地基地震液化问题的无网格相关方法研究
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摘要
砂土液化现象作为地震灾害的一种主要形式,常常会引起建筑物基础的不均匀沉降及土工构造物的破坏,给人类带来巨大的灾难。液化引起的大变形是强震中饱和砂土地基破坏的主要形式,定量地预测实际边值问题中液化引起的变形具有重要的工程价值。近年来,有限元方法已经广泛地应用于岩土工程问题,但是有限元方法的模拟结果依赖于网格质量,并且往往由于液化过程空间分布的不均匀性而引起局部单元严重扭曲,使得有限元计算无法正常运行。无网格法是通过一组离散的点来构造逼近函数,不需要节点间的连接信息,因而能够克服因网格扭曲而造成的计算中断,适合于易发生大变形的液化问题的数值模拟,本文的研究内容主要围绕无网格法在液化分析方面的应用,共分为三个方面:
1.将无网格法应用于液化问题的数值模拟,通过算例验证了无网格法能够克服有限元方法在液化模拟中由于大变形造成网格扭曲而引起的计算中断。同时,作为一种数值近似计算方法,无网格法的计算误差是不可避免的,因此引入自适应方法。本研究的自适应方法采用TB应力平滑技术和Z-Z误差估计,利用平滑应力和无网格法所得应力解差值的能量范数来估算误差,如果局部相对误差超过了允许误差,则在高误差域插入新的离散点进行加密。材料参数由加密点直接传递给新增节点,应力、应变等变量以插值的方式传递,下一步计算以新的节点布局为基础。通过对一上表面承受均布荷载作用的饱和土块进行数值模拟,验证了自适应程序能够有效的改善计算精度。选取了建筑在饱和砂土地基上的填筑坝作为算例进行地震反应分析,该算例也可采用有限元方法完成,以此来验证无网格法应用的有效性。通过将采用自适应方法分析的结果与疏松和精细节点布置方案的无网格法分析结果对比,既验证了自适应过程的有效性,又获得了填筑坝的地震响应规律。
2.无网格法在大变形模拟方面存在着诸多的优势,但也有计算时间长的缺点。将有限元与无网格法耦合起来,则可以很好地将这两种离散方法的优点组合在一起,充分发挥各自的优势。即根据经验在容易发生网格扭曲的部位使用无网格法离散,不易发生扭曲的区域使用有限元法离散。在交界区域引入过渡单元,按照Belytschko等人的方法构造过渡单元的位移和孔隙水压力近似函数,把两种方法耦合到一起。通过对可液化边坡模型的数值模拟,验证了该方法比单纯的无网格方法节约计算时间,并能够达到合理的精度。并采用该方法对边坡模型进行了参数分析。
3.分析可液化砂土地基上结构的动力响应,需要考虑土—结构相互作用。有限元方法在相互作用分析方面已经很成熟,但涉及到无网格法的相互作用分析还很少见。通过编制程序,将易液化产生大变形的饱和砂土地基采用无网格法进行离散,将结构采用有限元法来离散,在地基土与结构接触处采用无厚度的摩擦接触单元过渡,实现了土—结构相互作用的无网格—有限元接触耦合算法。通过桩—土相互作用分析验证了所编制程序的可靠性,而后,又对沉箱模型进行了数值模拟,得到了沉箱的动力响应规律,并进行了影响因素分析。
As a major form of earthquake disaster, liquefaction of sandy soil often causes uneven subsidence of building foundation and destruction of structure, which bring tremendous damage to the humanity. Large deformation caused by liquefaction is a main phenomenon of saturated sandy soil disruption under seismic excitation; it has an important engineering value to predict the deformation quantitatively of the actual boundary problem. In recent years, finite element method (FEM) has been widely used in geotechnical engineering problems. But the results simulated by FEM strongly depend on mesh quality, and it may not be able to complete calculation normally because of serious mesh distortion caused by non-uniformity spatial distribution of liquefaction process. Meshless method constructs the approximation functions by a set of discrete points; it does not require inter-node connection information, thus it can overcome the calculation interruption caused by mesh distortion, and it is suitable for large deformation simulation of liquefaction. This research is focused on the application of meshless method on liquefiable analysis, the main investigations consist of the following three portions:
1. Meshless method is applied to numerical simulation of liquefaction problem, then the merits that meshless method can overcome calculation interruption caused by mesh distortion when using FEM are verified. Meanwhile, as a numerical approximation method, calculation error of meshless method is inevitable, so the adaptive process is programmed. The adaptive program is calculated by T-B stress recovery scheme and z-z error estimation, the error is estimated by energy norm of difference of recovery stress and meshless stress. If the local relative error exceeds the limit relative error, then new nodes will be generated at the high error area. The material parameters of the refined node are transferred to the newly added nodes, and the variables of the new nodes are interpolated from the values of the old nodes. Next calculation step is based on the new node discretization. By numerical simulation of a saturated soil block that suffering uniformly distributed load on the surface, the verification that the adaptive process can improve accuracy is done. Seismic response analysis of an embankment constructed on saturated sandy foundation is carried out, by comparison the results with those of FEM and Centrifuge test, the effectiveness of EFGM is proved. Then, by comparison the results obtained by adaptive method with those obtained by coarse and fine nodal discretization, the effectiveness of the adaptive process is verified and the response rule of the embankment is shown.
