采用泰勒级数展开的方法由修正剑桥模型屈服函数得到新的P-L屈服函数,用于合理描述不同类型土的屈服面。该屈服函数满足临界状态力学的基本假定,屈服面与临界状态线的交点处的法向量始终垂直于p轴,当采用相关联的流动法则时,土体达到临界状态后不会产生额外的体积变形。修正P-L屈服函数所引入的形状因子α为临界状态有效平均主应力与前期固结应力之间的比值,增大α会导致屈服面沿着临界状态线向外扩张,材料的弹性区间也随之增大。剑桥模型和修正剑桥模型的屈服函数可以视作本文提出的屈服函数的特例,分别对应α为0.368和0.5时的情形,通过对Pancrudo堆石料的屈服面进行拟合,可以看出修正P-L屈服函数能够更好地描述屈服面的真实几何形状。在此基础上,可以采用该屈服函数对修正剑桥模型进行拓展以提升其对不同类型土的适用性。将模型计算结果与正常固结重塑Weald黏土和Kaolin黏土的不排水三轴压缩试验结果进行对比分析,发现适当调整屈服面的几何形状有助于提高模型的计算精度,尤其是对于Kaolin黏土,在不排水剪切条件下可以计算得到更为准确的不排水抗剪强度和有效应力路径。鉴于拓展后的修正剑桥模具有形式简单且计算精度高等优点,其在岩土变形计算领域有着广泛的应用前景。
The Taylor series expansion approach is used to develop a new P-L yield function based on the modified Cam-clay (MCC) model yield function,which can reasonably describe the yield surfaces of different types of soil. The P-L yield function can satisfies the basic assumptions of critical state mechanics and the normal vector of the yield locus at the intersection point is perpendicular to the p-axis. After reaching the critical state, no unrealistic volumetric deformation is produced in soil samples by assuming an associated flow rule. The extra introduced parameter α is defined as the ratio between the mean effective pressure at the critical state and the preconsolidated pressure. The yield functions of the original Cam-clay (CC) and MCC models can be obtained by letting α be 0.368 and 0.5, respectively. The predicted yield locus using the P-L yield function will be expanded along with the critical state line in the p-q plane as α increases. Through fitting the yield surface of Pancrudo rockfill, it can be seen that the modified P-L yield function can better describe the true geometric shape of the yield surface. Using the P-L yield function, a new extended modified Cam-clay (ExMCC) model was proposed in the current work to account for the effect of the shapes of the yield locus on the model performance. By comparing the model calculation results with the undrained triaxial compression test results of normally consolidated remolded Weald clay and Kaolin clay, it is found that appropriately adjusting the geometric shape of the yield surface helps to improve the calculation accuracy of the model. Especially for Kaolin clay, more accurate undrained shear strength and effective stress path can be calculated under undrained shear conditions. In view of the advantages of simple form and high calculation accuracy of the extended modified ExMCC model, it has broad application prospects in the field of geotechnical deformation calculation.
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