Modeling the Dynamic Response of Wrap-Faced Reinforced Soil Retaining Walls Downloaded from ascelibrary.org by INDIAN INST OF SCIENCE - BANGALORE on 01/06/14. Copyright ASCE. For personal use only; all rights reserved.
A. Murali Krishna, Aff.M.ASCE1; and G. Madhavi Latha2 Abstract: This paper describes the development of a numerical model for simulating the shaking table tests on wrap-faced reinforced soil retaining walls. Some of the physical model tests carried out on reinforced soil retaining walls subjected to dynamic excitation through uniaxial shaking tests are briefly discussed. Models of retaining walls are constructed in a perspex box with geotextile reinforcement using the wraparound technique with dry sand backfill and instrumented with displacement sensors, accelerometers, and soil pressure sensors. Results showed that the displacements decrease with the increase in number of reinforcement layers, whereas acceleration amplifications were not affected significantly. Numerical modeling of these shaking table tests is carried out using the Fast Lagrangian Analysis of Continua program. The numerical model is validated by comparing the results with experiments on physical models. Responses of wrap-faced walls with varying numbers of reinforcement layers are compared. Sensitivity analysis performed on the numerical models showed that the friction and dilation angle of backfill material and stiffness properties of the geotextile-soil interface are the most affecting parameters for the model response. DOI: 10.1061/(ASCE)GM.1943-5622.0000128. © 2012 American Society of Civil Engineers. CE Database subject headings: Geosynthetics; Retaining structures; Soil structures; Shake table tests; Seismic analysis; Numerical models; Dynamic response. Author keywords: Geosynthetics; Retaining walls; Shake table tests; Seismic analysis; Numerical models.
Introduction Reinforced soil technology is one of the most successful fields of civil engineering. Reinforced soil structures have gained wide popularity because of their functional, constructional, and economical benefits. Application of this technology to soil retaining structures has increased tremendously for various infrastructural projects across the globe. Because retaining walls were among the first geotechnical structures to be considered both critical and permanent as their service life was concerned (Koerner and Soong 2001), their seismic stability is of the utmost importance. Investigating the performance of reinforced retaining walls under cyclic ground shaking conditions aids in understanding how these walls actually behave during earthquakes and/or seismic conditions. Numerical modeling techniques are powerful tools that have been used to study the static and dynamic behavior of reinforced soil structures (e.g., Bathurst and Hatami 1998; El-Emam et al. 2004; Fakharian and Attar 2007). Numerical models are particularly advantageous because of the difficulties associated with situations in which the prototype structures are too big to be tested; problems related to scaling issues and instrumentations; and, especially, repetition of model construction, etc. However, the main key point to verify the applicability of any numerical model is by its validation with the available prototype studies and/or small scale 1 Assistant Professor, Dept. Civil Engineering, Indian Institute of Technology Guwahati, Guwahati 781039, India (corresponding author). E-mail:
[email protected] 2 Associate Professor, Dept. of Civil Engineering, Indian Institute of Science, Bangalore 560012, India. E-mail:
[email protected] Note. This manuscript was submitted on June 30, 2010; approved on March 4, 2011; published online on March 7, 2011. Discussion period open until January 1, 2013; separate discussions must be submitted for individual papers. This paper is part of the International Journal of Geomechanics, Vol. 12, No. 4, August 1, 2012. ©ASCE, ISSN 1532-3641/2012/4-439– 450/$25.00.
laboratory model studies. The calibrated numerical model can then be used for extensive parametric studies. This paper describes some of the physical model tests on geotextile reinforced soil retaining wall models subjected to dynamic loading conditions through uniaxial shaking tests. Numerical simulation of these shaking table tests is performed using a twodimensional, explicit dynamic finite difference program Fast Lagrangian Analysis of Continua (FLAC) (FLAC 2008). The formulation of the numerical model and steps in the analyses are also described. The results from the numerical simulations are verified using experimental observations. The calibrated model facilitated parametric studies of the reinforced soil retaining walls to better understand the individual effects of various parameters governing the behavior of reinforced soil retaining walls.
