment in Chamber Wall of Group 1 76

Figure 3.57: Plot of Bending Moment in Chamber Wall of Group 2

Figure 3.58: Plot of Thrust Force in Semi-Circular Chamber Wall . 77

Figure 3.59: Plot of Shear Force in Semi-Circular Chamber Wall

Figure 3.51 illustrates the node numbering system that was applied to the two chambers. Table 3.14 and Table 3.15 summarize and compare the structural performances of the four chambers. 78

Group 1

Group 2

Figure 3.60: Node Numbering System Applied to Multiple Chambers

Table 3.14: Summary of Multi-Chamber Responses at 40 psi Surface-Loading

1-in Spacing 6-in Spacing 12-in Spacing G1 G2 G1 G2 G1 G2 Max. Vertical -2.20 -2.10 -1.60 -1.40 -1.16 -1.19 Displacement (in) (Node 1; (Node 36; (Node 1; (Node 39; (Node 1; (Node 41; crown) left crown) upper left crown) crown) shoulder) shoulder) Max. Horizontal 0.130 0.314 -0.069 0.144 -0.064 0.079 Displacement (in) (Node (Node 31; (Node 8; (Node 25; (Node (Node 47; 21; feet) left side wall) left lower 18; lower right shoulder) shoulder) leg) shoulder) Max. Bending 109.2 480.5 162.2 305.9 136.7 277.9 Moment in Chamber (Node (Node 61; (Node (Node 61; (Node (Node 61; Wall (in-lb/in) 20; lower lower right 20; leg) lower right 20; leg) lower right leg) leg) leg) leg) Max. Thrust Force in -708 -746.7 -597.2 -557.2 -454.0 -460.3 Chamber Wall (lb/in) (Node (Node 26; (Node (Node 26; (Node (Node 26; 17; leg) left upper 17; upper left upper 17; upper left upper leg) leg) leg) leg) leg) Max. Shear Force in 45.5 217.1 68.6 139.3 64.2 127.6 Chamber Wall (lb/in) (Node (Node 62; (Node (Node 62; (Node (Node 62; 21; feet) feet) 21; feet) feet) 21; feet) feet) Vertical Soil -16.55 -19.74 -15.96 -15.15 -14.62 -15.53 Pressure at Chamber Crown (psi) Vertical Soil -245.5 L-299.9 -201.1 L-190.8 -146.75 L-136.7 Pressure at Chamber R-98.4 R-82.6 R-74.5 Feet (psi) Horizontal Soil -73.10 L-60.58 -40.96 L-38.64 -30.90 L-29.34 Pressure at Chamber R-24.91 R-20.14 R-16.0 Feet (psi) Factor of Safety 0.545 0.571 0.75 0.858 1.034 1.008 Against (> 0.25) (> 0.25) (> 0.25) (> 0.25) (> 0.25) (> 0.25) Over Deflection Factor of Safety 1.007 0.983 1.118 1.218 1.601 1.443 Against Combined Strain Factor of Safety 1.002 1.231 1.289 1.426 1.912 1.881 Against Wall Crushing Factor of Safety 2.246 2.687 2.718 2.945 3.753 3.656 Against Wall Buckling (Global) [Note] G1 = Chamber in the center; and G2 = Chamber on the outside.

Table 3.15: Surface Loading Level at Structure and Soil Failure

1-in Spacing 6-in Spacing 12-in Spacing G1 G2 G1 G2 G1 G2 Surface loading 50 psi 40 psi (Node 61; 50 psi 50 psi 70 psi 70 psi level at (Node 18; right feet) (Node 19; (Node 24; (Node (Node structural leg) leg) left leg) 19; leg) 60; right failure leg) Surface loading 10 psi (in between two chambers 10 psi (in between two 10 psi (in between level at soil and under the feet) chambers and under the two chambers and failure feet) under the feet)

There are a number of interesting observations that can be made by examining these plots and the summary tables.

The two chambers behaved differently in terms of their vertical deflection

behaviors. The chamber in the center deflected more vertically than the chamber

on the outside. This trend becomes less obvious as the chamber spacing increased.

At the industry minimum standard of 6-inch (152-mm) spacing, the center

chamber deflected 15% more vertically.

The horizontal deflection behavior of the center chamber varied significantly

depending on how the chamber spacing was. At the spacing of only 1 inch, the

chamber deflected outward. However, at the larger spacing the central chamber

deflected inward in the horizontal direction.

The right side of the outer chamber deflected outward less as the chamber spacing

widened.

The two chambers behaved differently in terms of their horizontal deflection

behavior. The chamber in the center deflected little horizontally. 81

The two chambers behaved differently in terms of the vertical soil pressure they

registered at the crown. The crown soil pressure remained relatively unchanged

for the center chamber regardless of how large the chamber spacing was. The

vertical soil pressure appearing over the crown of the outer chamber decreased

with the increasing chamber spacing. At the 12-inch (305-mm) spacing, the crown

pressure values were nearly the same between the two chambers.

The internal bending moment/thrust force/shear force responses were highly

unbalanced between the two chambers when the chamber spacing was narrow.

However, the imbalance became less remarkable as the chamber spacing widened.

As the chamber spacing became larger, the multi-chamber system was able to

support a higher level of surface loading. At the chamber spacing of 1 inch (25

mm), the right foot of the outer chamber failed under the surface loading of 50 psi

(345 kPa). At the chamber spacing of 12 inches (305 mm), it took 70 psi (483

kPa) of the surface loading to damage the chamber leg/feet.

Wall buckling was never a performance limiting factor regardless of how narrow

the chamber spacing became.

At the chamber spacing of 12 inches (305 mm), the structural performance of

each of the two chambers became fairly similar to that of the single chamber

structure (summarized previously in Table 3.6).

Overall, the larger the spacing is, the better the chamber-soil system performed.

This is because when the soil columns between two chambers get wider, it can provide 82

more passive pressure. The industry guideline states that minimum spacing between adjacent chamber rows is 6 inches.

CHAPTER 4 FIELD LOAD TESTING

4.1 Introduction

There has been a lack of published data on the structural performance of underground stormwater storage chambers. This may be due to the facts that many civil engineers are still not familiar with these chamber products and field load test data are often kept by each chamber manufacturer as proprietary information. In order to assess structural capabilities of stormwater chamber structures, a small research team at Ohio

University conducted a series of field load tests during the summer of 2007 (Masada,

2011). More specific aims of their field load test program were as follows:

Observe first hand if the chambers installed under a shallow soil cover can

support heavy live loads;

Use modern sensors to record the vertical pressure existing at the crown of the

buried chamber structures and changes in the chamber’s cross-sectional

shapes while applying the heavy live loads; and

Identify similarities and dissimilarities in behaviors between buried arch-

shaped chambers and buried circular pipe structures.

Observe, if possible, the maximum load carrying capacity and dominant

failure mode of shallowly installed chambers. 84

The aim of this chapter is to provide all essential details of the Ohio University team’s field testing program and try to verify the computer simulation results.