2. There are many advantages of meshless method in simulating large deformation, but there are also shortcomings in calculation time. FEM is coupled with meshless method, then, the coupled method can combine the advantages of the two methods and give full play to their advantages. It means that in the position prone to mesh distortion meshless method is used, in other regions FEM is used. In the interface region, transition elements are conducted, by constructing approximation functions of displacement and pore water pressure, the two methods are coupled together. By numerical modeling of liquefiable slope, it is validated that the coupled method can save computing time than the simple meshless method, and be able to achieve a reasonable accuracy. Then, parameter analysis is made to the slope model using the coupled method.
3. Analyzing the dynamic response of the structure constructed on liquefiable sand foundation, it is needed to consider soil-structure interaction. It is already very mature for FEM to analyzing interaction analysis, but it is still rare for meshless method when involving interaction analysis. Through programming Fortran procedure, saturated sand foundation which is easy to have a large deformation when liquefaction is discretized by meshless method; structure is discretized by FEM, then, the contact region between foundation and structure is modeled by non-thickness frictional contact elements, the meshless-finite element coupled contact algorithm for soil-structure interaction is implemented. The reliability of programming is verified through pile-soil interaction analysis, and then, the caisson model is simulated by the method obtaining the law of dynamic response, influence factors analysis is also made.
1.将无网格法应用于液化问题的数值模拟,通过算例验证了无网格法能够克服有限元方法在液化模拟中由于大变形造成网格扭曲而引起的计算中断。同时,作为一种数值近似计算方法,无网格法的计算误差是不可避免的,因此引入自适应方法。本研究的自适应方法采用TB应力平滑技术和Z-Z误差估计,利用平滑应力和无网格法所得应力解差值的能量范数来估算误差,如果局部相对误差超过了允许误差,则在高误差域插入新的离散点进行加密。材料参数由加密点直接传递给新增节点,应力、应变等变量以插值的方式传递,下一步计算以新的节点布局为基础。通过对一上表面承受均布荷载作用的饱和土块进行数值模拟,验证了自适应程序能够有效的改善计算精度。选取了建筑在饱和砂土地基上的填筑坝作为算例进行地震反应分析,该算例也可采用有限元方法完成,以此来验证无网格法应用的有效性。通过将采用自适应方法分析的结果与疏松和精细节点布置方案的无网格法分析结果对比,既验证了自适应过程的有效性,又获得了填筑坝的地震响应规律。
2.无网格法在大变形模拟方面存在着诸多的优势,但也有计算时间长的缺点。将有限元与无网格法耦合起来,则可以很好地将这两种离散方法的优点组合在一起,充分发挥各自的优势。即根据经验在容易发生网格扭曲的部位使用无网格法离散,不易发生扭曲的区域使用有限元法离散。在交界区域引入过渡单元,按照Belytschko等人的方法构造过渡单元的位移和孔隙水压力近似函数,把两种方法耦合到一起。通过对可液化边坡模型的数值模拟,验证了该方法比单纯的无网格方法节约计算时间,并能够达到合理的精度。并采用该方法对边坡模型进行了参数分析。
3.分析可液化砂土地基上结构的动力响应,需要考虑土—结构相互作用。有限元方法在相互作用分析方面已经很成熟,但涉及到无网格法的相互作用分析还很少见。通过编制程序,将易液化产生大变形的饱和砂土地基采用无网格法进行离散,将结构采用有限元法来离散,在地基土与结构接触处采用无厚度的摩擦接触单元过渡,实现了土—结构相互作用的无网格—有限元接触耦合算法。通过桩—土相互作用分析验证了所编制程序的可靠性,而后,又对沉箱模型进行了数值模拟,得到了沉箱的动力响应规律,并进行了影响因素分析。
As a major form of earthquake disaster, liquefaction of sandy soil often causes uneven subsidence of building foundation and destruction of structure, which bring tremendous damage to the humanity. Large deformation caused by liquefaction is a main phenomenon of saturated sandy soil disruption under seismic excitation; it has an important engineering value to predict the deformation quantitatively of the actual boundary problem. In recent years, finite element method (FEM) has been widely used in geotechnical engineering problems. But the results simulated by FEM strongly depend on mesh quality, and it may not be able to complete calculation normally because of serious mesh distortion caused by non-uniformity spatial distribution of liquefaction process. Meshless method constructs the approximation functions by a set of discrete points; it does not require inter-node connection information, thus it can overcome the calculation interruption caused by mesh distortion, and it is suitable for large deformation simulation of liquefaction. This research is focused on the application of meshless method on liquefiable analysis, the main investigations consist of the following three portions:
