Numerical Methods in – Hicks, Brinkgreve & Rohe (Eds) © 2014 Taylor & Francis Group, London, 978-1-138-00146-6

A numerical simulation on the dynamic response of MSE wall with LWA backfill

H. Munjy University of California, Irvine, CA, USA F.M. Tehrani California State University, Fresno, CA, USA M. Xiao Pennsylvania State University, University Park, PA, USA M. Zoghi California State University, Fresno, CA, USA

ABSTRACT: This paper describes the finite element analysis of an alternative mechanically-stabilized-earth (MSE) wall, subject to dynamic loading using PLAXIS®-2D. The model incorporates Lightweight expanded shale aggregates (LWA) as backfill materials. Dynamic loading includes sinusoidal harmonic motions from 0.2 to 6 Hz frequencies. The numerical simulation is used to verify experimental shake-table studies on a small-scale prototype. The model features multiple layers of backfill materials reinforced with synthetic geo-grid sheets and loaded with a shallow . Discussions include the effectiveness of numerical techniques to model various features of the MSE wall. Numerical results are compatible with the shake-table experimental data. Further, simulations indicate the effectiveness of using equivalent springs in the small-scale model to replicate absorbent boundaries in a true-scale MSE wall. Moreover, the numerical output shows the sensitivity of MSE wall response to the frequency of the base excitation. However, the effect of damping is not readily exhibited in analysis. In summary, the results contribute to better understanding of MSE response to seismic events, performance of lightweight backfills, and reliability of numerical solutions, while warranting further analytical work using advanced models.

1 INTRODUCTION 1.2 Background The pseudo-static approach (Mononobe 1929 and 1.1 Motivation Okabe 1924) and displacement approach (Newmark Mechanically stabilized earth (MSE) walls have been 1965) are common and classic methodologies in used extensively in bridge construction. The ease of practical analysis and design of retaining struc- construction is the key advantage of this system in the tures, including MSE walls. Researchers have also accelerated bridge construction (ABC) method. Also, used the finite-element method to analyze retain- the application of lightweight aggregates (LWA) as ing systems and have developed computer backfill material would further reduce the cost and for practical applications, e.g. Segrestian & Bastick time of construction for MSE walls. Nevertheless, the (1988), Yogendrakumar et al. (1992), Bathurst & seismic performance of these structures continues to Hatami (1998), Helwany & McCallen (2001), be a design concern. Moreover, the interaction between Zevgolis & Bourdeau (2007), and Stuedlein et al. MSE wall and foundation system should be considered (2008). The outcomes of these studies have gen- in the seismic performance. erally indicated the need for dynamic analysis in Experimental studies of full- or large-scale MSE addition to classic methods to understand the seismic models are limited due to practical challenges. There- performance of MSE walls. fore, full application of MSE walls in seismic regions would rely on analytical modeling as as prototype 1.3 Scope testing. Analytical results would facilitate develop- ment of design and construction guidelines for seismic This research study aims to investigate analytical solu- applications of MSE walls (Elias & Christopher 2001). tions to seismic performance of MSE walls with

1147 Figure 2. Basic geometry of the MSE wall and mesh Figure 1. MSE wall configuration and instrumentation. generation using PLAXIS.

LWA backfill in presence of light surcharge in close Table 1. Dynamic stiffness values. proximity to the wall’s interface. Results have been KKstatic Kdynamic verified using small-scale shake-table studies. Further, Direction k(ω) kN/mm kN/mm kN/mm a true-scale model is developed to compare and verify modeling techniques and size effects. Vertical 0.66 74.6 144.4 95.5 Horizontal 0.75 55.7 181.0 135.8

2 ANALYTICAL MODEL where: k(ω) = dynamic stiffness coefficient; K = static stiffness for arbitrarily shaped foundations on the sur- = 2.1 Geometry face of homogeneous half-space; Kstatic static stiffness; Kdynamic = dynamic stiffness. The basic model of the MSE wall replicates an exper- imental small-scale prototype (Fig. 1). The model is developed using PLAXIS®, a finite-element package Table 2. Backfill material properties. intended for the 2D and 3D analysis of deformation Material LWA and stability in geotechnical engineering. The MSE wall is 1.3 m wide and 1.5 m high. A 0.2 m layer Model Mohr-Coulomb is placed underneath to replicate the base . The Unit weight (kN/m3) 10.28 sand layer extends 0.47 m beyond MSE toe. Figure 2 Modulus of elasticity (MPa) 14290 illustrates the basic geometry and mesh generation for Posisson’s ratio 0.3 the finite element model. The presented geometry is 0.596 based on a plane strain concept utilizing the 6-node (kPa) 22.89 triangular elements with very-coarse mesh genera- Friction angle (degree) 35 tion. It is assumed that material behavior follows the Mohr-Coulomb model. reveal the effectiveness of these springs simulating the actual boundaries. Table 1 summarizes the calculation 2.2 Boundary conditions of dynamic stiffness values for the bottom and side Boundary conditions are defined using manual boundaries of the model.