4.2 Chamber Product

The chamber product evaluated during the field test project was a light-weight, elliptical arch-shaped, open-bottom, storage device available in the current market. A total of twenty-four (24) sections of the chamber product were delivered to the field test site. The chamber specimens were all supplied by a company based in Michigan and were made from soy vinyl ester. This “green” material was created by adding soy to a vinyl ester resin. Automotive and agricultural product manufacturers have been utilizing this material for a while. The main advantages this material has over more traditional thermosetting materials include sustainability, reduction of petroleum dependence, light weight, relatively high modulus/strength, and lower cost. Basic properties of this raw material were listed by Trition Storm-water Solutions (2010) as:

- Material modulus (min.) = 1,600 ksi (11.0 GPa)

- Material tensile strength @ Yield = 23.0 ksi (158.6 MPa)

- Material shear strength = 11.5 ksi (79.3 MPa)

Dimensional characteristics of the chamber product were as follows:

- Overall length = 35.0 inches (0.89 m)

- Rise (or height) = 36.0 inches (0.91 m), measured inside

- Span (or width at base) = 49.0 inches (1.24 m), measured inside

As shown in Figure 4.1, each chamber section was reinforced by three wide corrugation ribs that can be described as – 4.0 inches (102 mm) width x 2.0 inches (51 85

mm) depth. Each chamber foot located at the bottom was 5.0 inches (127 mm) wide.

Each section also contained intricate concentric circular patterns both at the top and sides to accept a riser pipe and lateral feeders.

Figure 4.1: General Appearance of Chamber Product Tested

4.3 Installation Procedures

An area having a width of 24 ft (7.3 m) and a length of 30 ft (9.1 m) was secured and excavated to a uniform depth of 5.0 ft (1.5 m), at a hilltop area located in Albany,

Ohio. The sides of the excavated area consisted of a combination of well-consolidated glacial till and weathered shale materials. The weathered sedimentary rock was encountered from the depth of 2.0 ft (0.6 m) below the ground surface. The bottom of the test area was all in the weathered rock. No perched or groundwater was encountered during digging. A non-woven geotextile sheet, that meets the AASHTO M-288 geotextile specifications, was directly draped over the bottom and sides of the excavated 86

area. A 6-inch (152-mm) thick bedding layer was formed over the entire bottom surface, by spreading AASHTO #4 crushed rock material. Three (3) parallel chamber structures

(identified as Chambers A through C), were erected side by side, on top of the bedding layer. Each structure had eight (8) sections of the chamber product being interlocked together at the ends. Also, the fourth dummy chamber structure or Chamber D was set up next to Chamber C. This was necessary for having symmetrical chamber installation arrangements in the field. The spacing between any two adjacent chamber structures was

7.5 inches (190-mm) from the edge of one foot to the edge of another foot. The distance between the wall of the excavated area and any nearest chamber was at least 12 inches

(305 mm). Additional AASHTO #4 crushed rock material was gravity-fed from a front- end loader bucket positioned over each chamber structure. This approach made sure that the self-compacting backfill material rolled off to both sides of each chamber structure, filling the spaces between chambers and against the wall of the excavated area.

Once each chamber received an initial cover of 6 inches (152 mm), the geotextile sheets were folded over from both sides of the excavated area to encapsulate the buried chamber structures. The two edges of the geotextile sheet met in the middle of the test area, with an overlap that was more than 6 inches (152-mm) in width. After completing the initial installation process, two 6-inch (152-mm) thick layers of AASHTO #8 crushed rock material were placed over the geotextile sheet, so that the overall cover thickness would be 17.5 inches (445 mm) for each chamber structure. Each #8 stone layer was compacted using a standard plate compactor. Throughout the steps of the installation 87

process, the front end of each chamber structure was left open to allow an installation of deformation measurement sensors and direct visual observations.

Figure 4.2 summarizes the installation plan for the chamber structures. The dotted line in the drawing represents the geotextile sheet which wrapped the encased chambers. Figure 4.3 presents a photograph taken in the field during the chambers installation stage.

Figure 4.2: Chambers Installation Plan [Note] All primary measurements are in mm.

Figure 4.3: A Photograph Taken During Field Installation of Chamber Structures 88

4.4 Chamber Instrumentations

Two different types of modern sensor were employed to instrument the preselected sections of each chamber structure. In Chambers A and C, the instrumented section was located at the mid-length section of the third segment (84 inches or 2.1 m from the front end). In Chamber B, the instrumented section was found at the mid-length section of the fourth segment (118 inches or 3.0 m from the front end).

First, a vibrating-wire soil pressure cell (Geokon, Model 4800E) was installed above the crown of the selected section of each chamber structure, while establishing the initial 6-inch (152-mm) cover. The purpose of this instrumentation was to record the magnitude of the vertical pressure induced by the subsequent live loading. All pressure cells had a diameter of 9 inches (229 mm) to have a relatively large sensing surface.

Each cell was embedded in a 2-inch (51-mm) thick sand lens to make sure that pressure will be evenly distributed over its sensing disk faces. Each pressure cell came with calibration values, which were ready to be applied. Figure 4.4 below shows a pressure cell being placed in the field.

Figure 4.4: A Soil Pressure Cell Placed Over a Buried Chamber Structure 89

Secondly, a total of four (4) linear wire potentiometers (Uni-Measure, Model LX-

PA) were attached to the inside wall surfaces of the selected chamber segment to measure the deformations induced by the applied live loads. Figure 4.5 illustrates the linear potentiometers installation plan. The shoulder point was identified at a location 26.5 inches (673 mm) above the base and 17.3 inches (438 mm) horizontally away from the crown. The span or base width was measured across the chamber at 5.3 inches (135 mm) above the chamber bottom to keep the sensor from contacting the bedding layer. The calibration constant of each wire potentiometer was checked prior to their field usage.

Figure 4.5: Four Linear Wire Potentiometers Installed Inside Each Chamber 90

4.5 Loading Methods

A dump truck was used to apply external loading to the installed chambers in a controlled manner. The truck had a single axle on the front and double axles on the rear, as seen in Figure 4.6. A photograph of the truck is provided in Figure 4.7. The gross weight of the truck was set at four different levels, so as to apply increasingly heavier axle loads to the buried chamber structures, as summarized in Table 4.1. The truck weight was incremented gradually by placing a larger volume of stones in the flat bed section. A set of portable digital scales were used to weigh the dead load underneath each wheel.

Figure 4.6: Axle Configurations of Dump Truck Used in Field Testing

Figure 4.7: Actual Photograph of Dump Truck 91

Table 4.1: Wheel and Axle Loads Measured in Field Load Level 1 – Empty Dump Truck: 13.95 kip (62.0 kN) on Rear Axles

Axle 1 (Front) Axle 2 (Rear 1) Axle 3 (Rear 2) Right Side Wheels 4.45 kip (19.8 kN) 4.40 kip (19.6 kN) 3.15 kip (14.0 kN) Left Side Wheels 5.00 kip (22.3 kN) 3.20 kip (14.2 kN) 3.20 kip (14.2 kN) Total 9.45 kip (42.1 kN) 7.60 kip (33.8 kN) 6.35 kip (28.2 kN)

Load Level 2 – Loaded Dump Truck – 144.2-kN or 32.4 kip (144 kN) on Rear Axles

Axle 1 (Front) Axle 2 (Rear 1) Axle 3 (Rear 2) Right Side Wheels 5.70 kip (25.4 kN) 8.15 kip (36.3 kN) 8.55 kip (38.0 kN) Left Side Wheels 6.11 kip (27.2 kN) 7.70 kip (34.3 kN) 8.00 kip (35.6 kN) Total 11.8 kip (52.5 kN) 15.85 kip (70.6 kN) 16.55 kip (73.6 kN)

Load Level 3 – Loaded Dump Truck – 40.4 kip (179.8 kN) on Rear Axles

Axle 1 (Front) Axle 2 (Rear 1) Axle 3 (Rear 2) Right Side Wheels 7.00 kip (31.2 kN) 10.45 kip (46.5 kN) 11.25 kip (50.1 kN) Left Side Wheels 6.40 kip (28.5 kN) 9.95 kip (44.3 kN) 8.75 kip (38.9 kN) Total 13.4 kip (59.6 kN) 20.4 kip (90.8 kN) 20.0 kip (89.0 kN)

Load Level 4 – Loaded Dump Truck – 48.0 kip (213.6 kN) on Rear Axles

Axle 1 (Front) Axle 2 (Rear 1) Axle 3 (Rear 2) Right Side Wheels NA 12.75 kip (56.7 kN) 11.8 kip (52.5 kN) Left Side Wheels NA 11.75 kip (52.3 kN) 11.7 kip (52.1 kN) Total NA 24.5 kip (109.0 kN) 23.5 kip (104.6 kN) [Note] “NA” = Not Available.

