جستجوی مقالات مرتبط با کلیدواژه « numerical modeling » در نشریات گروه « مهندسی زلزله »

The finite element method has been used comprehensively in traditional and academic works. The common finite element method is a powerful method in solving boundary value problems that transforms strong differential form equations into weak form equations using domain discretization. Even though the finite element method has sufficient accuracy in displacements, but calculating the stress field by FEM has low accuracy. This paper uses the modified element-free Galerkin method to solve some numerical elastostatics problems. At first, a one-dimensional elastic bar is considered, which is subjected to a volumetric force with linear changes along the length of the bar. A comparison between the original element-free Galerkin method, the modified element-free Galerkin method and the exact solution has been made to check the accuracy, efficiency and the required time cost. The presented study indicates that these mentioned methods have the same accuracy, but the modified EFG method can be very time-consuming compared to others, mainly when a large number of degrees of freedom is used with a large size of the support domain. The numerical solution of the modified and original element-free Galerkin methods is compared with Timoshenko’s analytical responses for the bending of an elastic beam. This comparison exhibits that modified and original methods have excellent agreements with the analytical ones in calculating displacement values. Despite the same accuracy in estimating the displacements, the calculation of the stress field indicates that the modified method is less accurate than the original method. It is shown that by increasing the number of degrees of freedom, the accuracy of the modified method for estimating the stress field improves. Increased degrees of freedom are used for introducing the domain of the beam. In this study accuracy of the stress solution in the modified EFG method is improved. However, the modified EFG method is yet more time-consuming than others. According to the results, the modified element-free Galerkin method can be nominated as a powerful mesh-free method based on moving least squares that has shape functions with interpolation properties. Having interpolator shape functions in this method makes it possible to combine it with other numerical methods and apply boundary conditions with less computational cost. The results exhibit that the displacement calculation error in the presented method was at most 5% compared to the analytical solution method. Also, the maximum error rate in the presented method for stress estimation was equal to 15%.

In a case study, behavior of an underground-railway tunnel of the Tehran metro subjected to tremendous explosive load was explored by numerical analysis. Blast wave propagation in the soil is studied by effective stress analysis in PLAXIS 2D finite element code. To assure reliability of the code in performing a robust dynamic calculation, Lamb Problem was modeled by the code and results were compared with analytical solutions, which was satisfactory. Due to the significant effect of the soil type and layering on the dynamic response of the buried structures in an explosive loading, care was taken in the study to resemble the real soil layering, relying on the available geotechnical investigations in the area. Based on the available data and also semi-empirical relations, HS Small soil model was calibrated to resemble soil behavior. In this regard, five parameters of density, elastic modulus, Poisson’s ratio, damping ration and layer thickness were carefully defined for each layer. Semi-empirical relationships were used to calculate soil dynamic shear modulus, which were larger than the static shear modulus. HS Small model has the ability to resemble the cyclic behavior of the soil by applying Masing’s rules in a load-unload-reload cycle. PLAXIS updates the stiffness matrix of the soil mass at each step of the analysis according to the strain and deformations that have been created in the soil, which increases the precision of the calculations. In this study, the Unified Facilities Criteria (UFC 3-340-03) manual was used to calculate the blast pressure. The weight of TNT explosive (charge weight) was considered 510 pounds (230 weight) in this regard. The type of explosion is assumed as an unconfined explosion, i.e., a surface burst. According to the UFC 3-340-03, the graph of changes of explosive pressure with time which is presented as a triangular pulse in the time domain, was defined in applied to the model geometry in the finite element code. Appropriate mesh dimensions relative to the transmitted wave-length in the numerical simulation play an important role in the precision of the results. Consequently, the frequency content of the pressure-time signal was probed in the frequency domain using the Fourier transform technique. To reduce the reflection of the waves from the model boundaries, viscous absorbent boundaries were defined in the model, as well as enlarging the model dimensions to reduce unwanted and unreal reflections from the boundaries of the model as much as possible.
