海积软土的延拓邓肯—张模型及其数值模拟研究

发布时间：2018-07-08 13:48

本文选题：海积软土 + 邓肯-张模型　；参考：《华侨大学》2013年硕士论文

【摘要】：土体本构模型的选用与岩土工程的计算精度息息相关，故诸多学者对其进行深入研究。本文引用“半值强度指数”的概念，指出了传统的邓肯-张模型公式存在特征方程不独立的数学缺陷。为了克服该缺陷，在传统邓肯-张模型的基础上，，引入控敛因子θ，提出了改进的邓肯-张模型，称为延拓模型。通过对延拓模型应力应变表达式进行数学分析，并且比较不同控敛因子的延拓模型与邓肯-张模型的应力应变曲线，可以得到以下结论：θ1时的延拓模型与邓肯-张模型有着相同的数学性质；邓肯-张模型是延拓模型θ=2时的特例；在初始切线模量和极限偏应力均确定的情况下，延拓模型可以通过调节控敛因子来模拟收敛速度大于或者小于邓肯-张模型的应力应变曲线，而邓肯-张模型则无法达到这种效果；延拓模型的控敛因子与模型应力应变曲线的收敛速度呈负相关。为了探究延拓模型的求参方法，将Matlab软件中的lsqcurvefit回归函数与最小二乘回归分析法相结合，编制了延拓模型多元回归、邓肯-张模型多元回归和延拓模型控敛因子回归这三个期望函数程序。并通过海积软土常规三轴试验数据，求解、比较以上三种回归的残差平方和。研究表明，延拓模型多元回归的拟合效果最好，邓肯-张模型多元回归的拟合效果最差，说明了最小二乘回归分析求解模型参数估计值的方法可作为延拓模型的求参方法。有限元计算参数的确定是有限元程序得以运用的前提条件。本文采用控制变量法对不同围压下的海积软土进行分析，最终确定了土样的最佳网格结点数为11*21个结点，试样帽的最佳高度为4个单元高，试样帽的最佳泊松比参数为0.3。通过比较邓肯-张模型模拟曲线、延拓模型模拟曲线、邓肯-张模型公式曲线与试验数据，证明了该有限元程序具有可行性，且延拓模型的模拟效果优于邓肯-张模型。为了观察控敛因子对土样网格单元结点的位移、应力、应变和安全性、胀缩性的影响，在求得不同围压下，邓肯-张模型和延拓模型的土样网格单元结点的位移等值线图、变形图、位移矢量图、应力等值线图和应变等值线图后，可归纳总结出，控敛因子对土样各网格单元结点的径向位移、轴向位移、径向应力和轴向应变均影响不大，但其与土样各网格单元的轴向应力呈负相关，与土样中部单元的径向应变呈负相关，却对土样上部和下部单元的径向应变影响不大。观察两种模型的最小安全系数等值线图和土样体积应变和轴向应变关系曲线，可以看出，控敛因子越小，部分单元的最小安全系数越小，剪缩现象越明显，安全性越高。
[Abstract]:The selection of soil constitutive model is closely related to the calculation accuracy of geotechnical engineering, so many scholars have deeply studied it. In this paper, the concept of "half value strength index" is introduced, and the mathematical defects of the traditional Duncan-Chang model formula are pointed out, in which the characteristic equation is not independent. In order to overcome this defect, based on the traditional Duncan-Zhang model, the convergent factor 胃 is introduced, and an improved Duncan-Zhang model is proposed, which is called the extension model. Through the mathematical analysis of the stress-strain expression of the extension model, the stress-strain curves of the extension model with different convergence factors are compared with those of the Duncan Chang model. The following conclusions can be obtained: the extension model of 胃 1 has the same mathematical properties as that of Duncan Chang model, the Duncan Zhang model is a special case of extension model 胃 = 2, and the initial tangent modulus and ultimate deflection stress are determined. The continuation model can simulate the stress-strain curve of Duncan-Chang model by adjusting the convergence factor, but the Duncan-Chang model can not achieve this effect. The convergence factor of the continuation model is negatively correlated with the convergence rate of the stress-strain curve. In order to explore the parameter finding method of the extension model, the multivariate regression of the extension model is compiled by combining the lsqcurvefit regression function in Matlab software with the least square regression analysis method. Duncan-Chang model multivariate regression and extended model controlled convergence factor regression are three expected function programs. Based on the conventional triaxial test data of marine soft soil, the sum of squared residuals of the above three kinds of regression is compared. The results show that the continuation model has the best fitting effect, and the Duncan-Zhang model has the worst fitting effect, which indicates that the least square regression method can be used as the parameter method of the extended model. The determination of finite element calculation parameters is a prerequisite for the application of finite element program. In this paper, the control variable method is used to analyze the marine soft soil under different confining pressures. Finally, it is determined that the optimum mesh node number of the soil sample is 11 * 21 nodes, the optimum height of the specimen cap is 4 unit height, and the optimum Poisson's ratio parameter of the specimen cap is 0.3. By comparing the simulation curve of Duncan-Zhang model, the simulation curve of extension model, the formula curve of Duncan-Zhang model and the experimental data, it is proved that the finite element program is feasible and the simulation effect of extension model is better than that of Duncan-Zhang model. In order to observe the effect of convergence factor on the displacement, stress, strain, security, dilatancy and shrinkage of soil sample grid cell node, the displacement isoline maps of soil sample grid cell node of Duncan Chang model and extension model are obtained under different confining pressures. After the deformation diagram, displacement vector diagram, stress isoline diagram and strain isoline diagram, it can be concluded that the convergence factor has little effect on the radial displacement, axial displacement, radial stress and axial strain of each mesh node of soil sample. However, it is negatively correlated with the axial stress of each grid element of the soil sample and the radial strain of the central unit of the soil sample, but has little effect on the radial strain of the upper and lower elements of the soil sample. By observing the contour diagram of the minimum safety factor and the curve of volumetric strain and axial strain of the two models, it can be seen that the smaller the convergence factor, the smaller the minimum safety factor of some elements, the more obvious the phenomenon of shearing shrinkage and the higher the security.
【学位授予单位】：华侨大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：TU447

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