Figures 4.8 and 4.9 together illustrate how the chamber structures were loaded statically in the transverse and longitudinal directions. Figures 4.10 and 4.11 show photographs taken during the live load applications. First, the empty truck (Load level 1 loading) moved slowly from Chamber C to Chamber A, positioning Axle 2 and then Axle 92

3 over each chamber transversely. Next, the truck was loaded with some stones to increase its weight to Load level 2 and applied a transverse loading to each chamber under Axle 2 and then Axle 3. After these transverse loadings, the truck was backed in to position Axle 3 longitudinally over Chambers C and a dummy chamber (installed next to it) and then over Chambers A and B. The same series of axle loading were repeated when more dead weight was added to the truck to apply the Load level 3 loading. Finally, the transverse and longitudinal loads were applied by the truck having a combined rear axle loading of 214 kN (48 kips). Each load application lasted for at least a few minutes, so that data acquisition systems could collect the sensor readings repeatedly. Initial readings were taken from all the sensors with the dump truck located a sufficient distance away from the test area. The differences in sensor readings between the initial readings and subsequent readings under the static loading reflected the effects of the live loading.

Figure 4.8: Schematics for Live Load Application Plan (Drawing 1) 93

Figure 4.9: Schematics for Live Load Application Plan (Drawing 2)

Figure 4.10: Transverse Loading – Axle 3 over Chamber C

Figure 4.11: Longitudinal Loading – Axle 3 over Chambers A & B

4.6 Field Load Test Results

4.6.1 Soil Pressure Measured at Crown

Tables 4.2 through 4.5 summarize the vertical soil pressure measured by the pressure cells during the live load applications. In these tables, pressure readings taken with the axle load applied directly above the chamber are shaded. No readings were available from the pressure cell installed above Chamber B, since it was damaged during the initial chamber installation.

Table 4.2: Soil Pressure Readings under Level 1 (Empty Dump Truck) Loading

Loading Axle Position & Soil Pressure in kPa (psi) Measured @ Crown of: Direction Chamber A Chamber B Chamber C Axle 2 on Chamber C; Transverse 3.58 (0.52) NA 6.96 (1.01) Axle 3 on Chamber C; Transverse 0.00 NA 5.24 (0.76) Axle 2 on Chamber B; Transverse 0.00 NA 3.45 (0.50) Axle 3 on Chamber B; Transverse 0.52 NA 1.72 (0.25) Axle 2 on Chamber A; Transverse 16.0 (2.32) NA 1.72 (0.25) Axle 3 on Chamber A; Transverse 14.2 (2.06) NA 1.72 (0.25) [Note] “NA” = Not Available. 95

Table 4.3: Soil Pressure Readings under Level 2 (144-kN; 32.4-kip) Loading

Loading Axle Position & Direction Soil Pressure in kPa (psi) Measured @ Crown of: Chamber A Chamber B Chamber C Axle 2 on Chamber C; Transverse 5.31 (0.77) NA 22.6 (3.28) Axle 3 on Chamber C; Transverse 1.72 (0.25) NA 20.8 (3.02) Axle 2 on Chamber B; Transverse 1.72 (0.25) NA 15.6 (2.27) Axle 3 on Chamber B; Transverse 7.10 (1.03) NA 12.1 (1.76) Axle 2 on Chamber A; Transverse 28.4 (4.12) NA 12.1 (1.76) Axle 3 on Chamber A; Transverse 33.8 (4.90) NA 10.4 (1.51) Axle 3 on Chambers C; Longit. 0.00 NA 20.8 (3.02) Axle 3 on Chambers A & B; 46.2 (6.70) NA 17.3 (2.51) Longit.

Table 4.4: Soil Pressure Readings under Level 3 (180-kN; 40.4-kip) Loading

Loading Axle Position & Direction Soil Pressure in kPa (psi) Measured @ Crown of: Chamber A Chamber B Chamber C Axle 2 on Chamber C; Transverse 8.82 (1.28) NA 24.3 (3.52) Axle 3 on Chamber C; Transverse 3.52 (0.51) NA 57.4 (8.32) Axle 2 on Chamber B; Transverse 1.72 (0.25) NA 24.3 (3.52) Axle 3 on Chamber B; Transverse 1.72 (0.25) NA 27.8 (4.03) Axle 2 on Chamber A; Transverse 40.9 (5.93) NA 13.8 (2.00) Axle 3 on Chamber A; Transverse 74.7 (10.83) NA 13.8 (2.00) Axle 3 on Chambers C; Longit. 3.52 (0.51) NA 52.1 (7.56) Axle 3 on Chambers A & B; Longit. 71.1 (10.32) NA 20.8 (3.02)

Table 4.5: Soil Pressure Readings under Level 4 (214-kN; 48-kip) Loading

Loading Axle Position & Direction Soil Pressure in kPa (psi) Measured @ Crown of: Chamber A Chamber B Chamber C Axle 2 on Chamber C; Transverse 8.82 (1.28) NA 34.7 (5.04) Axle 3 on Chamber C; Transverse 5.31 (0.77) NA 52.1 (7.56) Axle 2 on Chamber B; Transverse 5.31 (0.77) NA 34.7 (5.04) Axle 3 on Chamber B; Transverse 44.5 (6.45) NA 24.3 (3.52) Axle 2 on Chamber A; Transverse 78.2 (11.35) NA 24.3 (3.52) Axle 3 on Chamber A; Transverse 74.7 (10.84) NA 20.8 (3.02) Axle 3 on Chambers C; Longit. 5.31 (0.77) NA 67.8 (9.83) Axle 3 on Chambers A & B; Longit. 90.7 (13.16) NA 41.7 (6.05) [Note] “Longit.” = Longitudinal; and “NA” = Not Available. 96

The readings taken over Chamber C had a tendency to be smaller than those taken over Chamber A, because the soil pressure cell placed above Chamber C was actually smaller in diameter (diameter 4 inches or 102 mm) and the wheel path might not have been directly above this small pressure cell. In some cases, under the same axle load configuration the longitudinal loading induced a slightly higher soil pressure at the chamber crown than the transverse loading. This is seen for Chamber A placed under

Axle 3 of the Level 2 and Level 4 loadings, and for Chamber C placed under Axle 3 of the Level 4 loading. Figures 4.12 (a) and (b) show this graphically. These confirm the fact that the longitudinal direction loading can have a larger impact on the chambers than the transverse direction loading.

