两种滑动面型式下边坡稳定性计算方法的研究

基于圆弧和任意曲线两种滑动面型式，对边坡稳定性计算方法中的瑞典法、简化Bishop法、简化Janbu法、严格Janbu法、Morgenster-Price法、Sarma法和不平衡推力法进行研究。对上述各种方法的研究成果进行了总结，并对Morgenster-Price法中的条间力函数 选择了4种形式（即 为常数0.1、0.5、1.0及半正弦函数），对不平衡推力法中的公式进行了改进。通过算例对比，及当条分数不同、边坡坡角和坡高变化时，分析了这些方法的特点，由分析结果可知：（1）瑞典法和简化Janbu法计算得的安全系数最小，简化Bishop法和不平衡推力法与严格法得到的结果颇为接近；（2）任意曲线滑动面方法较圆弧滑动面方法计算得的安全系数稍小，且得到的临界滑动面与临界圆弧滑动面相接近，因而表明，圆弧滑动面作为一种近似的临界滑动面能够满足实际工程需要；（3）均质边坡采用较少条分数即可获得较高的安全系数计算精度，非均质边坡需一定数量的条分保证结果的可靠性；（4）Sarma法对土条侧面法向力和剪切的假设，使得其在均质边坡计算得的安全系数比其他方法要大，有偏于不安全的考虑，但Sarma法能够考虑边坡非均质对条分法的影响；（5）当边坡外形（如坡角、坡高）变化时，严格Janbu法在两种滑动面型式下计算得的安全系数相差很小，而其他方法稍大一些；（6）Morgenster- Price法中，条间力函数 对计算得到的结果影响很小。

Research on calculation methods of slope stability under two types of sliding surface

Based on two types of sliding surface, arc and arbitrary curve, the calculation methods of slope stability, including Sweden method, simplified Bishop method, simplified Janbu method, corrected Janbu methods, Morgenster-Price method, Sarma method and unbalanced thrust force method, are studied. Research results of above-mentioned methods are summarized. At the same time, four forms in Morgenster-Price method inter-slice force function f(x) are chosen, i.e. the constants of 0.1, 0.5, 1.0 and semi-sine function, and the formula in unbalanced thrust force method is improved. Through comparing some examples and analyzing the characteristics of these methods with different slice numbers slope angles, slope heights, and the conclusions can be obtained as follows: the factor of safety (FOS) calculated by Swedish method and simplified Janbu method is the least, and the results obtained by simplified Bishop method and the unbalanced thrust force method are quite close to the corrected method. The FOS calculated by arbitrary curve sliding surface method is slightly smaller than that of circular sliding surface method; and the critical sliding surface got by this method is close to the critical circular sliding face; so it shows that circular sliding surface, as an approximation of the critical sliding surface, can meet the need of practical engineering. Adopting a small amount of slices can obtain high accuracy of FOS in homogeneous slope; and a certain number of slices are needed to ensure reliability of the results in heterogeneous slope. In Sarma method assumption for the normal force and shear force on the side of slices makes calculated FOS larger than that obtained by other methods in homogeneous slope; then there are unsafe considerations, but Sarma method can consider the impact of heterogeneity in slope on slice method. When the slope shape (such as slope angle, slope height) changes, difference of FOS calculated by corrected Janbu method under two types of sliding surface is small; but the difference of FOS calculated by other methods is slightly larger. In Morgenster-Price method inter-slice force function f(x) has little effect on the calculated results.