Background Dynamic behavior of reinforced soil retaining structures has been the subject of several researchers for the past three decades (Richardson and Lee 1975; Cai and Bathurst 1995; Ling et al. 1997; Bathurst and Hatami 1998; Matsuo et al. 1998; Perez and Holtz 2004; Nova-Roessig and Sitar 2006; Won and Kim 2007; Huang et al. 2008; Krishna and Latha 2009). Bathurst et al. (2002) summarized many studies related to seismic aspects of geosynthetic reinforced soil (GRS) walls and reviewed the work associated with the properties of cohesionless soil, geosynthetic reinforcement, and facing components under cyclic loading. As different types of reinforced soil walls are used in practice, different researchers worked on different types of walls. Different types of physical model studies are reported in the literature for seismic and/ or dynamic studies, such as the tilting table test, shaking table test, dynamic centrifuge test, and full-scale tests. Nova-Roessig and Sitar (2006) summarized experimental studies of seismic response of reinforced soil walls and slopes. Recent studies in this area
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include Perez and Holtz 2004; El Emam and Bathurst 2004; Ling et al. 2005; Saito et al. 2006; Huang et al. 2008; Krishna and Latha 2007, 2009; Ling et al. 2009; Sabermahani et al. 2009; and Yang et al. 2010. Despite many problems associated with the modeling of reinforcement structural elements and their interacting behavior with the neighboring soil, numerical and analytical studies on reinforced soil walls progressed well along with their physical model tests. Many researchers worked numerically and/or analytically on the static performance of reinforced soil retaining walls and soilstructure interaction problems (Jewell et al. 1984; Schmertmann et al. 1987; Hird and Kwok 1989; Berg et al. 1989; Karpurapu and Bathurst 1992; Rowe and Ho 1997; Zornberg et al. 1998; Rowe and Skinner 2001; Ling and Leshchinsky 2003; Hatami and Bathurst 2005, 2006). However, limited studies related to the dynamic behavior of these structures are reported in the literature. Yogendrakumar et al. (1992) performed dynamic finite-element analysis of reinforced earth walls using an iterative equivalent linear elastic approach and an incremental elastic approach. The response of the walls was compared with the tests conducted by Richardson et al. (1977). The results were in good agreement for actual and model responses using incremental loading. Cai and Bathurst (1995) presented the results of finite-element analysis of the dynamic response of a GRS retaining wall that was constructed with dry-stacked modular concrete blocks. It was observed that the relative displacement, dynamic tensile forces in reinforcement, and interface shear forces between modular units increased with the duration and magnitude of base excitation during simulated seismic events. Bathurst and Cai (1995) presented pseudostatic seismic analysis for limit equilibrium stability analysis of geosyntheticreinforced segmental retaining walls. Lindquist (1998) conducted a series of parametric numerical analyses using the explicit finite difference program FLAC to investigate the influence of various input parameters on the seismic behavior of geosynthetic reinforced slopes. Bathurst and Hatami (1998) investigated the influence of reinforcement stiffness, reinforcement length, and base boundary conditions on the seismic response of an idealized 6-m-high GRS retaining wall constructed with a very stiff continuous facing panel using FLAC. Hatami and Bathurst (2000) discussed the influence of a number of structural design parameters on the fundamental frequency of reinforced soil retaining wall models in the light of numerical simulations carried out using FLAC. Lee et al. (2003) examined the case histories and laboratory studies related to the seismic performance of GRS walls and carried out numerical simulations on the walls in FLAC. In these simulations, backfill material was modeled using Mohr-Coulomb material coded with a hyperbolic soil modulus model. Paulsen and Kramer (2004) developed a practical model for the estimation of permanent displacement of reinforced slopes subjected to earthquake loading. Kramer and Paulsen (2004) discussed the performance-based design concepts for the reinforced soil slopes and illustrated the applicability of the developed practical model. Ling et al. (2004) analyzed the dynamic behavior of GRS retaining walls using an advanced generalized plasticity soil model and bounding surface geosynthetic model in conjunction with a dynamic finite-element procedure. El-Emam et al. (2004) presented numerical simulation of experimental shaking table studies on full-height propped panel reinforced soil retaining wall models using FLAC. Vieira et al. (2006) also used FLAC to study the seismic response of GRS walls. Huang et al. (2009) performed a numerical study to investigate the response of full-scale reinforced soil walls during construction and surcharge loading using three different constitute models: linear elastic-plastic Mohr-Coulomb, modified Duncan-Chang hyperbolic model, and Lade’s single
hardening model, implementing all in FLAC. They concluded that the modified Duncan-Chang model was a good compromise between prediction accuracy and availability of model parameters from conventional laboratory testing. Lee et al. (2010) presented numerical simulation of GRS walls under seismic shaking using LS-DYNA, a finite-element computer code (Lee et al. 2010). Huang et al. (2010) used a FLAC model with the Duncan-Chang hyperbolic model to investigate the influence of toe restraining conditions on the performance of segmental reinforced soil walls. Recently, the finite difference method-based program FLAC became popular for modeling the performance of reinforced soil walls because of its excellent capability to model geotechnical engineering stability problems and its extended programming ability. Many researchers who worked on the performance of reinforced soil structures and other geotechnical engineering problems under both static and dynamic conditions used FLAC and proved its caliber for the same conditions (e.g., Bathurst and Hatami 1998; Lindquist 1998; Vieira et al. 2006; Hatami and Bathurst 2006; Zarnani and Bathurst 2008, 2009; Huang et al. 2009, 2010). Therefore FLAC is adopted for numerical simulations of shaking table tests.
