基于中主应力修正关系的边坡稳定性分析

边坡稳定性分析时通常将应力条件简化为平面应变状态，采用三轴试验强度计算出的边坡稳定性偏于保守。在充分考虑中主应力物理含义及力学机制的基础上，将Mises屈服准则与Mohr-Coulomb（简称M-C）内切圆屈服准则进行匹配，得到了平面应变条件下土体屈服破坏时中主应力的理论修正关系，进而也得到了该条件下最大主应力与最小主应力的比值关系，从理论上证明了该比值关系是与土体平面应变破坏时内摩擦角成一定关系的常数，也在平面应变试验中得到了验证，从侧面反映出中主应力理论修正关系的合理性。由上述两种关系建立了土体平面应变破坏条件下的应力路径，结合Lade-Duncan强度准则，建立了平面应变条件下强度参数与三轴试验试验条件下强度参数转换公式，由该转换公式得到的平面应变条件下的强度参数与平面应变试验实测值误差在2%左右，大幅缩小了三轴试验实测值与平面应变试验实测值的误差。在均质边坡稳定分析中分别采用常规三轴试验强度值与由公式转换得到的平面应变强度值进行计算。研究结果表明，三轴试验条件下内摩擦角为10°～20°之间时，基于两种强度参数得出的安全系数相差不大；当三轴试验条件下内摩擦角大于20°时，平面应变条件下安全系数较三轴试验条件下提高19%左右，但该成果只在文中计算案例有效，两者误差的准确关系还有待于进一步研究。值得关注的是，由于平面应变条件下土体强度变大，边坡的临界滑面深度变浅了，其形态相应变陡。

Analysis of slope stability based on modified relationship of intermediate principal stress

Usually, stress state of the soil is replaced by plane strain state when slope stability is analyzed, which leads to conservative results adopting triaxial tests. Based on fully considering the physical meanings and mechanisms of the intermediate principal stress, this paper proposes a modified relationship of intermediate principal stress in plane strain state when soil approaches ultimate strength making. Mises strength criterion identical to the circle internally tangent to M-C strength criterion, and we further derive the ratio of maximum principal stress to minor principal stress, which is a constant associated with internal frictional angle under plane strain state. The ratio has been proved by tests, which demonstrates the modified relationship of intermediate principal stress is reasonable. Based on the ratio and the modified relationship, the stress path under plane strain state is derived. Combined with Lade-Duncan strength criterion, the strength formula transformation between plane strain state and triaxial state is established. Then, comparisons between internal frictional angle derived from plane strain experiment and strength formula transformation show that the errors between the two frictional angle are only about 2%, which largely decrease the errors caused by triaxial test. Two different strength parameters, one of which is derived from triaxial test and another of which is derived from strength formula transformation, are used to evaluate the stability of a homogeneous slope. The results show that, when the internal friction angle in triaxial test state is between 10°-20°, the difference of safety factor based on the two different strength parameters is small; if it beyond 20°, the safety factor in plane strain state is about 19% larger than that under triaxial state. However, the results are only effective in this study, a further study is needed. Furthermore, the critical slip surface depth becomes shallower and shape becomes steeper with larger strength of soil under plane strain state.