Figure 4.12: Vertical Soil Pressure Measured at Chamber Crown for Chamber A 97

(b) Chamber C

Figure 4.13: Vertical Soil Pressure Measured at Chamber Crown for Chamber B

4.6.2 Deformation Behaviors of Buried Chambers

The initial dimensions taken inside the chambers were 36.0 inches (914 mm) for the rise, 47.5 inches (1,207 mm) for the base span, 32.5 inches (823 mm) for the shoulder span, and 32.0 inches (813 mm) for the diagonal distance. Tables 4.6 through 4.8 and

Figures 4.13 (a) through (c) present the dimensional changes experienced by the chambers during the live load applications.

Table 4.6: Dimensional Changes Experienced by Chamber A

Wheel Load Loading Dimensional Changes in (percentage): kN (kips) Direction Rise Diagonal Shoulder Span Base Span 14.2 (3.20) Transverse -0.609 0.018 0.014 0.011 14.2 (3.20) Transverse -0.778 0.016 0.014 0.010 34.3 (7.70) Transverse -0.826 0.027 0.016 -0.028 35.6 (8.00) Transverse -0.665 0.021 0.084 -0.031 35.6 (8.00) Longitud. -0.661 0.031 0.104 -0.025 44.3 (9.95) Transverse -0.484 -0.024 0.155 -0.117 98

Table 4.6: Dimensional Changes Experienced by Chamber A (Cont’d)

Wheel Load Loading Dimensional Changes in (percentage): kN (kips) Direction Rise Diagonal Shoulder Span Base Span 38.9 (8.75) Transverse -0.416 -0.017 0.373 -0.055 38.9 (8.75) Longitud. -2.237 0.127 0.201 -0.052 52.3 (11.75) Transverse -0.407 -0.294 0.324 -0.185 52.1 (11.70) Transverse -0.252 -0.042 0.458 -0.126 52.1 (11.70) Longitud. -0.298 0.206 0.134 -0.126

Table 4.7: Dimensional Changes Experienced by Chamber B

Axle Load Loading Dimensional Changes in (percentage): kN (kips) Direction Rise Diagonal Shoulder Span Base Span 33.8 (7.60) Transverse -1.021 0.014 0.003 0.011 28.2 (6.35) Transverse -0.812 0.013 0.002 0.009 70.6 (15.9) Transverse -1.563 -0.149 0.005 0.001 73.6 (16.6) Transverse -1.236 -0.060 0.077 0.001 73.6 (16.6) Longitud. -1.057 0.085 0.112 -0.015 90.8 (20.4) Transverse -0.916 -0.214 0.089 -0.029 89.0 (20.0) Transverse -0.885 -0.027 0.162 -0.011 89.0 (20.0) Longitud. -1.068 0.349 0.314 0.0237 109.0 (24.5) Transverse -1.600 -0.361 0.188 -0.084 104.6 (23.5) Transverse -1.266 0.063 0.358 -0.029 104.6 (23.5) Longitud. -1.522 0.228 0.167 -0.095

Table 4.8: Dimensional Changes Experienced by Chamber C

Wheel Load Loading Dimensional Changes in (percentage): kN (kips) Direction Rise Diagonal Shoulder Span Base Span 14.2 (3.20) Transverse -0.074 0.026 -0.025 0.014 14.2 (3.20) Transverse -0.069 0.027 -0.025 0.015 34.3 (7.70) Transverse -0.340 -0.198 -0.154 -0.037 35.6 (8.00) Transverse -0.378 -0.063 0.081 -0.036 35.6 (8.00) Longitud. -0.030 0.182 -0.162 -0.042 44.3 (9.95) Transverse -0.715 -0.283 0.020 -0.143 38.9 (8.75) Transverse -0.857 0.014 0.179 -0.116 38.9 (8.75) Longitud. -0.477 -0.362 0.225 -0.176 52.3 (11.75) Transverse -1.063 -0.192 0.239 -0.252 52.1 (11.70) Transverse -1.098 0.263 0.343 -0.225 52.1 (11.70) Longitud. -0.700 0.510 -0.115 -0.292 99

(a) Chamber A

(b) Chamber B 100

In these tables, the most pronounced deformations measured are shaded under all the load increments. In some cases, under the same axle load configuration the longitudinal loading induced larger deformations on the chamber structure. This is seen for the rise dimension changes experienced by Chambers A and B under Axle 3 of Load levels 3 and 4. The same trend can be seen for the span dimension changes experienced by Chamber B under Axle 3 of Load level 4, as well as for the diagonal distance and span dimension changes experienced by Chamber C under Axle 3 of Load levels 3 and 4.

These results support the fact that the longitudinal direction loading can be harsher than the transverse direction loading.

The largest chamber deformations were not detected under the highest level loading. It is speculated that the backfill material became denser and stiffer as it was 101

subjected to increasingly heavier loading during numerous loading and unloading cycles involved in the field tests.

Comparing the deformation performances across the three test chambers, we can state that the rise dimension of Chamber B decreased more than the rise of Chamber A or

C. The instrumented section of Chamber B was subjected more to the effect of full axle loading, since it was located between the right and left wheel loads.

Examinations of Figures 4.13 (a) through (c) show that the chamber structure responds to the live loads such that under increasing axle load:

its rise dimension decreases;

its base span dimension decreases by less than 1%;

its shoulder-level span increases by less than 0.5%; and

its diagonal distance to the shoulder point changes by less than 0.5%.

The changes in the rise dimension are larger than its changes in any other dimensions measured. These results point out the fact that the chamber structure behaves somewhat differently from buried flexible pipes. It is a common knowledge in the engineering community that a buried flexible pipe’s cross-sectional shape changes from a circle to a horizontal ellipse, when it is loaded vertically. This means that the span (or horizontal diameter) tends to increase while the rise (vertical diameter) decreases, as shown in Figure4.14. If the chamber deformation behavior is similar to that of a flexible pipe, then the base span should increase as the rise dimension decreases. Actually the base span of chamber is decreasing as the rise dimension decreases, as shown in Figure

4.14. This conforms to computer simulation results. The totally different behavior 102

exhibited by the chamber’s base span is believed to be due to the presence of the outward feet at the base, which are somewhat anchored under the weight of the stone column.

Figure 4.15: Deformation Characteristics of Buried Circular Pipe and Arch Chamber

The instrumented section of each chamber structure was visually inspected shortly after each series of live load application and at the conclusion of the field load test program. During inspection, no signs of structural distress (cracking, excessive deformations, reversal of curvature, localized wall buckling, plastic hinge formation …) were ever detected inside any of the chamber structures. This implies that in the current study it was not possible to determine the maximum load carrying capacity and dominant failure mode of shallowly installed chambers. Key findings made through the field observations were as follows:

The chamber feet settled only a small amount into the bedding layer. 103

The surface of the bedding layer between the chamber feet exhibited a minor heaving, inside most of the chambers.

While applying the Load level 2 to the chambers, the wheel path developed a rut depth of about 0.5 inches (13 mm) along the entire soil cover surface. The rut depth grew to 1.5 inches (37 mm) by the time Load level 4 was applied.

104

CHAPTER 5 ANALYSIS OF BURIED CHAMBER STRUCTURE

5.1 Introduction

Despite the fact that several different chamber products are currently marketed and their applications are growing rapidly, there has been a lack of even a simple design/analysis method available to the practicing engineers. And, some engineers assume conveniently that the arch-shaped chambers behave basically just like circular pipes. This chapter presents the first attempt in developing an organized analysis method for the buried chamber structure.