Physical Model Tests Physical model tests conducted in the rigid perspex container by Krishna (2008) and Krishna and Latha (2009) were adopted as the reference case models for developing the numerical model and are briefly described here. A computer-controlled, hydraulically driven single degree of freedom (horizontal) shaking table with a loading platform of 1 × 1 m size and payload capacity of 1 ton was used in the experiments. Models of retaining walls were constructed in a perspex box (size 1;100 × 500 mm in plan and 800 mm deep) with geotextile reinforcement using the wraparound technique with dry sand backfill. The test wall was constructed to a size of 750 × 500 mm in plan and 600 mm height (H). The model retaining wall was constructed in lifts, each lift (150 mm) being reinforced with a layer of geotextile and wrapped at the facing for a length of 150 mm using wooden plank-formwork for each lift. Each model retaining wall was instrumented with accelerometers and pressure sensors at different locations within the backfill soil. To measure the horizontal displacements, three noncontact ultrasonic displacement transducers (USDTs) were positioned at different elevations along the facing. Figs. 1 and 2 show the schematic diagram and picture of the wrap faced wall, respectively, as reported by Krishna and Latha (2009). The response of the reinforced retaining walls with the variation in the number of reinforcing layers was monitored. In all of the tests, the length of reinforcement (Lrein ) was kept as 420 mm, which corresponds to the Lrein ∕H ratio of 0.7. After completion of all lifts up to full height of the wall (H, 600 mm), a nominal surcharge of 0.5 kPa in the form of concrete slabs was applied at the top. After the support removal and positioning of ultrasonic displacement transducers, each model wall was subjected to 20 cycles of sinusoidal seismic excitation corresponding to 0.2 g acceleration at 3 Hz frequency. Data from different instrumentations were obtained through a data acquisition system associated with the shaking table facility during the seismic excitation. Backfill Material The backfill material used was locally available poorly graded dry sand. The maximum and minimum dry unit weights for the sand were reported as 17.66 and 14:03 kN∕m3 , respectively, and the specific gravity of the sand was determined as 2.64. To achieve uniform density, sand was placed in the perspex box using the
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T-shape bracket made up of L-section
Surcharge (concrete slabs, 0.5 kPa)
U3
P4
U2
P3
A3 Lrein
800
Perspex Box sv = 150
P2 A1
z
Shaking table
P1
350
A0
750 All dimensions are in mm
Fig. 1. Schematic diagram of model wall configuration and instrumentation; USDT, ultrasonic displacement transducers (data from Krishna and Latha 2009)
Table 2. Properties of Geotextile Parameter Breaking strength Elongation at break
Direction
Value
Warp Weft Warp Weft
55.5 kN/m 46.0 kN/m 38% 21.3% 1 mm 230 g∕m2
Thickness Mass per unit area
Results
Fig. 2. Finished wrap-faced four layers model wall in perspex container
pluviation (raining) technique. The average unit weight and relative density achieved were within the range of 16:08–16:20 kN∕m3 and 62–65%, respectively, for the same height of fall. Other index properties were reported as per Indian Standard (IS: 2720 are shown in Table 1. Reinforcement Woven geotextile was used as the material for reinforcing the sand in the tests. This was a polypropylene multifilament woven fabric. The individual multifilaments were woven together to provide dimensional stability relative to each other. The properties of the reported geotextiles are shown in Table 2. Table 1. Index Properties of the Backfill Material Parameter
Value
emin emax D-10, mm D-50, mm Coefficient of curvature (Cc ) Uniformity coefficient (Cu )
0.467 0.846 0.174 0.512 1.054 3.553
Model walls with test codes WT33, WT37, and WT43 were constructed with 4, 3, and 6 layers of reinforcement, respectively, and were considered for the numerical modeling. More details about the model preparation and testing procedure are given in Krishna (2008) and Krishna and Latha (2009), and are omitted here for brevity. Typical results obtained from the physical model tests are shown in Figs. 3 and 4. Fig. 3 shows the variations of horizontal displacements, at different elevations corresponding to U1, U2, and U3 locations for the model wall (WT43) with a six-layer configuration, with number of cycles. Fig. 3 shows that the 14
