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

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1 Numerical Methods in Geotechnical Engineering Hicks, Brinkgreve & Rohe (Eds) 2014 Taylor & Francis Group, London, 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 foundation. 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 soil models. 1 INTRODUCTION 1.1 Motivation Mechanically stabilized earth (MSE) walls have been used extensively in bridge construction. The ease of construction is the key advantage of this system in the accelerated bridge construction (ABC) method. Also, the application of lightweight aggregates (LWA) as backfill material would further reduce the cost and time of construction for MSE walls. Nevertheless, the seismic performance of these structures continues to be a design concern. Moreover, the interaction between MSE wall and foundation system should be considered in the seismic performance. Experimental studies of full- or large-scale MSE models are limited due to practical challenges. Therefore, full application of MSE walls in seismic regions would rely on analytical modeling as well as prototype testing. Analytical results would facilitate development of design and construction guidelines for seismic applications of MSE walls (Elias & Christopher 2001). 1.2 Background The pseudo-static approach (Mononobe 1929 and Okabe 1924) and displacement approach (Newmark 1965) are common and classic methodologies in practical analysis and design of retaining structures, including MSE walls. Researchers have also used the finite-element method to analyze retaining systems and have developed computer software for practical applications, e.g. Segrestian & Bastick (1988), Yogendrakumar et al. (1992), Bathurst & Hatami (1998), Helwany & McCallen (2001), Zevgolis & Bourdeau (2007), and Stuedlein et al. (2008). The outcomes of these studies have generally indicated the need for dynamic analysis in addition to classic methods to understand the seismic performance of MSE walls. 1.3 Scope This research study aims to investigate analytical solutions to seismic performance of MSE walls with 1147

2 Downloaded by [Pennsylvania State University (Penn State)] at 14:51 09 August 2015 Figure 1. MSE wall configuration and instrumentation. LWA backfill in presence of light surcharge in close proximity to the wall s interface. Results have been verified using small-scale shake-table studies. Further, a true-scale model is developed to compare and verify modeling techniques and size effects. 2 ANALYTICAL MODEL 2.1 Geometry The basic model of the MSE wall replicates an experimental small-scale prototype (Fig. 1). The model is developed using PLAXIS, a finite-element package intended for the 2D and 3D analysis of deformation and stability in geotechnical engineering. The MSE wall is 1.3 m wide and 1.5 m high. A 0.2 m sand layer is placed underneath to replicate the base friction. The sand layer extends 0.47 m beyond MSE toe. Figure 2 illustrates the basic geometry and mesh generation for the finite element model. The presented geometry is based on a plane strain concept utilizing the 6-node triangular elements with very-coarse mesh generation. It is assumed that material behavior follows the Mohr-Coulomb model. 2.2 Boundary conditions Boundary conditions are defined using manual constraints via tool available in PLAXIS. These constraints restrict the bottom of the model to prescribed horizontal displacement and restrain the bottom of the model against vertical displacement. The prescribed displacement represents the base excitation from the shake table, transferred through a rigid frame to the bottom and the right side of the prototype. Due to small size of the prototype, no absorbent boundaries were used in this model. Rather, horizontal and vertical 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 methodology proposed by Gazetas (1991). Analytical studies Figure 2. Basic geometry of the MSE wall and mesh generation using PLAXIS. Table 1. Dynamic stiffness values. K K static K dynamic Direction k(ω) kn/mm kn/mm kn/mm Vertical Horizontal where: k(ω) = dynamic stiffness coefficient; K = static stiffness for arbitrarily shaped foundations on the surface of homogeneous half-space; K static = static stiffness; K dynamic = dynamic stiffness. Table 2. Material Backfill material properties. LWA Model Mohr-Coulomb Unit weight (kn/m 3 ) Modulus of elasticity (MPa) Posisson s ratio 0.3 Void ratio Cohesion (kpa) Friction angle (degree) 35 reveal the effectiveness of these springs simulating the actual boundaries. Table 1 summarizes the calculation of dynamic stiffness values for the bottom and side boundaries of the model. 2.3 Material properties Material properties were obtained from laboratory testing or manufacturer s specifications. Table 2 provides properties of the LWA backfill. The dynamic modulus of elasticity for LWA is extracted using the Shultz estimation (1970): where, E dyn = dynamic modulus of elasticity (MPa); and γ = bulk density (kgf/dm 3 = kn/m 3 ). 1148

3 Table 3. Verification of boundary conditions. Downloaded by [Pennsylvania State University (Penn State)] at 14:51 09 August 2015 Time Frequency Velocity Acceleration sec Hz mm/sec g 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. 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 sinusoidal motion at 0.2, 0.5, 1, 2, 3, 4, 5, and 6 Hz frequencies. The amplitude of the load remains at 10 mm during the total 80-sec excitation. Theoretical values 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 illustrates 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 deformation in this figure is 49 mm, which is close to measured value in shake table studies (Fig. 4). Moreover, Figure 4 reveals a change in vibration mode as a result of change in the frequency of base excitation. Close examination of this figure shows that the lateral displacement increases with height in the first 20 seconds of the excitation, i.e. lower frequencies. But, the bottom layer has larger lateral displacements than middle layer during the last 20 seconds of the excitation, i.e. higher frequencies. Nevertheless, the profile of maximum lateral displacement (Fig. 5) indicates that MSE body s motion is governed by a cantilever mode of vibration. Thus, higher modes of vibration do not govern the response. Figure 3. Figure 4. studies. Figure 5. Deformed shape. Measured lateral displacement in shake table Maximum lateral deformation profile. Figure 6 captures the time history of acceleration at the top MSE wall. It should be noted that singular high values in this graph might be the result of non-convergence in certain time steps. Nevertheless, comparison of the base acceleration values with those shown in Table 3 reveals that top acceleration is substantially higher than base acceleration. Table 4 highlights maximum accelerations measured during 1149