Downloaded by [Pennsylvania State University (Penn State)] at 14:51 09 August 2015 constraints via tool available in PLAXIS. These con- straints restrict the bottom of the model to prescribed 2.3 Material properties horizontal displacement and restrain the bottom of the model against vertical displacement. The prescribed Material properties were obtained from laboratory displacement represents the base excitation from the testing or manufacturer’s specifications. Table 2 pro- shake table, transferred through a rigid frame to the vides properties of the LWA backfill. The dynamic bottom and the right side of the prototype. Due to modulus of elasticity for LWA is extracted using the small size of the prototype, no absorbent boundaries Shultz’ estimation (1970): were used in this model. Rather, horizontal and verti- cal spring-supported plywood panels on the right side and at the bottom of the model simulate assumed dense sand adjacent to the MSE wall, based on the method- where, Edyn = dynamic modulus of elasticity (MPa); ology proposed by Gazetas (1991). Analytical studies and γ = (kgf/dm3 = 9.807 kN/m3).

1148 Table 3. Verification of boundary conditions.

Time Frequency Velocity Acceleration sec Hz mm/sec g

0-10 0.2 12.57 0.002 10-20 0.5 31.42 0.010 20-30 1.0 62.83 0.040 30-40 2.0 125.7 0.161 40-50 3.0 188.5 0.362 50-60 4.0 251.3 0.644 60-70 5.0 314.2 1.006 70-80 6.0 377.0 1.449

Amplitude of base displacement = 10 mm.

The geogird is modeled using an elasto-plastic model with secant modulus of elasticity of 280 kN/m obtained at 5% deformation, and ultimate tensile strength of 35 kN/m. Figure 3. Deformed shape. The concrete slab applies a 3.4 kPa surcharge on the backfill to replicate the effect of an overburden stress near the wall’s interface. Plywood plates at the bottom as well the side model a nominal 1.9 cm thick plate. Further, steel anchors secure the concrete slab to the LWA backfill against uplift.

2.4 Dynamic loading This prototype model was subjected to the harmonic loading. The loading consists of eight 10-sec sinu- Figure 4. Measured lateral displacement in shake table soidal motion at 0.2, 0.5, 1, 2, 3, 4, 5, and 6 Hz studies. frequencies. The amplitude of the load remains at 10 mm during the total 80-sec excitation. Theoretical val- ues of base velocity and acceleration are presented in Table 3.

3 RESULTS

3.1 Kinematics Figure 3 depicts the deformed shape of the MSE model at the end of 80-sec base excitations. This figure illus- trates how the MSE body moves away from the rigid wall due to lack of tensile resistance. Further, the MSE body demonstrates slight counter-clockwise rotation about the toe.The maximum value of horizontal defor- mation in this figure is 49 mm, which is close to

Downloaded by [Pennsylvania State University (Penn State)] at 14:51 09 August 2015 measured value in shake table studies (Fig. 4). More- over, Figure 4 reveals a change in vibration mode as a result of change in the frequency of base excitation. Figure 5. Maximum lateral deformation profile. Close examination of this figure shows that the lat- eral displacement increases with height in the first 20 seconds of the excitation, i.e. lower frequencies. But, Figure 6 captures the time history of acceleration the bottom layer has larger lateral displacements than at the top MSE wall. It should be noted that sin- middle layer during the last 20 seconds of the excita- gular high values in this graph might be the result tion, i.e. higher frequencies. Nevertheless, the profile of non-convergence in certain time steps. Neverthe- of maximum lateral displacement (Fig. 5) indicates less, comparison of the base acceleration values with that MSE body’s motion is governed by a cantilever those shown in Table 3 reveals that top acceleration mode of vibration. Thus, higher modes of vibration do is substantially higher than base acceleration. Table 4 not govern the response. highlights maximum accelerations measured during

1149 Figure 6. Time history of horizontal acceleration at the top of MSE wall.

Table 4. Maximum accelerations in shake-table studies.

Layer12345Figure 8. Tension -off (hollow squares) points at 10 sec (0.2 Hz). Acceleration (g) 2.4 3.2 4.8 3.0 3.2 Time (sec) 71.8 70.3 70.7 74.2 50.5

Amplitude of base displacement = 10 mm.

