土质斜坡存在唯一最小安全系数的数据作图论证及原因分析

EXISTENCE AND REASON OF A GLOBAL MINIMUM FACTOR OF SAFETY OF SOIL SLOPES

本文通过数据作图法揭示了土体黏聚力和内摩擦角对斜坡安全系数作用的不同规律,并论证了一般土质斜坡存在唯一最小安全系数及其原因。本文在土质斜坡中划分了大量的潜在滑移面,并定义了每一个潜在滑移面所拥有的4类安全系数FOS^(c×φ)、FOS^(c)、FOS^(φ)和FOS^(c+φ)。基于极限平衡的条分法计算了滑移面的4类安全系数,并使用数据作图法揭示和确定了这4类安全系数值随潜在滑移面深度d变化的4条特征和规律。由土体黏聚力和内摩擦角共同作用的安全系数FOS^(c×φ)包络线随d的增加先单调下降,到达一段最小值区间后,再单调上升。因此,它必然存在一个总体最小值。仅由土体黏聚力贡献的FOS^(c)包络线随d的增加先快速、再缓慢单调下降。仅由土体内摩擦角贡献的安全系数FOS^(φ)包络线随d的增加线性上升。FOS^(c)与FOS^(φ)之和FOS^(c+φ)数值几乎等同于FOS^(c×φ)数值。这4条规律揭示了土体黏聚力和内摩擦角对斜坡安全系数作用的不同规律,并论证了一般斜坡存在最小安全系数及其原因。本文进一步论证和揭示了这4条特征和规律适用于5种经典有限条分法的计算结果,适用于考虑地下孔隙水压强作用的计算结果,和考虑斜坡土体分层不均质影响的计算结果。特别地,地下孔隙水会加深拥有最小安全系数的潜在滑移面深度。土体黏聚力对斜坡安全系数贡献随潜在滑移面深度增大而减小,土体内摩擦角对斜坡安全系数贡献随潜在滑移面深度增大而增大。这两种强度随深度的相反贡献规律导致了一般土质斜坡存在唯一最小安全系数。

This study reveals the different contributions of soil cohesion and internal friction angle on factor of safety(FOS)of soil slope.It shows the existence and reason of a critical slip surface with a global minimum factor of safety(FOS)value in soil slopes.It selects a large number of potential slip surfaces in soil slopes,and then defines four types of FOS values(FOS^(c×φ),FOS^(c),FOS^(φ)and FOS^(c+φ))for each potential slip surface.It calculates these FOS values by conventional slice methods under the limited equilibrium principle,and then plots these FOS values against their associated slip depths and finds their variation features in terms of the slip depth d.The FOS^(c×φ)is defined as the conventional FOS value contributed by both soil cohesion and internal frictional angle of a soil slope.The plots show that local FOS^(c×φ)value decreases and then increases as slip depth increases.Therefore,FOS^(c×φ)have a global minimum value.The FOS^(c) is defined as the FOS value contributed by only the internal cohesion of a soil slope.The plots show that local minimum FOS^(c) value decreases as slip depth increases.The FOS^(φ)is defined as the FOS value contributed by only internal friction angle of a soil slope.The plots show that local minimum FOS^(φ)value always near-linearly increases as slip depth increases.The FOS^(c+φ)is defined as the sum of FOS^(c) and FOS^(φ).The results show FOS^(c+φ)value is approximately equal to FOS^(c×φ)value for each potential slip surface.The above four features are further shown in the results of the five conventional slice methods,the slopes with ground water effect,and the slopes comprising of heterogeneous soils.Hence,this paper shows that a general soil slope has a global minimum value among its numerous FOS values associated with numerous potential slip surfaces.The reasons for the existence of a global minimum FOS value are(1)the individual contributions of the cohesion and friction angle to FOS values against the depth d and(2)the approximate equal values of FOS^(c+φ)to FOS^(c×φ)for any potential slip surface.