4 Downloaded by [Pennsylvania State University (Penn State)] at 14:51 09 August 2015 Figure 6. Time history of horizontal acceleration at the top of MSE wall. Table 4. Maximum accelerations in shake-table studies. Layer Acceleration (g) Time (sec) Amplitude of base displacement = 10 mm. Figure 7. Acceleration spectrum at the top of MSE wall. shake-table studies. All layers, except top layer, reach the peak acceleration in the last 10 seconds of base excitation, i.e. during 6 HZ frequency motion. Moreover, the acceleration spectrum in Figure 7 corroborates that the MSE system is sensitive to two distinctive time periods corresponding to 6 and 0.5 HZ motions. However, damping has more impact on higher frequency mode than lower frequency mode. This is consistent with the effect of stiffness-related coefficient in Rayleigh damping on higher modes, as the source of damping in LWA is primarily due to friction. 3.2 Kinetics Figures 8 and 9 portray the failure points at the end of 0.2 Hz and 6 Hz sinusoidal excitations, respectively. These graphs indicate how failure initiates and spreads to the front face of lower layers of the MSE wall. These failures are associated with the motion of wall away Figure 8. (0.2 Hz). Tension cut-off (hollow squares) points at 10 sec Figure 9. Plastic (solid squares) and tension cut-off (hollow squares) points at 80 sec (6 Hz). from the springs on the right side, as springs do not resist tension. Figure 10 depicts the distribution of compressive forces (shown with negative sign) in horizontal springs, which are associated with the motion of MSE wall toward the rigid frame. Figure 11 shows the lateral dynamic pressures at the top and bottom of the model. These values are measures at the plywood panels. The lateral pressure 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 with these frequencies have caused these changes in lateral pressures. 3.3 Boundary conditions Figure 12 represents an alternative model using absorbent boundary conditions. This model 1150

5 Figure 10. Distribution of horizontal spring forces. Figure 13. Acceleration spectrums (5% damping) at the top of MSE wall with absorbent boundaries. Downloaded by [Pennsylvania State University (Penn State)] at 14:51 09 August 2015 Figure 11. Time-history of dynamic lateral pressures on the LWA backfill at top and bottom of the model. Figure 12. Geometry of alternative model with absorbent boundaries. incorporates the MSE wall within a larger space of dense sand, which extends 5 m from the toe at each direction. The acceleration spectrum (Fig. 13) indicates a dominant frequency of 6 Hz similar to the spectrum shown in Figure 7. 4 CONCLUSIONS The dynamic response of a small-scale, prototype, MSE wall with LWA backfill is simulated using PLAXIS software. The backfill material was modeled using Mohr-Coulomb model. Numerical results are compatible with the shake-table experimental data. The effect of damping is not, however, exhibited readily in the analysis. Nevertheless, the outcome of the presented simulations warrants further analytical work 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 This research was funded by the California Department oftransportation (agreement number: 65A0449). REFERENCES Bathurst, R. J. & Cai, Z Pseudo-static seismic analysis of geosynthetic-reinforced segmental retaining walls. Geosynthetics Int. 2(5): Elias, V. & Christopher, B.R Mechanically stabilized earth walls and reinforced soil slopes design and construction guidelines. FHWA-NHI Federal Highway Administration (FHWA). Washington: DC. Expanded Shale Clay and Slate Institute (ESCSI) Lightweight expanded shale, clay and slate aggregate for geotechnical applications. Information Sheet Gazetas, G Formulas and charts for impedances of surface and embedded foundation. J. of Geotech. Engrg. ASCE. 117(9): Hartman, D. et al Shake table tests of MSE walls with tire derived aggregates (TDA) backfill. Proc Geo- Congress. ASCE. San Diego: CA. Helwany S.M.B. et al Seismic analysis of segmental retaining walls. I: Model Verification. J. of Geotech. and Geoenviron. Engrg. ASCE 127(9): Stoll, R.R. & Holm, T.A Expanded shale lightweight fill: geotechnical properties. J. of Geotech. Engrg. ASCE 111(8): Stuedlein, A.W. et al Design and performance of a 46-m high MSE wall. J. of Geotech. And Geoenviron. Engrg. ASCE. 136(6): Valsangkar, A.J. & Holm, T.A Geotechnical properties of expanded shale lightweight aggregate. Geotech. Testing J. ASTM 13(1): Zevgolis, I. & Bourdeau, P.L Mechanically stabilized earth wall abutments for bridge support. FHWA/IN/JTRP- 2006/38. Joint Transportation Research Program. West Lafayette: IN. 1151