5.2 Basic Analysis of Loaded Chamber Product

Let us first secure a solution for a chamber product loaded by a single concentrated load. This simple load test may be used as a quality control measure by chamber product manufacturers. The test method is in line with the parallel-plate load test

(ASTM D-2412) protocol developed for the thermoplastic pipe industry. A chamber may be idealized as a semi-circular elastic arch structure (shown in Figure 5.1). Let us assume that Points A and D, chamber bottoms, cannot experience any displacements. This is not an unrealistic assumption, as a well-installed chamber is supposed to behave in this manner. The chamber is now treated as a semi-circular arch on pinned supports. This is illustrated in Figure 5.1. (a). Figure 5.1.(b) shows the idealized chamber structure detached from its supports. 105

P B C

r Ph A D Ph

0.5P 0.5Pv v

(a) Idealized Chamber Structure (b) Free-Body Diagram

Figure 5.1: Loading of Idealized Chamber Product

Introduction of the horizontal forces Ph is necessary to keep the structure from expanding horizontally at the base. According to Spangler (1941), the vertical and horizontal deflections of a circular elastic pipe under a concentrated vertical load Pv are:

rP 3 y 149.0 v Eq. 5-1 EI

rP 3 x 136.0 v EI Eq. 5-2

where Δy = vertical deflection; Δx = horizontal deflection; r = radius; E = modulus of elasticity; and I = moment of inertia of wall cross-section (per unit length).

The semi-circular ring or chamber structure in Figure 5.1 is loaded essentially by two concentrated loads Pv and Ph. Its horizontal deflection can be determined through superposition rule as: 106

rP 3 rP 3 x v 149.0136.0 h EI EI Eq. 5-3

If we set the above horizontal deflection to zero (this assumption will be discussed in depth later), the following relationship is obtained between the two forces:

Ph = 0.913Pv Eq. 5-4

The vertical deflection of the semi-circular chamber structure, loaded by a single concentrated load Pv, is then expressed as:

rP 3 rP 3 rP 3 y .0 149 v .0 136 h .0 025 v EI EI EI Eq. 5-5

From Eq. 5-5, the chamber stiffness (CS) can be defined as:

Pv EI EI CS 3 40 3 y .0 025r r Eq. 5-6

The above solution is for a highly idealized elastic arch-shaped chamber and ignores moment reactions at the supports. Eq. 5-4 predicts that a horizontal load having the magnitude nearly equal to that of the vertical load is needed to keep the chamber structure from deflecting horizontally at the base. Eq. 5-5 implies that the vertical deflection of a chamber product is about 17% of that of an equivalent pipe product, which is characterized by the same raw material, same radius, and same wall moment of inertia.

Anchoring of the chamber bottom feet provides a significant reduction in its vertical deflection, in a way similar to a placement of a stiff backfill does to a circular pipe. Eq. 5-

6 points out that the flexural stiffness of a chamber product can be about six times larger than the flexural stiffness of an equivalent pipe product. This finding explains partially 107

why a cluster of properly installed chambers separated only by thin soil columns can support relatively large live loads with no difficulties.

5.3 Assumptions for Buried Chamber Analysis

From the full-scale field load tests on chamber products, the following key observations were made:

The chamber products made from thermoplastic or thermosetting plastic materials

have the ability to relieve some of the vertical load coming from above through

interactions with the soil envelope surrounding them. However, their ability to do

this is somewhat limited, due to a thinner soil envelope surrounding them. The

thinner soil envelope around each chamber is the result of installing multiple

chambers closely side by side.

The chambers behaved differently from the way the pipes behave when buried in

soil and subjected to vertical loads.

Next, some assumptions must be made to make the buried chamber problem simple enough to be analyzed by the traditional method. These assumptions are largely based on the field load test results and computer simulation results. Figure 5.2 is prepared to explain the assumptions. The assumptions are summarized below:

1) The field installation conditions are uniform along the length of the chamber

structure. Thus, plain-strain analysis within a 2-D cross-section is justifiable.

2) The chamber is shaped as a semi-circle with flat flanges extending outwardly

from the bottom ends. 108

3) The chamber bottom legs are somewhat anchored to the ground due to the weight

of the soil column existing above the bottom flanges. This implies that Points A

and E, located at the junction of the curved chamber wall and the bottom flange,

do not move easily horizontally or vertically. This anchoring of the bottom

flanges has been discussed already before. This is observed in the computer

simulation results, that in terms of movement of the foot region, both horizontal

and vertical deflections are relatively small comparing with other regions.

Figure 5.2: Illustration for Analysis of Buried Chamber Structure

4) A uniform vertical soil pressure (v) exists over the chamber structure, as a result

of the uniformly distributed external loading q applied at the ground surface. The

average value of v may be estimated using the Boussinesq’s theory. The width of

the uniform soil pressure extends across the entire span of the chamber. This

assumption is reasonable when the chamber is buried under moderate to deep soil 109

cover. The distribution of the soil pressure becomes less uniform when the

chamber is buried under shallow cover and a live load is placed above the

chamber.

5) A uniform vertical reaction pressure (v ) exists underneath each chamber bottom

foot. When this pressure is multiplied by the chamber foot width (F), the resulting

force becomes equal to one half of the total load acting over the chamber.

6) The largest outward movement of the chamber wall is experienced right at the

shoulder locations (where the angle equal to 45°), when the chamber is loaded

vertically from above. This was also observed in the finite element simulations in

Chapter 3. This assumption implies that the lateral soil pressure may be the largest

against Points B and D. The lateral soil pressure is zero at the crown (Point C) and

the bottom (Points A and E).

7) The lateral soil pressures acting against the sides of the chamber are distributed

parabolically. The maximum pressure, found at Points B and D, is equal to the

modulus of passive pressure (e) of the backfill material multiplied by one half of

the horizontal deflection of the chamber. This is expressed mathematically as:

Ex x eh r 22 Eq. 5-7

where h = maximum lateral soil pressure; e = modulus of passive pressure; Δx =

horizontal deflection; and E = modulus of soil reaction = e r.

This assumption was previously used by Spangler (1941) to obtain his horizontal

deflection formula or “Iowa” formula for buried flexible pipe structure. 110

5.4 Analysis of Buried Chamber Structure

We can now proceed with the analysis of a buried single chamber structure. The approach taken here is similar to the one previously taken by Dr. Masada for analyzing a buried circular pipe structure (see Masada, 2000). The horizontal and vertical deflections of the chamber shown in Figure 5-2 can be obtained from:

Eq. 5-8.a

Eq. 5-8.b

The general expression for bending moment (M) in the chamber wall is given as:

for 0 < < π/2 Eq. 5-9

where Me = moment acting at chamber bottom (in-lb/in or N-m/m); Re = thrust force acting in chamber foot (lb/in or N/m); = arbitrary angle taken counterclockwise from the right bottom foot (radians); v = uniform vertical reaction pressure acting underneath each chamber foot (psi or kPa); and v = uniform vertical pressure acting over the chamber (psi or kPa).

By inspection, we can see that:

Eq. 5-10

where F = width of chamber foot (inches or m).

Integrating the moment over the limit of equal to 0 to π/2, we will obtain:

2/ 2 2 2 Md e rR .0 127hr .0 178vr .0 785 Fv 0 0 Eq. 5-11 111

From the above, Eq. 5-12

Inputting Eq. 5-12 into Eq. 5-9 will result in:

M = hr2 (0.402 – 0.127sin – 0.804cos + 0.804cos3 – 0.402cos4 )

+ vr2 (0.5 – 0.178sin – cos + 0.5cos2 ) + v F2 (0.5 - 0.785sin ) Eq. 5-9

The integrations given by Eqs. 5-8.a and 5-8.b can now be performed. The results are as follows:

Eq. 5-13.a

Eq. 5-13.b

Here we can specify that v = P and v = Pr/F. We can also apply Eqs. 5-5 and 5-7.