Horizonatal displacement, mm
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Geotextile reinforcement A2
H=600 U1
P: Pressure sensors A: Accelerometer U: USDT
Dry sand back fill
U1 U2 U3
12 10 8 6 4 2 0 0
5
10
15
20
25
Number of cycles
Fig. 3. Typical displacement variation with number of cycles: physical model tests
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Accelerations at different elevation, g
0
5
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A3
Numerical Modeling
A2
Numerical models to simulate shaking table tests were developed using the computer program FLAC. FLAC is an explicit, dynamic, finite difference code based on the Lagrangian calculation scheme. Various built-in constitutive models are available in FLAC and can be modified by the user with minimal effort through FISH programming code. FLAC also provides some built-in structural elements, which can be used as reinforcement or structural supports, and interface elements as well (FLAC 2008).
A0
Numerical Grid
20
25
Number of cycles
Fig. 4. Typical accelerations variation with number of cycles: physical model tests
displacements increase nonlinearly with an increase in the number of cycles of seismic excitation. Further higher displacements at higher elevations are noted. Variation of accelerations with number of cycles at different elevations corresponding to A0, A2, and A3 locations are presented in Fig. 4 for the model wall (WT43) with six layers of configuration. It is observed that the acceleration recorded at 600-mm elevation (A3) is amplified to about 1.22 times of the base acceleration, whereas the acceleration at the 300-mm elevation (A2) is amplified to about 1.08 times to the base acceleration. Fig. 5 presents the comparison among the responses of wrapfaced model walls with different reinforcing layers in terms of horizontal displacements, acceleration amplifications, and incremental pressures at the end of 20 cycles of dynamic excitation. Fig. 5 shows that the displacements decrease with the increase in number of reinforcement layers. However, acceleration amplifications are not affected significantly. Incremental pressures also decrease with increasing reinforcing layers; nevertheless, their variations along the height of model wall are not consistent. 600
A 600-mm-high and 750-mm-long grid is considered to represent the model wall in plan strain analysis. This whole grid is discretized into 500 small zones in x and y directions. A nonyielding region was necessary at the right end because FLAC does not allow a freefield boundary to be in contact with yielded material. Hence, a nonyielding zone is considered at the end of the wall grid. A smooth interface is considered to facilitate the backfill material to slide along the nonyielding zone that simulates the actual physical model. A rigid nonyielding zone is considered at the base of the wall model that simulates the base of the shaking table. Fig. 6 shows the numerical grid considered to simulate the reinforced soil retaining wall model along with the rigid container boundary and base shaking table. The construction sequence in the numerical model grid is followed similar to that of the physical model (i.e., building the wall stage wise with front lateral support), applying the surcharge pressure and removal of supports after building up to the full height. The numerical grid is solved for equilibrium in every stage of the construction process. The typical displaced profile of the wrap-faced retaining wall at the end of construction to the full height is shown in Fig. 7. Backfill Material Backfill sand is modeled using Mohr-Coulomb material elements coded with the hyperbolic soil modulus model. The properties required for a Mohr-Coulomb material are mass density, shear, and bulk moduli (or Young’s modulus and Poisson’s ratio), friction angle, and dilation angle. Although the modulus is supposed to be updated as per the hyperbolic model, a representative modulus is assigned for initialization. Friction angle and dilation angle of
