Modelling and Numerical Simulation. Geomechanics of Failures. Plasticity and geomechanics. Plasticity and Geomechanics.
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Material properties are listed in Table 1. The prototype single pile is 0. The model has an inclination angle of 2 o model scale and is subjected to the predominantly 2Hz harmonic base excitation shown in Figure 14 with a peak acceleration of 0. The centrifuge test was simulated using the above-described three-dimensional finite element model. As it may be observed in Figure 13 b , the soil domain and the single pile were discretized using 3D node and 8-node brick finite elements, respectively. The finite element size in the mesh is limited to a maximum value in order to permit a good wave transmission see example of section 3.
A half mesh configuration is used due to symmetry considerations. The number of degrees of freedom in the mesh is The boundary conditions were i dynamic excitation was defined as the recorded base acceleration, ii at any depth, displacement degrees of freedom of the downslope and upslope boundaries were tied together both horizontally and vertically to reproduced a 1D shear beam effect, iii the soil surface was traction free, with zero prescribed pore pressure, and iv the base and lateral boundaries were impervious. A static application of gravity model own weight was performed before seismic excitation.
The resulting fluid hydrostatic pressures and soil stress-states served as initial conditions for the subsequent dynamic analysis. With a mild inclination of 2 o , model 3 attempts to simulate an infinite slope subjected to shaking parallel to the slope. However, it was noted that, in the centrifuge test, the soil surface gradually lost the slope and became level during the shaking phase.
To simulate such behavior of losing the surface slope, a horizontal component of gravity varying with time was applied to the finite element simulation. The load-time history of the applied horizontal gravity component was calculated based on the recorded lateral displacement at ground surface Lu et al. Figures 15 a - b displays the computed lateral displacements and pore pressure ratios, respectively, at the end of the analysis.
As it can be seen, liquefaction was reached down to a depth of 5. The Nevada sand layer remained liquefied until the end of shaking and beyond. Thereafter, excess pore pressure started to dissipate. The mild inclination of model 3 also imposed a static shear stress component due to gravity , causing accumulated cycle-by-cycle lateral deformation. The recorded and computed short-term and long-term excess pore pressure histories for two control points PP1 and PP2 at depths of 1 m and 5 m are compared in Figure 16 and Figure 17 , respectively.
Both computed and recorded results displayed a number of instantaneous sharp pore pressure drops after initial liquefaction. The numerical results obtained in the works of Lu et al.
The permanent lateral displacement of the ground surface after shaking is approximately cm. All lateral displacement occurred in the top 6.
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The top graph in Figure 18 shows the recorded and computed pile lateral displacement at the soil surface during and after shaking. The computed pile lateral displacement increased to 40 cm and decreased to approximately 8 cm at the end of shaking. The bottom slightly cemented sand layer, as indicated in the bottom graph, did not slide with respect to the base of the laminar box.
Lateral displacements at some other control points in the soil mass are also shown in Figure Figure 19 shows the profile of pile lateral displacements obtained with the present numerical model for the time in which the maximum lateral displacement occurs at the pile head. In the same graph are also depicted the pile displacement predictions according to some simplifying approaches based on the works of Valsamis et al.
All these references have used a methodology based on the subgrade reaction approach p-y method.
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As it may be observed, there is a great difference among all methodologies. Because it is true that major liquefaction does not necessarily takes place at the end of the shaking, in Figure 20 is depicted the liquefaction evolution measured by the r u factor at different time instants. As it may be observed, a dilatation zone appears close to the pile head blue color zones. At the end of the shaking after 25 seconds of analysis , liquefaction almost took place in the top liquefiable sand layer, thus reflecting a similar condition as established in the experimental work Lu et al.
Figure 21 shows the cycles of shear stress-strain histories in the soil mass for depths of 1. As it may be observed, the maximum shear deformation component expressed in percentage occurs for a depth of 1. As it was stated in the introduction section, liquefaction and associated shear deformation in the present example are considerable.
Figure 22 shows the shear stress- effective vertical stress paths during shaking for the soil zones located in the near field and free-field. As it may be inferred from the graphs, all soil samples have an initial effective vertical stress and a static shear stress value as a result of the initial conditions of the soil gravity load and due to the surface inclination. During shaking the effective vertical stress is almost reduced to zero for various soil depths due to soil liquefaction.
In order to show the potentiality of the present numerical model, a soil-structure interaction problem is studied. A steel frame building is supported by a group of concrete piles which are square and have a length and side length of The soil domain is defined by a region of The typical story height of the steel frame is 3 m and this story is composed of three and two spans of 3. The finite element mesh used in the analysis is shown in Figure 23 and it is formed by 8-node hexahedral finite elements for modeling the pile and cap, node hexahedral finite elements for modeling the soil domain, 8-node quadrilateral zero-thickness contact elements for modeling the soil-pile interface and 2-node truss elements for modeling the steel frame.