1. Meshless method is applied to numerical simulation of liquefaction problem, then the merits that meshless method can overcome calculation interruption caused by mesh distortion when using FEM are verified. Meanwhile, as a numerical approximation method, calculation error of meshless method is inevitable, so the adaptive process is programmed. The adaptive program is calculated by T-B stress recovery scheme and z-z error estimation, the error is estimated by energy norm of difference of recovery stress and meshless stress. If the local relative error exceeds the limit relative error, then new nodes will be generated at the high error area. The material parameters of the refined node are transferred to the newly added nodes, and the variables of the new nodes are interpolated from the values of the old nodes. Next calculation step is based on the new node discretization. By numerical simulation of a saturated soil block that suffering uniformly distributed load on the surface, the verification that the adaptive process can improve accuracy is done. Seismic response analysis of an embankment constructed on saturated sandy foundation is carried out, by comparison the results with those of FEM and Centrifuge test, the effectiveness of EFGM is proved. Then, by comparison the results obtained by adaptive method with those obtained by coarse and fine nodal discretization, the effectiveness of the adaptive process is verified and the response rule of the embankment is shown.
2. There are many advantages of meshless method in simulating large deformation, but there are also shortcomings in calculation time. FEM is coupled with meshless method, then, the coupled method can combine the advantages of the two methods and give full play to their advantages. It means that in the position prone to mesh distortion meshless method is used, in other regions FEM is used. In the interface region, transition elements are conducted, by constructing approximation functions of displacement and pore water pressure, the two methods are coupled together. By numerical modeling of liquefiable slope, it is validated that the coupled method can save computing time than the simple meshless method, and be able to achieve a reasonable accuracy. Then, parameter analysis is made to the slope model using the coupled method.
3. Analyzing the dynamic response of the structure constructed on liquefiable sand foundation, it is needed to consider soil-structure interaction. It is already very mature for FEM to analyzing interaction analysis, but it is still rare for meshless method when involving interaction analysis. Through programming Fortran procedure, saturated sand foundation which is easy to have a large deformation when liquefaction is discretized by meshless method; structure is discretized by FEM, then, the contact region between foundation and structure is modeled by non-thickness frictional contact elements, the meshless-finite element coupled contact algorithm for soil-structure interaction is implemented. The reliability of programming is verified through pile-soil interaction analysis, and then, the caisson model is simulated by the method obtaining the law of dynamic response, influence factors analysis is also made.
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