600
(b)
(a) 500
400
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200
Test Code WT33 WT37 WT43
500
100
Layers 4 3 6
300
10
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30
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50
Horizontal displacement, mm
300
200
100 100
0 0
Layers 4 3 6
400
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Test Code WT33 WT37 WT43
Test Code WT33 WT37 WT43
(c)
Layers 4 3 6
Elevation, mm
500
Elevation, mm
Elevation, mm
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0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3 0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3 0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3
60
0 0.0
0.5
1.0
1.5
Acceleration amplification
2.0
0
1
2
3
4
5
Horizontal incremental pressure, kPa
Fig. 5. Response of wrap-faced walls with different reinforcing layers at the end of seismic excitation: (a) displacement profiles; (b) acceleration amplifications; (c) incremental pressures 442 / INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / JULY/AUGUST 2012
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750
Surcharge
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Very Stiff back
pressure dependent, especially for granular soils. Moduli of granular soils increase with the increase in confining pressure. To include the effect of confining pressure on soil modulus during construction, the modified hyperbolic soil modulus model (Duncan et al. 1980) is introduced into the FLAC Mohr-Coulomb material model. The stress-dependent modulus is calculated as per Eq. (1) n Rf ð1 sin ϕÞðσ1 σ3 Þ 2 σ Et ¼ 1 K:Pa 3 ð1Þ 2ðc: cos ϕ þ σ3 sin ϕÞ Pa
600
Reinforcement Layers
Wrapped Reinforcement
Stiff bottom (shake table) 420
All dimensions are in mm
Fig. 6. Numerical grid considered for reinforced soil retaining wall model
750
Very Stiff back
600
Reinforcement Layers
Stiff bottom (shake table) 420
where Et = the deformation modulus of the soil; Rf = the failure ratio; K and n = Duncan model parameters; Pa = the atmospheric pressure; ϕ = the friction angle of the soil; c = the cohesion; σ1 = the effective vertical (overburden) pressure; and σ3 = the effective confining pressure. Eq. (1) is incorporated into a FISH subroutine that updates the soil modulus according to the stress conditions of the soil elements. The coefficients of the hyperbolic model (Rf , K, n) are calculated from the triaxial test results as per Duncan et al. (1980). Tangent elastic modulus (E t ) of the backfill soil and, therefore, shear and bulk moduli are updated after each 10 calculation steps by Eq. (1), until removal of the supports is started. Some studies on numerical modeling of reinforced soil retaining walls suggested the use of plane strain soil properties for the analysis of geosynthetic reinforced walls (Zornberg and Mitchell 1993; Hatami and Bathurst 2005). Because the stress-strain response of soil under plane strain loading conditions is different (higher modulus) from that under triaxial conditions, Lee (2000) proposed to increase the modulus number K obtained from the triaxial test data by 100% to account for the large values of the plane strain soil moduli, keeping the failure ratio (Rf ) and modulus exponent (n) the same. This same proposal was adopted by several other researchers for studies on GRS walls (Hatami and Bathurst 2005 and 2006). Also, in the present analysis, the modulus number obtained from the triaxial tests is increased by 100% to account for the plane strain loading. It should be noted that the constitutive model adopted in the simulations do not account for the critical state concepts and dynamic cycles of loading, unloading, or reloading. As the target physical models’ behavior is reasonably within the working conditions, the use of a simple constitute model can be reasonably justified. The damping ratio of 5% is used for the soil element during dynamic analysis. This damping value is adopted in the numerical simulations as a local damping value because it is frequency independent and is an approximate way to include hysteretic damping (FLAC 2008).
