基于Drucker-Prager准则的边坡安全系数定义及其转换

DEFINITION AND TRANSFORMATION OF SLOPE SAFETY FACTOR BASED ON DRUCKER-PRAGER CRITERION

探讨了基于D-P(Drucker-Prager)准则的边坡稳定安全系数定义形式,提出了各D-P准则之间的安全系数转换关系,并据此建立了基于D-P准则的边坡稳定安全系数与传统莫尔–库仑准则条件下安全系数的关系表达式。目前,ANSYS有限元软件采用的岩土材料屈服准则为莫尔–库仑六边形外接圆D-P准则,在利用有限元强度折减法计算边坡稳定安全系数时,可以先求出外接圆D-P准则条件下的安全系数,然后利用所提出的安全系数转换公式就可直接计算出各D-P准则条件下的安全系数。对于平面应变条件下的强度问题,平面应变莫尔–库仑匹配D-P准则(分关联和非关联两种情况)与莫尔–库仑准则等效,因此,通过转换就可以在ANSYS程序中实现莫尔–库仑准则,而不需要进行二次开发。这样就解决了基于D-P准则的有限元强度折减安全系数与传统工程中采用的安全系数(基于莫尔–库仑准则)间的接轨问题。大量算例结果表明:在平面应变条件下采用平面应变莫尔–库仑匹配D-P准则求得的安全系数与传统极限平衡条分法中用Spencer法求得的安全系数非常接近,且误差在1%～2%,已经具有相当高的计算精度,也同时证明所提出的方法是可行的。

Slope stability analysis was carried out using strength reduction finite element method(FEM) based on the Drucker-Prager criterion.The definition of slope stability safety factor based on the Drucker-Prager criterion was proposed,and the safety factor conversion formula with different Drucker-Prager yield criteria was deduced.The substitutive relationship of safety factor based on the Drucker-Prager yield criterion and Mohr-Coulomb yield criterion was set up.Currently,the Mohr-Coulomb hexagon circumcircle Drucker-Prager criterion was adopted in the ANSYS programme.So,the safety factor using ANSYS with the Mohr-Coulomb hexagon circumcircle Drucker-Prager criterion is calculated,thus the safety factor based on the Drucker-Prager yield criterion(such as the Mohr-Coulomb matching Drucker-Prager yield criterion under the plane strain condition) can be obtained using the deduced conversion formulae.Under the plane strain condition,the Mohr-Coulomb yield criterion in the ANSYS programme without secondary programming development through equivalent substitution is adopted.A series of case studies indicate that the average error of safety factors between those obtained by strength reduction FEM based on plane strain Mohr-Coulomb matching D-P yield criterion and those by Spencer method is 1%–2%.The applicability of the proposed method was clearly exhibited.