Then, the above can be transformed into the following percent deflection formulas:

Eq. 5-14.a

Eq. 5-14.b

where d = diameter or full breadth of the chamber structure (inches or m).

There are a few notable comments we can make here regarding the deflection formulas obtained for the buried chamber structure.

The chamber deflection formulas do not contain any parameters that depend

on the installation conditions of the chamber such as the bedding constant (K)

that appears in the deflection formulas established for the buried flexible pipe

structures. This implies that in general the installation procedure is somewhat

less delicate for the chambers. 112

The coefficient in front of the E term in Eq. 5-14.a is about half of the

coefficient (0.061) in front of the E term that appears in the modified Iowa

formula for buried flexible pipe structure. This implies that the chamber

structure tends to mobilize less lateral support from its adjacent soil envelope

than its equivalent buried pipe structure does.

The development of the set of formulas is largely based on Modified Iowa

Formula for buried flexible pipe. Checking calculations shows that results from these formulas appear to be reasonable, and conform to the field test results and computer simulation results. However, more serious evaluation and validation need to be done in the future study. 113

CHAPTER 6 SUMMARY AND CONCLUSIONS

In this thesis, the author made a thorough study on this new stormwater collection product, chamber. Literature review was conducted on this area. Computer simulations were done on this product to analyze its structural performance. Also, field test results were examined to study its behavior in the field. Based on the results of computer simulations and field load test, a set of analytical methods were proposed. A brief summary of each chapter is presented below.

6.1 Literature Review

In the literature review section, the author talked about the history of stormwater management, available chamber product, standards in this area, general installation guidelines and researches in this area.

Since the Refuse Act in 1899, a series of regulations were enacted in the following years, including FWPA, CWA and NPDES. The CWA 1972 and NPDES 2002 are the current governmental regulations that require the application of BMP. The stormwater chamber is one of the most widely used structural BMPs today. Currently, various types of chamber products are available in the market. Typically they are made of

PP (Polypropylene) or HDPE (High Density Polyethylene) material. These materials are usually chemically stable, light-weighted, and low-cost. The ASTM International established standard specification F-2418 for polypropylene corrugated wall stormwater collection chambers in 2005. It covers dimensional and material requirements as well as a 114

simple load test method for the chamber structures. The AASHTO provides the specifications for buried culvert structures in section 12, based on the LRFD approach.

However, no arch-shaped stormwater chamber structures are presented in the current

AASHTO LRFD specifications. The main steps of installation of chamber product contain materials preparation, excavation, subgrade preparation, chamber installation and backfilling. Detailed process would not be repeated here. Readers may refer to each company’s installation manuals for detailed instructions. Currently there are a limited number of literatures available on this subject. Beaver, et al. (2003) tested and analyzed structural performance of buried stormwater chamber. A research team at Ohio

University conducted a series of field load tests on stormwater chambers. More researches are needed to be done on this new product.

6.2 Computer Simulations

In the current thesis project, CANDE 2007 computer software was utilized to conduct a series of computer simulation studies to gain insights into the structural performance/behavior of buried chamber structures. Although frictional interface elements are available, they could not be utilized due to serious convergence issues.

6.2.1 Chamber vs. Pipe

There are some similarities between the circular pipe and an equivalent size semi- circular chamber when they are placed under identical installation and loading conditions.

The similarities are listed below:

They both deform into a horizontal ellipse. 115

The vertical deflection behavior tends to be about the same.

They both promote about the same degree of positive soil arching.

They tend to exhibit a similar maximum load carrying capacity.

There are also some differences in the way chamber structure performs in comparison to an equivalent pipe structure. The dissimilarities are listed below:

Under the uniform surface loading, the soil underneath the chamber feet was most

stressed vertically.

The side wall of the chamber moved inward, while the side wall of the circular

pipe moved outward.

The maximum horizontal displacement occurred in the lower leg region as well as

in the upper shoulder region for the chamber, while that occurred at the springline

for the pipe.

In terms of the bending moment, thrust force, and shear force development, they

were generally more pronounced in the chamber wall than in the pipe wall. And,

the leg region appears to be more critical than any other regions within the

chamber’s cross-section.

116

6.2.2 External Loading Type

For an added feature, the structural performance of the semi-circular chamber was examined under two surface-loading types – widely distributed loading and narrowly distributed central loading. The following summarizes key observations made regarding the effects of the external loading type:

The narrowly distributed central loading proved to be much harsher than the

widely distributed loading to the chamber-soil composite.

Under the narrow distributing loading, the cover soil layer became over stressed.

Under the narrow loading, the chamber deformed much more vertically compared

to the case with the wide uniform surface loading was applied to the chamber.

Under the narrow loading, the chamber’s side tends to move outward. Under the

widely distributed loading, the chamber’s side tends to move inward.

The degree of positive arching was much less under the narrowly focused loading.

The premature shear failure of the soil occurred near the chamber’s leg region

regardless of the type of surface loading being applied. The failure in that region

stayed localized throughout the loading steps.

Eventually, the narrow surface loading caused the chamber’s crown region to fail.

This was triggered by the bearing capacity failure of the soil cover over the

chamber crown. The previous wide surface loading caused the chamber’s leg

region to fail before the cover soil can have a bearing capacity failure.

In terms of the bending moment, thrust force, and shear force development, they

became more magnified under the narrow surface loading. 117

During construction stages prior to paving, cautions are needed to make sure that

this type of loading is not going to be applied to the buried chamber structure.

6.2.3 Chamber’s Cross-Sectional Geometry

Five different cross-sectional shapes (semi-circular, triangular, vertical ellipse, rectangular, and trapezoidal) were examined in order to identify the best possible geometry for the chamber structure. The following summarizes key observations made regarding to the chamber’s cross-sectional shape:

The rectangular shape may be the worst geometry for the buried chambers,

although it maximizes the storage capacity. Its top section can act as a flexible

beam and deflect excessively under the external loading. Also, the corners where

the top section and the vertical side section meet can act as stress raisers. This

shape provided the chamber the lowest load carrying capacity among all the

cross-sectional shapes considered.

The triangular shape also proved to be questionable for the buried chambers. This

shape did not help the structure to promote a decent degree of positive soil

arching. The pointed tip acted as a vertical stress magnet. This geometry may 118

also lead to a development of relatively high vertical soil pressure under the

chamber feet.

The trapezoidal shape is a hybrid of the rectangular and triangle shapes. As

expected, the structural performance of this geometry chamber reflected those of

both triangular and rectangular chambers. Thus, this type of chamber suffered

from the problems possessed by the two deriving chapes.

The elliptical shape chamber performed very well compared to any other chamber

shapes. This may explain why some commercial products currently available are

elliptically shaped. The maximum vertical deflection experienced by this

chamber was a lot less than those experienced by other three (rectangular,

triangular, and trapezoidal) chambers. This vertical ellipse shape chamber can

behave very similar to the semi-circular chamber. The elliptical chamber was

able to promote a mild degree of positive arching. The leg region appears to be

more critical than any other regions within the chamber’s cross-section. The

elliptical chamber may be considered to be a taller version of the equivalent semi-

circular chamber. By making the chamber taller the leg region of the chamber

can become more vulnerable to bending/thrust/shear actions.