Fig. 7. Typical displaced profile of numerical grid at the end of construction
Reinforcement (Geotextile)
backfill material are adopted as 45° and 15°, respectively, based on the triaxial and direct shear tests carried out on the test sand at 63% relative density. As the expected stress levels in the model walls (0.6 m high) were low, the confining pressures used for the triaxial tests to determine the internal friction angle of the backfill materials were within the range of 10–50 kPa (10, 20, 30, and 50 kPa). During the construction of the retaining wall, the backfill material is placed and compacted layer by layer. As the height of the wall increases, the confining pressures in the finished lifts increase. At the end of construction, the lower part of the wall has a higher confining pressure, and the upper part of the wall has lower confining pressure. This difference in confining pressures at different elevations of the wall has a very important effect on the performance of the reinforced soil walls, because moduli of soil are actually
Geotextile layers are modeled using structural beam elements in FLAC. Beam elements are two-dimensional elements with three degrees of freedom (x-translation, y-translation, and rotation) at each end node. In general, the beam is assumed to behave as a linearly elastic material with both the axial tensile and compressive failure limit. Because beam elements are attached to the subgrids via interface elements to simulate the geotextiles, interface elements are attached to both sides of beam elements to simulate the frictional interaction of the reinforcement with soil. By assigning a zero moment of inertia to the beam, it will act like a flexible member that takes no moments (FLAC 2008), which can simulate the geotextile behavior. The required input parameters for the beam elements in FLAC are (1) elastic modulus, (2) cross-sectional area, (3) second moment of area (commonly referred to as the moment of inertia, “0” to model geotextiles), (4) axial peak tensile yield strength, (5) axial
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Interface Properties The interfaces between dissimilar materials were modeled as linear spring-slider systems with interface shear strength defined by the Mohr-Coulomb failure criterion. Three types of interfaces are used in the present model: (1) interface between the backfill soil and reinforcement (INT1); (2) interface between the two reinforcement surfaces (INT2); and (3) interface between stiff back and/or bottom and backfill soil (INT3). A typical interface requires the following properties: normal stiffness (kn ) and shear stiffness (k s ) in units of stress; friction angle (degrees); and tensile strength (t bond ) (optional). Further, the interface can be assigned as glued to avoid slip or separation. It is recommended in FLAC that the values for normal and shear stiffness of the interface should be set to ten times the equivalent stiffness of the stiffest neighboring zone (FLAC 2008). The normal and shear stiffness values are approximated based on the apparent stiffness (expressed in stress-per-distance units) of a zone in the normal direction obtained from Eq. (2) (FLAC 2008) K þ 43 G Apparent stiffness ¼ max ð2Þ Δzmin where K and G = the bulk and shear moduli, respectively; and zmin = the smallest width of an adjoining zone in the normal direction. For simplicity, the same values of 1e7 and 1e5 kPa as normal and shear stiffness values, respectively, are used for all the three interfaces. The interfaces INT1 and INT2 are declared as glued, with a friction angle of 40°, to prevent it from sliding or opening along. In contrast, INT3 is allowed to slide without any friction. Table 3 shows the typical material properties used to model the backfill material and other nonyielding zones. Boundary Conditions Boundary conditions for the numerical model are assigned to represent the actual experimental boundary conditions. The farend boundary of the backfill is fixed in the horizontal direction as shown in Fig. 6, representing the rigid end of the perspex container. The bottom boundary is completely fixed (in both horizontal and vertical directions), matching the shaking table and the container bottom (Fig. 6). The facing of the model wall is fixed in the horizontal direction during the construction of layers up to the total height and applying surcharge load, representing the temporary supporting system during wall construction in the laboratory experiments. After complete building up of the total wall, these fixed boundary face regions are freed stage by stage to represent the support removal in physical model tests. After the support removal for the total height of the wall and obtaining the equilibrium state, dynamic boundary conditions are applied to the model wall in the form of velocity in horizontal direction (uniaxial shaking) to both the stiff bottom and stiff back regions using a FISH function. The corresponding velocity in the vertical direction is assigned as null to ensure that the stiff bottom and back should not move in the vertical direction.
Table 3. Material Properties Used in Numerical Simulations Soil properties kg∕m3
Mass density, Poisson’s ratio Friction angle, degrees Dilation angle, degrees Hyperbolic properties for Duncan's model Atmospheric pressure (kPa ) Modulus number (K) Modulus exponent (n) Failure ratio (Rf ) Reinforcement (geotextile) properties Mass density, kg∕m3 Stiffness, kN∕m Area, m2 Moment of inertia, m4 Tensile yield strength, kPa Compressive yield strength, kPa
101.3 1660 0.678 0.9 0.23 150 0.001 0 55000 0
Reinforcement and soil (INT1), reinforcement and reinforcement (INT2) Normal stiffness (k n ), kPa Shear stiffness (ks ), kPa Interface friction, degrees Soil and nonyielding zone (INT3) Normal stiffness (k n ), kPa Shear stiffness (ks ), kPa Interface friction, degrees
1:00E þ 07 1:00E þ 05 40 1:00E þ 07 1:00E þ 05 0
Figs. 8 and 9, respectively. In comparison with Figs. 3 and 4, Figs. 8 and 9 present the typical results from numerical simulations similar to results from the physical model tests, confirming the ability of the numerical model in capturing the behavior of the physical model tests. Further, validation of the numerical model is presented in Fig. 10, which compares the response of the model wall in terms of displacements, acceleration amplifications, and incremental 25
20
15
10
Elevation 240 mm 390 mm 540 mm
5
0 0
Typical Results and Validation
1.63 0.3 45 15
Interface properties
Horizontal displacement, mm
compressive yield strength (0 to model geotextiles), and (6) density. Properties of geotextile beam elements used in the numerical analyses are modulus ¼ 150;000 kN∕m2 (J ¼ 150 kN∕m as obtained from the wide width tension test) and area ¼ 0:001 m2 , which were identical to geotextile properties used in physical model tests.