After careful definition of the model geometry and loadings, both static and dynamic calculations were performed. The former simulated the construction of the underground tunnel, and the latter simulated the surface burst after tunnel construction, ignoring the crater caused by the explosion on the surface. The results show that the peak stress at the crown and bottom of the tunnel decreases as the soil density of the first layer increases, irrespective of static or dynamic values of the soil modulus. However, the stress values corresponding to the static parameters are greater than those of dynamic parameters. This comparison shows that if the static shear modulus values are preferred, the tunnel should be designed regarding larger stresses, which is not economical. Despite the decreasing effect of the first layer density on the stress magnitudes, the increase of the density of the second layer -that surrounds the tunnel- increases the stresses at the crown and bottom of the tunnel. The results also revealed that the effect of Poisson’s ratio of the soil on the tunnel's stresses are very small, but with the increase in the damping ratio, the amount of stress in the tunnel crown decreases dramatically. As the soil layers thicknesses increase, stress at the crown of tunnel decreases. These findings are useful to plan a safer design for crowded subway stations, regarding proper soil layering and properties

A growing body of evidence suggests that the possibility of nonlinear rocking oscillations can protect the structure from serious damage. One of the potential concerns about this design approach is the magnitude of residual settlement and maximum rotation. Several improvement techniques have been proposed to ameliorate the nonlinear behavior of rocking foundations based on the vertical factor of safety. Rocking systems with a large factor of safety against vertical load are more prone to toppling collapse under severe ground motions. This research explored the effectiveness of using soft walls next to a rocking foundation for mitigating seismic risk. The vital advantage of this improvement technique is that it is a feasible strategy for both new construction and existing structures.
The soil-foundation-structure system has been analyzed using the numerical finite element (FE) method that takes the material and geometric nonlinearities into account. In this case, the nonlinear response mainly involves the interaction between footing uplift and soil failure, which may induce additional (gravitational) aggravating moment (P-Δ effect).
In the first step, a three-dimensional (3D) numerical model has been constructed for the rocking foundation-soil system experiment. In order to verify the accuracy of the simulation, the numerical modeling and the experimental test results have been compared. The results of the centrifuge physical testing conducted were used to validate the numerical simulation. All FE analyses were performed in Abaqus software. This software has been utilized by a number of researchers to study complex soil-foundation–structure interaction phenomena.
Because the initial conditions play an important role in simulating geotechnical problems, a staged analysis procedure has been adopted. In the dynamic analysis stage, an incremental-iterative procedure was used to integrate the equations of motion. The Hilber-Hughes-Taylor algorithm was used to conduct the transient analysis phase. The modified Newton–Raphson method was employed to decrease the calculation cost needed for the great number of degrees of freedom of the model.
Finely refined 3D FE mesh was used to precisely reproduce the mechanism of bearing capacity failure and the rocking behavior. The soil medium and foundation were discretized into eight-node hexahedral continuum elements (C3D8 element type). Two-node linear beam elements were used to model the superstructure (B31 element type). A special surface-to-surface contact formulation between the foundation and soil was used for the realistic simulation of possible uplift and sliding of the foundation. Surface-to-surface contact can calculate contact stresses accurately by reducing the possibility of large-localized penetration of the two surfaces. The properties of the contact element were defined by the interface stiffness in the normal and the tangential directions.
Nonlinear soil behavior was modeled using a kinematic hardening model with the Von Mises failure criterion and associated plastic flow rule. This simplified constitutive model is applicable for the prediction of the undrained behavior of clay as normal pressure independent. In contrast to soil, the behavior of the structure-foundation model is assumed to be linear elastic. A parametric study was carried out to explore the sensitivity of the geometric design variables of the diaphragm wall, such as height and thickness on the behavior of the isolated foundation-soil system.
It should be mentioned that the values of model parameters were determined based on their practical feasibility. The distance of walls has been determined far from the edge of the foundation to avoid static bearing capacity failure.