Overall, the semicircular and elliptical shape turns out to be the best shape comparing with other shapes. Basically they are arch-shaped. They performed better in avoiding soil stress concentration and can sustain larger loading levels. Also, arch-shape is the typical shape in the market.

119

6.2.4 Chamber Spacing in Multi-Chamber Installation

Effects that the chamber spacing may have on the chamber’s structural performance were also examined, using CANDE 2007, for a three-chamber installation case. The industry guideline states that minimum spacing between adjacent rows is 6 inches (152 mm). In the computer simulations, the chamber spacing was set at 1, 6, and

12 inches (25, 152, and 305 mm). The following summarizes key observations made with regards to the effects of chamber spacing:

The center and outside chambers behaved differently in terms of their vertical

deflection behaviors. The chamber in the center deflected more vertically than

the chamber on the outside. This trend becomes less obvious as the chamber

spacing increased. At the industry minimum standard of 6-inch (152-mm)

spacing, the center chamber deflected 20% more vertically.

The horizontal deflection behavior of the center chamber varied significantly

depending on how the chamber spacing was. At the spacing of only 1 inch (25

mm), the chamber deflected outward. However, at the larger spacing the central

chamber deflected inward in the horizontal direction.

The center and outside chambers behaved differently in terms of the vertical soil

pressure they registered at the crown. The crown soil pressure remained

relatively unchanged for the center chamber regardless of how large the chamber

spacing was. The vertical soil pressure appearing over the crown of the outer

chamber decreased with the increasing chamber spacing. At the 12-inch (305- 120

mm) spacing, the crown pressure values were nearly the same between the two

chambers.

The internal bending moment/thrust force/shear force responses were highly

unbalanced between the two chambers when the chamber spacing was narrow.

However, the imbalance became less remarkable as the chamber spacing widened.

As the chamber spacing became larger, the multi-chamber system was able to

support a higher level of surface loading.

Wall buckling was never a performance limiting factor regardless of how narrow

the chamber spacing became.

At the chamber spacing of 12 inches (305 mm), the structural performance of

each of the three chambers became fairly similar to that of the single chamber

structure.

Overall, the larger the spacing is, the better the chamber-soil system performed.

This is because when the soil columns between two chambers get wider, it can provide more passive pressure. The industry guideline states that minimum spacing between adjacent chamber rows is 6 inches.

6.3 Field Load Tests

In the current project, three chamber structures were backfilled side by side under a granular soil cover of 17.5 inches (445 mm), instrumented with sensors, and subjected to a series of live load tests at a field site located in Albany, Ohio. The chambers were 121

load-tested under the worst possible conditions, as no pavement layer existed at the top to distribute the loads uniformly.

Four levels of rear axle loading were applied to each buried chamber statically in both transverse and longitudinal directions. It was partially confirmed during the field load tests that the longitudinal direction loading would have a slightly larger impact on the chambers. The same observation was made previously by Beaver, et al. (2003).

The sensor readings and visual inspection results indicate that the chamber with a soil cover of 445 mm (17.5 inches) managed to support wheel load of 52.3 kN (11.8 kips) and axle load of 109.0 kN (24.5 kips), applied in both transverse or longitudinal directions. Maximum reduction in the rise dimension was only about 2.3%, when the chambers were subjected to these live loads. During the field load tests, no early signs of structural failure or instability were observed inside any of the chamber structures. The largest chamber deformations were not always detected under the heaviest load. It is speculated that the backfill material most likely became denser and stiffer as it was subjected to increasingly larger axle loading during numerous loading and unloading cycles involved in the field tests. The chamber feet settled very little across all four chamber structures. Thus, the foot width of 127 mm (5.0 inches) appears to be adequate for the range of loading applied in the test program.

The chamber deformation data indicated that the chamber structure behaves somewhat differently from buried flexible pipes. If its deformation behavior is similar to that of a flexible pipe, the base span should increase as the rise dimension decreases.

Instead, the base span had a tendency to decrease slightly under increasing live loading. 122

This is believed to be largely due to the presence of the outward feet at the base, which tend to make the legs anchored.

6.4 Proposed Analytical Methods

This chapter first analyzed a chamber under a single concentrated load applied to its crown to derive an expression for its flexural stiffness. This analysis showed that the chamber structure can attain flexural stiffness that is about six times that of an equivalent pipe structure by simply locking its bottom feet in position. The chapter then derived relatively simple deflection formulas for the buried chamber structure. The formulas were developed on the basis of a number of assumptions, which were necessary to simplify the nature of the problem. They were supported by the observations and sensor readings made during the university team’s previous field load tests. The previous analytical approaches taken by Spangler (1941) and Masada (2000) were followed to obtain the chamber deflection formulas. The solutions expressed the horizontal and vertical deflections of the chamber in terms of the vertical pressure acting over the chamber, chamber radius, chamber foot width, chamber stiffness, and soil stiffness. The vertical deflection represented the decrease in the overall chamber rise, while the horizontal deflection represented the increase in the chamber span at the shoulder level.

The analysis presented in this paper revealed how simple yet remarkable the chamber structure design is. If the chamber can anchor its feet, it can easily attain flexural stiffness that is about six times higher than the flexural stiffness of an equivalent flexible 123

pipe. The vertical deflection and stresses/strains in the chamber wall must be considered as primary performance indicators for the buried chamber structure.

6.5 Recommendations

Due to the time limitation placed on the current thesis research, additional components of the study were left unexplored. They are briefly mentioned below and constitute recommendations for possible future investigations by others.

First of all, in terms of raw materials PVC was the main material studied in this research. Other common materials such as PP and HDPE should be also studied.

Secondly, in terms of the profile-wall design, variations of the typical profile-wall design adopted in the current study should be created by modifying the corrugation depth/ pitch and wall thickness to name a few. This additional investigation can lead to identifying better profile-wall designs for the chamber structures.

Thirdly, no interface elements were utilized in this study’s computer analysis, due to the limitations of CANDE 2007. When interface elements were added to the mesh, convergence problem persisted and no meaningful numerical results could be reached.

With a lack of interface elements, the interface between the chamber structure and the surrounding soil was modeled as fully bonded, which is unrealistic in view of the type of interface that should exist in reality. In the future study, additional time/effort should be spent to conduct computer simulations of the chamber/soil composite system with frictional interface elements being incorporated. 124

Fourthly, during the current thesis study no attempts were made to bridge the field load testing phase and the computer simulations phase. This was because the main goal of the computer simulations was to gain fundamental insights into the buried chamber’s structural performance/behavior rather than to duplicate the field test results. In a future study, additional computer simulations may be needed to see if computer simulation tools are capable of replicating the field test results.

Fifthly, in the study of effects of loading position, only narrow central loading was modeled. In a future study, narrow loading applied on the shoulder area should also be looked into. This is helpful to study the asymmetric deformation behavior of this chamber structure. Also, a full mesh might be needed to do this study.

Finally, the analysis carried out in this thesis did not address other important chamber performance issues, such as the chamber failure mode, circumferential shortening behavior, and time-dependent behaviors. The deflection formulas proposed in this thesis should be evaluated in light of actual field test data. In addition, multiple chamber installation case should be analyzed carefully to establish theoretical guidelines.