1
2
3
4
5
6
7
Time, sec
Typical results obtained from the numerical model tests in terms of displacement-time and acceleration-time histories are shown in
Fig. 8. Typical displacement histories obtained in numerical simulation
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Acceleration, g
and physical models with three layers of reinforcement for different reinforcement lengths. Two different reinforcement lengths, Lrein ∕H as 0.7 and 1.0, are considered, and the walls are subjected to base excitation of 0.2 g acceleration and 3 Hz frequency. Although the results from the numerical analysis do not exactly match the results from physical model tests, the trends are similar as observed from the figures. Comparison between the results from physical and numerical models showed that the numerical model is able to simulate the physical model shaking table tests on wrap-faced reinforced soil walls reasonably well.
A3
A2
A1
A0
Sensitivity Analysis 0
1
2
3
4
5
6
7
Time, sec
Fig. 9. Typical acceleration histories obtained in numerical simulation
pressures for the model wall with 4 layers of reinforcement at the end of 20 cycles of dynamic excitation of 0.2 g acceleration at 3 Hz frequency. Fig. 10 provides reasonable comparison between the results from the physical and numerical models to validate the numerical model in simulating the physical model shaking table tests on wrap-faced reinforced soil walls. Fig. 11 presents the response of different wrap-faced reinforced numerical model walls with different numbers of reinforcing layers in terms of horizontal displacements, acceleration amplification, and incremental pressures. Fig. 11 shows the similar behavior of decreasing displacements with an increase in reinforcement layers and the insignificant effect of acceleration amplifications as that of physical model walls. Fig. 11 shows that the numerical model captures the response of the walls with the variation in the number of reinforcement layers reasonably well. Similarly, Figs. 12 and 13 compare the displacement profiles and acceleration amplifications, respectively, for the numerical
Sensitivity analysis is performed to understand the response of the numerical model for the variation of different parameters. Table 4 summarizes the different material properties that varied in the numerical simulations for the sensitivity analysis. Figs. 14–17 show the sensitivity of the numerical model to the variation of friction angle and dilation angle of backfill soil, stiffness (modulus) of reinforcement material, and the stiffness properties of reinforcement-soil interface, respectively. All the numerical model walls were subjected to 20 cycles of sinusoidal base excitation with 0.2 g acceleration at 3 Hz frequency. Fig. 14 presents the response of the numerical model walls of identical model configuration and parameters, except for the different backfill friction angle values of 30° and 52°, which represented very loose and very dense backfill soils, respectively, with reference to the backfill soil having a friction angle of 45°. From the numerical simulations, it is noted that the model wall with loose backfill soil with a friction angle of 30° could not complete the 20 cycles of excitation and failed with excessive deformation, as shown in the Fig. 14(a). A slight decrease in the top displacement and a little increase in the acceleration amplification factors were observed for the model wall with a 52° friction angle (very stiff backfill). Fig. 15 presents the variation of model response of the numerical models with different backfill dilation angles of 15° (reference case), 20°, and 10°. Fig. 15 shows that the acceleration amplification factors and incremental pressures are
4layer wall, 0.2g, 3Hz Flac simulation WT33 Experiment 600
(a)
(b)
600
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(c)
500 500
Elevation, mm
400
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Elevation, mm
400
Elevation, mm
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0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3 0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3 0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3 0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3
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Fig. 10. Comparison of response of experimental and numerical [Fast Lagrangian Analysis of Continua (FLAC)] models of four layer wrap-faced reinforced soil walls: (a) displacement profiles; (b) acceleration amplifications; (c) incremental pressures INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / JULY/AUGUST 2012 / 445