The results showed that the placement of vertical soft walls next to the foundation could limit the transmitted forces onto the superstructure. This could be lessened the maximum motion of the structure and the following overturning moment of the foundation. Hence, adequate safety margins against toppling collapse could be easily achieved under strong motions.

In current modern cities, the use of buried pipelines in the conveying of vital fluids such as water, oil, and gas have become very important. Investigations on the behavior of the buried pipelines after the occurrence of the severe earthquakes have indicated that one of the primary sources of the failures of these kinds of linear structures were due to surface fault rupture. Therefore, if the buried pipelines are designed and implemented correctly, the permanent ground displacement due to the movement of the bedrock fault will not lead to such rupture of the pipes. On this basis, different researchers have concentrated their studies on investigating the interaction of pipe and soil during the permanent ground displacement. Due to the difficulty and cost of laboratory tests on this phenomenon, the number of available experimental data is very few. On the other hand, analytical studies have various limitations and complexities that have made it difficult for engineers to use these methods. In addition, numerical methods used to study the interaction of pipes and faults are mostly prepared for academic environments. These numerical approaches usually need the knowledge of soil or pipe advanced constitutive models and require the familiarity with mathematical parameters necessary for the convergence of the computational efforts.In order to investigate the behavior of buried pipes against faulting displacement, in this paper, a numerical method has been developed by combining finite difference and Newton multivariable techniques. The equilibrium equation of forces in x and y directions along with the equilibrium equation of bending moment for an infinite section of the pipe under the influence of the displaced soil pressure has been obtained first. Then the system of equations for all of the discretized nodes of a pipeline has been solved using the proposed hybrid method. The proposed method simultaneously considers the nonlinear behavior of pipes, soil equivalent springs, and large strains in the beam-spring model. In addition, to more precisely assess the shear factor in the beam behavior, the Timoshenko beam model has been applied to model the pipe.The validity of the proposed method has been performed using the results of a laboratory centrifuge test on HDPE pipe and 90° normal fault. In addition, this hybrid method is also validated with the results of a finite element numerical analysis on 70° normal fault and API5L-X65 oil transfer pipe. Comparison of the obtained results for different parameters such as longitudinal strains, settlement, and flexural bending of the pipes shows that the presented numerical method is very suitable in predicting the interaction behavior of pipes against dip-slip faults. At the same time, a lower computational effort has been required to arrive in the final answers. In addition, using the proposed numerical method, the effect of fault zone width with values equal to 0.001, 10, 30, 60, and 100 m on the behavior of a pipeline against a normal 70-degree fault has been investigated. The results of this study show that increasing the width of the fault zone significantly reduces the amount of tensile strain in the pipes. Also, increasing the width of the fault zone causes the pipe to rupture from two different points, while in the small fault width equal to 0.001 m, the pipe failure occurs only at one point. Maximum bending moment and pipe curvature also increased with decreasing fault width.