125

REFERENCES

A. Aysen. (2002). Soil mechanics. The Netherlands: A.A. Balkema Publishers.

American Society for Testing & Materials (2005). Standard specification of

polypropylene (PP) corrugated wall stormwater collection chambers. F 2418-05,

West Conshohocken, PA.

Beaver, J. L., McGrath, T. J., & Sharff P. A. (2003). Structural design of stormwater

chambers. Transportation Research Board Annual Meeting, Washington, D.C.

Federal Highway Administration (1989). CANDE-89 Culvert analysis and design computer program user manual. Publication No. FHWA-RD-89-169. McLean, Virginia.

Cultec, Inc., (2007). Stormwater systems. Retrieved from

http://www.cultec.com/stormwater_systems

Duncan, J.M., Byrne, Peter, Wong, K.S., and Mabry, Philip. (1980). Strength, stress-

strain and bulk modulus parameters for finite element analysis of stresses and

movements in soil masses. Report No. UCB/GT/80-01, University of California,

College of Engineering, Berkeley, California.

Emre A., Havvanur K. (2010). Use of empirical approaches and numerical analyses in

design of buried flexible pipes. Scientific Research and Essays, 5(24), pp. 3972-

3986

EPA (1973). The “national pollutant discharge elimination system”(NPDES), section

402, federal water pollution amendments of 1972 . Washington, DC. 126

EPA (2012). National pollutant discharge elimination systems. Retrieved from

http://www.epa.gov/npdes/stormwater/menuofbmps

Filshill A. S. (2010). Long term structural design of geosynthetic stormwater chambers

and the use of nanocompsites to enhance their performance. A MS thesis, Civil

Engineering Dept., Drexel University, Philadelphia, PA.

Hesham M., John B. K. (1996). Economical design for long-span soil-metal structures.

Canadian Journal of Civil Engineers, 23: pp. 838-849

Masada T. (2000). Modified Iowa formula for vertical deflection of buried flexible pipe.

Journal of Transportation Engineering, American Society of Civil Engineers, 126

(5): pp. 440-446

Masada T. (2011). Full scale field load testing of storm-water storage chamber structures.

Journal of Performance of Constructed Facilities, American Society of Civil

Engineers, 25(4): pp. 317-325

Mark M., Michael G. K., Timothy J. M. (2007). Cande-2007 user manual and guideline.

National Cooperative Highway Research Project, Washington, D.C.

Spangler, M. G. (1941). The structural design of flexible pipe culverts. The Iowa State

college Bulletin, No. 30, Vol. XL, Iowa Engineering Experiment Station, Iowa

State College, Ames, Iowa, 84 pp.

Stormtec, Inc. (2012). Developers. Retrieved from http://www.stormtech.com/developers

Trition Storm-water Solutions. (2010). Triton chamber system for stormwater

management installation manual. Retrieved from

http://www.tritonsws.com/support/installation-manual 127

APPENDIX A: CANDE RESULTS OF ELLIPTICAL CHAMBER

Figure A.1: Half Mesh Plot of Elliptical Chamber

Figure A.2: Plots of Displacement in Elliptical Chamber Wall 128

Figure A.3: Plot of Bending Moment in Elliptical Chamber Wall

Figure A.4: Plot of Thrust Force in Elliptical Chamber Wall

Figure A.5: Plot of Shear Force in Elliptical Chamber Wall 129

APPENDIX B: CANDE RESULTS OF TRAPEZOIDAL CHAMBER

Figure B.1: Half-Mesh Used for Trapezoidal Chamber

Figure B.2: Plots of Trapezoidal Chamber Deflections 130

Figure B.3: Plot of Bending Moment in Trapezoidal Chamber Wall

Figure B.4: Plot of Thrust Force in Trapezoidal Chamber Wall

Figure B.5: Plot of Shear Force in Trapezoidal Chamber Wall 131

APPENDIX C: CANDE RESULTS OF TRIANGULAR CHAMBER

Figure C.1: Half-Mesh Used for Triangular Chamber

Figure C.2: Plots of Triangular Chamber Deflections 132

Figure C.3: Plot of Bending Moment in Triangular Chamber Wall

Figure C.4: Plot of Thrust Force in Triangular Chamber Wall

Figure C.5: Plot of Shear Force in Triangular Chamber Wall 133

APPENDIX D: CANDE RESULTS OF RECTANGULAR CHAMBER

Figure D.1: Half-Mesh Used for Rectangular Chamber

Figure D.2: Plots of Rectangular Chamber Deflections 134

Figure D.3: Plot of Bending Moment in Rectangular Chamber Wall

Figure D.4: Plot of Thrust Force in Rectangular Chamber Wall

Figure D.5: Plot of Shear Force in Rectangular Chamber Wall

135

APPENDIX E: COMPARISON TABLES FOR DIFFERENT CROSS-SECTIONAL

SHAPE CHAMBERS

Table E.1: Performance of different shapes under 50 psi

Elliptical Trapezoidal Triangular Max. Vertical Dis-placement -1.341 -1.84 -2.018 Experienced by Chamber (in) (Node 1; crown) (Node 1; top (Node 3; near center) apex) Max. Horizontal Displacement -0.161 -0.313 -0.451 Experienced by Chamber (in) (Node 18; leg) (Node 9; lower (Node 5; middle side) of side) Max. Bending Moment in Chamber Wall 250.3 -407 172 (in-lb/in) (Node 20; bottom (Node 5; top (Node 2; near of leg) corner) apex) Max. Thrust Force in Chamber Wall -535 -539 -588 (lb/in) (Node 17;side) (Node 10; lower (Node 8; bottom side) of side) Max. Shear Force in Chamber Wall 110 100 -69 (lb/in) (Node 21; edge of (Node 12; edge of (Node 1; apex) feet) feet) Vertical Soil Pressure at Crown (psi) -25.75 2.33 -102 Vertical Soil Pressure at Chamber Feet -137 -135 -129 (psi) Horizontal Soil Pressure at Chamber Feet -31 -26.5 -78 (psi) Factor of Safety Against Over- 1.342 0.652 (> 0.25) 0.595 Deflection Factor of Safety Against Combined 1.112 0.889 1.099 Strain Factor of Safety 1.529 1.514 1.334 Fs Against Wall Crushing Factor of Safety 3.529 3.186 2.898 Fs Against Wall Buckling (Global)

136

Table E.2: Performance of different shapes under 60 psi

Elliptical Triangular Max. Vertical Dis-placement (in) 60 psi (Node 19; leg) 60 psi (Node 7; lower side) Max. Horizontal Displacement (in) -1.49 -2.41 (Node 1; crown) (Node 3; near apex) Max. Bending Moment in Chamber Wall -0.20 -0.60 (in-lb/in) (Node 18; leg) (Node 5; middle of side) Max. Thrust Force in Chamber Wall 266.5 (Node 20; bottom 230 (lb/in) of leg) (Node 2; near apex) Max. Shear Force in Chamber Wall -607 -702 (Node 8; bottom of (lb/in) (Node 17; leg) side) Vertical Soil Pressure at Crown (psi) 115 (Node 21; edge of -92 feet) (Node 1; apex) Vertical Soil Pressure at Chamber Feet -29.3 -134 (psi) Horizontal Soil Pressure at Chamber -159.6 -155 Feet (psi) Factor of Safety Against Over- -36.9 -38.6 Deflection Factor of Safety Against Combined 1.208 (> 0.25) 0.498 (> 0.25) Strain Factor of Safety Against Wall Crushing 0.971 0.907 Factor of Safety Against Wall Buckling 1.276 1.031 (Global)

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