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unaffected. However, the maximum horizontal displacements for model walls with 20° and 10° dilation angles are observed to be 15.5 and 33.5 mm, respectively, whereas the displacement is 20.6 mm for the model with 45° dilation angle. Figs. 14 and 15, together, emphasize the role of the backfill compactness on the behavior of the reinforced soil retaining wall. Although the denser backfill may amplify the accelerations slightly, the benefit in reducing the lateral displacements is very significant. Fig. 16 exhibits the response of reinforced soil numerical model walls with different reinforcement stiffness values: 150, 75, and 20 kN∕m. Fig. 16 shows a little decrease in the horizontal displacement from 23 to 19 mm for an increase of reinforcement stiffness from 20 to 150 kN∕m, whereas the acceleration amplification factors and incremental pressures are affected insignificantly. The effect of soil-reinforcement interaction properties was presented in Fig. 17 in terms of reinforced soil wall response with different interface stiffness values. The normal stiffness values of 1 × 107 , 1 × 106 , and 1 × 105 kPa were adopted in different numerical model walls. Very significant changes in the model response are
Fig. 13. Acceleration amplifications for different lengths of reinforcement; FLAC, Fast Lagrangian Analysis of Continua; RMSA, root mean square acceleration
Table 4. Material Properties Used for Sensitivity Analysis Parameter Friction angle, degrees Dilation angle, degrees Reinforcement stiffness, kN∕m Tensile yield strength, kPa Normal stiffness (kn ), kPa Shear stiffness (kn ), kPa
Values 45, 35, 52 15, 10, 20 75, 20, 150 55,000, 20,000, 150,000 1:00E þ 07, 1:00E þ 06, 1:00E þ 05 1:00E 02 kn
observed in Fig. 17 for the change in the interface stiffness values. Reinforcement yield strength is also varied in some simulations, and it is observed that for the range of strength values (55,000, 20,000, and 150,000 kPa) and the model size, the response is similar and the effect of reinforcement yield strength is not prominent for the applied dynamic loading. From the results observed in Figs. 16 and 17, it can be noted that soil-reinforcement interaction
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Fig. 15. Sensitivity of the numerical model with respect to dilation angle of backfill soil material: (a) displacement profiles; (b) acceleration amplifications; (c) incremental pressures; RMSA, root mean square acceleration
properties affect the model wall behavior more significantly than the reinforcement property alone. Figs. 14–17 show that the model is sensitive to different material properties and efficient in capturing the behavior of the model wall under seismic excitation. Among the different parameters considered in the sensitivity analysis, friction and dilation angle of backfill material and stiffness properties of geotextile-soil interface (INT1) are the most affecting parameters on the model response in terms of displacements, accelerations, and incremental pressures. It is established from this analysis that the numerical model is sensitive to different material properties.
Conclusions Modeling of shaking table tests on wrap-faced reinforced soil retaining walls is discussed and presented. The effect of number of reinforcement layers is studied through different physical model tests. Methodology adopted in the development of numerical models to simulate the physical model tests is explained along with the validation of a numerical model with the physical model. Results from the dynamic tests on physical and numerical models of geotextile-reinforced wrap-around soil retaining walls are presented and compared. The numerical model developed is
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Fig. 17. Fig. 17. Sensitivity of the numerical model with respect to stiffness properties of reinforcement-soil interface: (a) displacement profiles; (b) acceleration amplifications; (c) incremental pressures; RMSA, root mean square acceleration
reasonably good in simulating the dynamic response of wrap-faced wall models. It is established from the sensitivity analysis that the developed numerical model is sensitive to different material properties. Among the different parameters considered in the sensitivity analysis, friction and dilation angles of backfill material and stiffness properties of geotextile-soil interface are the most affecting parameters on the model response in terms of displacements, accelerations, and incremental pressures. Backfill soil with higher friction angle and dilation angle (a denser backfill) results in better seismic performance. It is also observed that the effect of soil-reinforcement interaction parameters is more prominent than
the reinforcement parameters, like stiffness and/or modulus alone. To conclude, the design and the construction of a reinforced soil retaining wall should ensure a denser backfill that results in better soil-reinforcement interaction for effective seismic performance.
References Bathurst, R. J., and Cai, Z. (1995). “Pseudo-static seismic analysis of geosynthetic reinforced segmental retaining walls.” Geosynth. Int., 2(5), 787–830.
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