Chapter 5. Studies on Rigid-Faced Walls
5.2 Developement of Numerical Models of Rigid-Faced Walls
5.2.2 Development of numerical grid
The finite difference programme, FLAC3D, is used for development of numerical model of rigid-faced reinforced soil walls. Physical model construction and testing sequence, implemented in experimental procedure, are followed in development of numerical model. The shaking table is first generated as rigid zone of 800 mm long and 50 mm thick. The backfill soil is built up in layers with same sequence as physical model and reinforcements are placed on each layer. The model grid of 25 mm wide and 600 mm high is considered to simulate the rigid wall and fixed at the bottom against lateral sliding. A grid of size 600 mm high and 750 mm long is generated to represent the backfill of rigid-faced retaining wall. Though the width of physical model is 500 mm, model of 100 mm lateral dimension is considered
Fig. 5.2Typical horizontal displacements histories of unreinforced wall with number
Fig. 5.3Typical acceleration hist
ypical horizontal displacements histories of unreinforced wall with number of cycles (after Krishna and Latha, 2009)
ypical acceleration histories of reinforced wall with number of cycles (after Krishna and Latha, 2009)
ypical horizontal displacements histories of unreinforced wall with number
ories of reinforced wall with number of cycles (after
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for ease of model solving in numerical simulation. The entire grid, representing shaking table, rigid wall and backfill is divided in number of zones of 25 mm each.
Four layers of geotextile reinforcement of length (Lrein) 420 mm, (Krishna and Latha 2009) are used in the model. Various interfaces are also considered for proper interaction between dissimilar elements. Fig. 5.4(a) shows the numerical grid considered to simulate the rigid-faced retaining wall.
The construction sequence followed in the numerical model generation is similar to that of physical model. The foundation zone is first brought to static equilibrium before placing the rigid wall and backfill. The wall is then placed over the foundation zone and brought to static equilibrium. Horizontal movement of the wall is restricted to represent temporary support during construction. The backfill model is generated in equal lifts and reinforcement is placed after each lift. The reinforcements are extended to the wall and attached with the wall to represent rigid connection between wall and reinforcement. The structural elements in FLAC3D interact with main grid only at structural nodes (Itasca 2008). The geogrid is rigidly attached to the wall. But at the interface between wall and soil, the geogrid nodes may arbitrarily select nodes either from wall or from soil. So the finer geogrid is considered for wall portion, so that more structural nodes interact with wall elements. The model is brought to static equilibrium after each lift. A surcharge of 0.5 kPa is applied at top and model is brought to static equilibrium. The supports of the walls are removed after the end of construction.
The material properties for backfill soil and reinforcements are assigned based on their respective constitutive models as described in Section 3.3.1 and Section 4.2.2.
The rigid wall is modeled as elastic material. The elastic modulus, Poisson’s ratio and density of concrete are considered for numerical simulation. Two different interfaces
are considered in the present model: interface between backfill soil and wall; and interface between soil and reinforcement. The interface between the backfill soil and wall is controlled by relative interface movement, that depend on interface normal stiffness (kn) and shear stiffness (ks) as explained in Section 3.3.4. The interface between the soil and reinforcement is modeled as linear spring-slider system (Section 3.3.4 and Section 4.2.2).
Fig. 5.4 Grid adopted for numerical simulation (a) static simulation (b) dynamic simulation
Boundary conditions
The boundary conditions applied to the model represent the actual boundary of the physical model tests (Krishna and Latha, 2009). The bottom boundary is completely fixed in vertical direction to represent the rigid boundary between the model wall and shaking table. The far end boundary elements are fixed in x direction to represent the fixed container. During the construction, the model wall is fixed in horizontal direction to represent the temporary facing support. The lateral boundaries are fixed in y direction to represent the lateral boundaries at the side of the physical model. After the completion of all the layers construction, and the model was brought to equilibrium, the facing boundaries are removed layer by layer representing the stage wise removal of temporary support. The boundary conditions after support removal are shown in Fig. 5.5.
(a) (b)
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Fig. 5.5 Boundary conditions of the model (not to scale) in X-Y plane (plan) and Z-X plane (side elevation)
During dynamic modeling, free field boundary is applied at far end. The free field boundary conditions are applied to the lateral boundary grid points automatically.
The cyclic hysteresis and damping are applied as described in Chapter 4. The dynamic excitation is applied at the stiff bottom in the form of velocity in horizontal direction (uni-axial shaking). The model considered for dynamic analysis with free field boundary is shown in Fig. 5.4(b).
Selection of grid size of model
Sensitivity analysis was carried out by considering three models with different grid sizes of 50 mm, 25 mm and 12.5 mm. The horizontal displacements after support removal, during static analysis, are 1.06 mm, 1.93 mm and 2.03 mm. The variation of horizontal displacements is within 5% for grid size of 25 mm and 12.5 mm. For dynamic analysis, the maximum range of frequency propagation for 25 mm and 12.5 mm grids are 38 Hz and 78 Hz, respectively (calculated for model with density 1600 kg/m3 and average shear modulus of 150 kPa as mentioned in Section 3.2.1). The grid size of 25 mm is adopted for numerical simulation by considering the speed of calculation.