Figure 7. Acceleration spectrum at the top of MSE wall. Figure 9. Plastic (solid squares) and tension cut-off (hollow shake-table studies. All layers, except top layer, reach squares) points at 80 sec (6 Hz). the peak acceleration in the last 10 seconds of base excitation, i.e. during 6 HZ frequency motion. from the springs on the right side, as springs do not Moreover, the acceleration spectrum in Figure 7 resist tension. corroborates that the MSE system is sensitive to Figure 10 depicts the distribution of compres- two distinctive time periods corresponding to 6 and sive forces (shown with negative sign) in horizontal 0.5 HZ motions. However, damping has more impact springs, which are associated with the motion of MSE on higher frequency mode than lower frequency mode. wall toward the rigid frame. Downloaded by [Pennsylvania State University (Penn State)] at 14:51 09 August 2015 This is consistent with the effect of stiffness-related Figure 11 shows the lateral dynamic pressures at coefficient in Rayleigh damping on higher modes, as the top and bottom of the model. These values are the source of damping in LWA is primarily due to measures at the plywood panels. The lateral pressure friction. at the bottom layer gains substantial increase at 3 Hz excitations. But, the top layer is attenuated at 5 Hz.The results suggest that different mode shapes associated 3.2 Kinetics with these frequencies have caused these changes in lateral pressures. Figures 8 and9 portray the failure points at the end of 0.2 Hz and 6 Hz sinusoidal excitations, respectively. 3.3 Boundary conditions These graphs indicate how failure initiates and spreads to the front face of lower layers of the MSE wall.These Figure 12 represents an alternative model using failures are associated with the motion of wall away absorbent boundary conditions. This model

1150 Figure 10. Distribution of horizontal spring forces. Figure 13. Acceleration spectrums (5% damping) at the top of MSE wall with absorbent boundaries.

using advanced soil models, such as the hardening soil model with small strain stiffness. Further, simulation of an alternative model with absorbent boundaries reveals that equivalent springs in the small-scale mode may effectively replicate absorbent boundaries.

ACKNOWLEDGEMENTS

Figure 11. Time-history of dynamic lateral pressures on the This research was funded by the California Depart- LWA backfill at top and bottom of the model. ment ofTransportation (agreement number: 65A0449).

REFERENCES

Bathurst, R. J. & Cai, Z. 1995. Pseudo-static seismic analy- sis of geosynthetic-reinforced segmental retaining walls. Int. 2(5): 787–830. Elias, V. & Christopher, B.R. 2001. Mechanically stabilized earth walls and reinforced soil slopes design and construc- tion guidelines. FHWA-NHI-00-043. Federal Highway Administration (FHWA). Washington: DC. Expanded Shale and Slate Institute (ESCSI). 2008. Lightweight expanded shale, clay and slate aggregate for geotechnical applications. Information Sheet 6001. Gazetas, G. 1991. Formulas and charts for impedances of surface and embedded foundation. J. of Geotech. Engrg. ASCE. 117(9): 1363–1381. Figure 12. Geometry of alternative model with absorbent Hartman, D. et al. 2013. Shake table tests of MSE walls with boundaries. tire derived aggregates (TDA) backfill. Proc. 2013 Geo- Congress. ASCE. San Diego: CA. Helwany S.M.B. et al. 2001. Seismic analysis of segmental incorporates the MSE wall within a larger space of retaining walls. I: Model Verification. J. of Geotech. and dense sand, which extends 5 m from the toe at each Geoenviron. Engrg. ASCE 127(9): 741–749. direction. The acceleration spectrum (Fig. 13) indi- Stoll, R.R. & Holm, T.A. 1985. Expanded shale lightweight cates a dominant frequency of 6 Hz similar to the fill: geotechnical properties. J. of Geotech. Engrg. ASCE 111(8): 1023–1027. Downloaded by [Pennsylvania State University (Penn State)] at 14:51 09 August 2015 spectrum shown in Figure 7. Stuedlein, A.W. et al. 2010. Design and performance of a 46-m high MSE wall. J. of Geotech. And Geoenviron. Engrg. ASCE. 136(6): 786–796. 4 CONCLUSIONS Valsangkar, A.J. & Holm, T.A. 1990. Geotechnical properties of expanded shale lightweight aggregate. Geotech.Testing The dynamic response of a small-scale, prototype, J. ASTM 13(1): 10–15. MSE wall with LWA backfill is simulated using Zevgolis, I. & Bourdeau, P.L. 2007. Mechanically stabilized PLAXIS® software. The backfill material was mod- earth wall abutments for bridge support. FHWA/IN/JTRP- eled using Mohr-Coulomb model. Numerical results 2006/38. Joint Transportation Research Program. West are compatible with the shake-table experimental data. Lafayette: IN. The effect of damping is not, however, exhibited read- ily in the analysis. Nevertheless, the outcome of the presented simulations warrants further analytical work

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