Failures caused by surface rupture in recent earthquakes emphasize the need to investigate fault-structurefoundation interaction while designing engineering structures and life lines in fault zones. Many civil projects, especially buildings on problematic soils (e.g. loose soils with low carrying capacity, high settleability and liquefaction, made grounds, and others), use micropiles in the sub-base to improve the soil and increase its carrying capacity. If such structures are positioned in fault zones, however, the interaction between the faulting and the micropiles located at the faulting zone is often neglected. Therefore, this paper used numerical modeling in Abacus to investigate the reverse fault-micropile interaction, and modeled and analyzed the three-dimensional soil, foundation and micropile system using the finite element method in Abacus. In this regard, a footing with an 11m length and width and a 91 kPa load (equivalent to a 9-floor building) was modeled atop a 15m-thick sandy soil layer. S set of 36 concrete micropiles with 20cm diameter, 10m length and 2m distance to each other were also used for investigating the base-fault-micropile interaction. The numerical analysis was validated using laboratory results. The ratio of the distance between the faulting and sub-base contact to base width (S/B) was the most important criterion used in this study, and the parametric study investigated the effect of the micropile foundation’s location relative to faulting after selecting the S/B parameter. Results show that the foundation and micropile response depends on their position relative to the fault, and responses to deviation or rupture propagation around the structure differ by structure position. The overall results show that the presence of micropiles does not significantly affect horizontal displacement control, resulting in a 10- 15% reduction in horizontal displacement compared to the no-micropile state for S/B>1.0. Micropiles are consistently effective for controlling vertical foundation displacement and reduce vertical displacement by about 60% compared to the non-micropile state. This is caused by the faulting’s contact with the micropile-foundation block, which makes it act as a retaining wall and leads to rupture diffraction, distribution, and diversion. However, results differ by foundation rotation in different conditions. Due to the residual stress between micropile rows in 0.9<S/B<1.5, the faulting-micropile interaction increases the foundation rotation in the micropile state by approximately 40% compared to the non-micropile state, that points to the inefficiency of micropiles in controlling foundation rotation when put in such a condition. Therefore, if the objective, importance, limitations and other criteria affecting engineering structure placement call for a mixed “foundation and micropile” structure adjacent to the fault, the position of the foundation with the micropile set relative to the faulting is a determinant factor of soil-faulting-micropile and foundation interaction results. Accordingly, investigating horizontal and vertical displacement as well as foundation rotation with S/B ratio changes can determine the optimal structure position relative to the fault and fault path and prevent damages.

Observations after the 1999 Turkey and Taiwan earthquakes and the 2008 China earthquake have indicated that the structures experience different levels of damages induced by faulting dislocation. Numerous studies have been conducted on the most common types of foundations such as shallow foundations, pile and caisson foundations subjected to faulting by means of numerical and experimental investigations. The parameters affecting the interaction of a reverse fault rupture with a shallow embedded foundation have been investigated by experimentally validated numerical models using ABAQUS software. These parameters are the embedment depth of foundation, the bearing pressure of foundation, the rigidity of foundation and the foundation position. The reverse fault rupture at a dip angle of 60° propagates in a moderately dense sand layer and interplays with the embedded foundation. A summary of conclusions is as follows: The behavior of foundation and the development of rupture mechanisms are fully dependent on the location of the foundation relative to the fault rupture and the magnitude of the fault offset. Depending on the foundation position, the loss of support of the foundation takes place either under the edges (i.e. the hogging deformation) or under the middle (i.e. the sagging deformation) of the foundation. The foundation experiences the loss of support and stressing even for the indirect-hit case when the fault rupture emerges outside the foundation width. The increase of the weight of the foundation leads to diverting the fault rupture and less stressing of the foundation. However, the rotation of foundation depends strongly on the foundation position relative to the fault outcrop compared to the weight of the foundation. By increasing the embedment depth of the foundation, the weight of the foundation has no beneficial effect for the behavior of shallow foundation and the kinematic constraint of deeper foundation causes to significantly increase the rotation of the embedded foundations. As the embedment depth increases, the rotation of the foundation decreases for the same rupturing mechanism. It can be attributed to the similar performance of a deeper shallow embedded foundation to that of a deep foundation (such as a caisson foundation). However, the rotation of the foundations with the different embedment depths is largely dependent on the position of the foundation relative to the outcropping fault rupture and the magnitude of the fault offset. Also, the results show that the different fault-induced mechanisms such as footwall, gapping and hanging wall may happen depending on the magnitude of fault offset for a given embedment depth and position of the foundation. Depending on the rigidity of the foundation, the rigid shallow foundation may diffuse/divert the fault rupture beyond the foundation, whereas by contrast with a flexible foundation, the fault rupture will develop as a distinct rupture and strike the foundation underneath. In all cases, the foundation rigidity is an important parameter controlling the stressing of the foundation. Decreasing the rigidity of the foundation causes to increase the normalized bending moment of the foundation and the foundation may experience substantial distress. The results indicate that rigid shallow foundations are more suitable than flexible ones for a structure subjected to a major reverse fault rupturing underneath.