A half mesh configuration is used due to symmetry considerations and the number of degrees of freedom to solve is The structural steel properties used in the computations correspond to a W13x section with a specific weight of 7. The load is applied at the base of the model by using the E-W component of the Centro earthquake as shown in Figure The boundary conditions used in the example of section 3.
In Figure 25 is shown the evolution of the liquefaction potential factor r u for different time steps. As it may be observed, liquefaction starts after 4 seconds of analysis in the soil zones among piles. Thereafter, the liquefaction mechanism spreads out to the lateral edges of the soil domain. Figure 26 shows the lateral displacement histories at the pile cap and stories of the steel frame.
As it may be observed, the maximum lateral displacement at the cap is around 0. Because the soil zones among piles are almost liquefied and there is not exist a non-liquefiable surface layer, the soil zones surrounding the piles do not provide a rigid lateral support, thus pile lateral displacements increase considerably. In order to study the soil-structure effect in the problem, Figure 27 shows the axial force histories in truss elements for the case of the steel frame clamped to the ground directly fixed base and when the soil domain is included in the analysis flexible case.
It may be observed that both cases yielded considerably different axial forces in the elements with the absolute higher values associated to the flexible base condition. Precisely, Figure 28 shows the axial force histories in two representative elements namely element 1 and element 2 see Figure 23 of the steel frame for both supporting conditions.
As it may be observed, the axial forces in these elements are significantly different for the cases of rigid and flexible base support.
Thus, for the present example, the soil deposit must be included in the analysis. This result was expected since the soil mass is represented by a loose sand layer, which is not rigid at all. In this study, a computer program for the three dimensional finite element analysis of soil-structure systems was developed.
The numerical model uses the coupled dynamic field equation with the u-p formulation of Biot's theory for modeling saturated soils, while concrete caps and piles are modeled as monophasic materials. The superstructure can be modeled by using shell, solid and beam-column finite elements. The numerical model is firstly validated with some benchmarks found in the technical literature. Detailed comparison between numerical and experimental results for soil and soil-pile systems showed acceptable matching. Also, the numerical model was able to predict dilatation zones close to the pile heads, which characterize soil-pile systems involving liquefaction.
Only after validation processes have been successfully completed, the following parametric studies can be done with the aim of the present numerical tool. Numerical modeling and simulation can be used to predict the behavior of piles or pile groups embedded in fully saturated soils and thus used to improve design in terms of safety and economy. When liquefaction is involved in the analysis, a complex constitutive model capable of simulating dilatancy and cyclic mobility in the soil mass was proved to perform well. Potentiality of the numerical tool is shown by modeling a steel frame building supported by a group of concrete piles under seismic load.
The obtained results showed that the soil zones among piles have a high potential of liquefaction r u close to one. Also, axial forces in the steel frame elements are underestimated when the frame is considered to be clamped to the ground directly. Studies are in progress in order to improve the modeling of hysteretic damping in the soil.
Abdoun T. Modeling of seismically induced lateral spreading of multi-layered soil and its effect on pile foundations. API Brandenberg SJ. Behavior of pile foundations in liquefied and laterally spreading ground. Chaloulos Y.
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D, Karamitros D. Chatterjee K. Cubrinovski M. Cuellar, P. Pile foundations for offshore wind turbines: numerical and experimental investigations on the behavior under short-term and long-term cyclic loading. Jeremic B.
Numerical Analysis and Modelling in Geomechanics
Domain reduction method for soil-foundation-structure interaction analysis. Khodair Y. Kumari S. Leung K. Earthquake response of saturated soil and liquefaction, Ph. Lewis R.
Analysis of calculation models while solving geomechanical problems in elastic approach
Three dimensional finite element analysis of dynamic pile behavior in liquefied ground. Maheshwari B. McGann C. Three dimensional numerical modeling of dynamic saturated soil and pore fluid interaction. Pastor M. Taboada V. M, Dobry R. Experimental results and numerical predictions of model No 1. Proceedings of the International Conference on the Verification of Numerical Procedures for the analysis of soil liquefaction problems, California, United States.
Taiebat H. Tamayo J. Numerical simulation of soil-pile interaction by using the finite element method. B, Awruch A. Tasiopoulou P. Tokimatsu K. Valsamis A. I Numerical simulation of single pile response under liquefaction induced lateral spreading. I, Bouckovalas G. D, Chaloulos Y. Zienkiewicz O.
This is an open-access article distributed under the terms of the Creative Commons Attribution License. Services on Demand Journal. Abstract Modeling and simulation of mechanical response of structures, relies on the use of computational models. The variables u and p are interpolated by suitable shape functions N u and N p , respectively, in the following manner: 7. Using GN22 for the displacements u and GN11 for the pore pressure p , the following expressions are obtained: