Chapter 7 Slope Stability Part 1|边坡工程『支挡|防护』 - 领先的岩土技术社区，岩土领域的媒体、社区与应用平台！

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Chapter 7 Slope Stability Part 1 [边坡稳定]

7.1 Types of slope failure [滑坡的类型]

The most common types of slope failure [滑坡] are illustrated in Fig.7.1. Translational slide tends to occur where an adjacent weak zone [软弱层] of soil is at a relatively shallow depth below the surface of the slope. The failure surface tends to be plane and roughly parallel to the slope. [滑动面为平面与坡面平行]
Rotational slide is common for cohesive soil [粘性土] (e.g. clays) slope. The shape of the failure surface in section may be a circular arc or a non-circular curve. In general circular slides are associated with homogeneous soil conditions and non-circular slides are associated with non-homogeneous soil conditions. [滑动面为一曲面]

7.2 Methods of slope stability analysis [边坡稳定分析方法]

The stability of a slope can be analysed using one or more of the following methods:
– Limit equilibrium method (equilibrium of forces) [极限平衡法]
– Limit analysis based on plasticity (equilibrium of stresses) [极限应力分析法]
– Finite difference method [有限差分法]
– Finite element method [有限元法]
Although a finite element or a finite difference method is more flexible and general, in practice, the limit equilibrium method (LEM) is used in the slope stability analysis.
In LEM, the soil is considered to be on the verge of failure along an assumed or a known sliding surface. [在某一假设滑动面,整个块体处于极限平衡状态] In general, the sliding surface is assumed to be a circular arc for clays or a logarithmic spiral for sands and gravels. The shear strength required to maintain a condition of limiting equilibrium is compared with the available shear strength of the soil, giving the average factor of safety along the sliding surface [安全糸数定义为抗剪力与下滑力之比]. The problem is normally considered in two dimensions. [土坡的稳定分析可简化为平面问题]
For the slope stability analysis using the LEM, two analyses are considered for each slope:
– Effective Stress Analysis [有效应力分析] (ESA) which represents drained or long-term behaviour of the slope. Cohesion (c’) and angle of internal friction (’) are used in the analysis.
– Total Stress Analysis [总应力分析] (TSA) which represents undrained or short-term behaviour of the slope. Undrained shear strength (cu) is used in the analysis.

7.3 Analysis of a plane translational slide

It is assumed that the potential failure surface is parallel to the surface of the slope and is at a depth that is small compared with the length of the slope. The slope can then be considered as being of infinite length, with end effects being ignored. [假设滑动面与坡面平行, 滑动块体深度远小于边坡长度, 边坡为无限长]
The slope is inclined at angle  to the horizontal and the depth of the failure plane is z, as shown in Fig.7.2. Consider a slice of soil element of width b. [坡角为, 滑动面深度z, 土条宽度为b] Assume the side forces on the soil element can be neglected in the stability analysis, ground water table is below the failure plane and the soil is cohesionless. [假设不考虑土条两边的合力,地下水位低于滑动面,无粘性土] The forces acting on the element are shown in Fig.7.2. W is weight of soil element [土条重量], T is shear force on the failure plane [平行于滑动面的下滑剪切力] and N is normal force on the failure plane [滑动面法线方向的分力]. Consider equilibrium of forces parallel to the slope surface, [边坡平行方向的静力平衡]
(7.1)
Consider equilibrium of forces normal to the slope surface, [边坡法线方向的静力平衡]
(7.2)
The available shear strength (Tf) along the failure surface is [滑动面上的抗剪力]
(7.3)
where  is the angle of internal friction. Factor of safety (FS) is defined as the ratio of Tf and T. [安全糸数定义为抗剪力与下滑力之比]
(7.4)
If water table coincides with the slope surface, the forces acting on the element are shown in Fig.7.3. [地下水位于坡面] An additional hydrostatic force (U) is acting on the failure plane normal to the slope surface [边坡法线方向的静水力]. The equilibrium of forces parallel to the slope surface is also represented by equation (7.1). Consider equilibrium of forces normal to the slope surface,
(7.5)
The available shear strength (Tf) along the slip surface is
(7.6)
Then, factor of safety (FS) is expressed as:
(7.7)
The weight W is expressed as:
(7.8)
where sat is saturated unit weight of soil. The hydrostatic force U is expressed as
(7.9)
where u is pore-water pressure at failure plane and w is unit weight of water. Substitute equations (7.8) and (7.9) into equation (7.7)
(7.10)
Comparing Equations (7.4) and (7.10), the factor of safety is reduced by a factor ’/s if the water table rises to the slope surface.

7.4 Total stress analysis (u = 0) [总应力分析]

This total stress analysis covers the case of a fully saturated clay under undrained condition, or for the condition immediately after construction. [总应力分析合适用于饱和粘土在不排水条件下或短期的稳定分析] Only moment equilibrium is considered in the analysis. [满足力矩平衡条件] In section, the potential failure surface is assumed to be a circular arc [滑动面为弧形]. A trial failure surface (center O, radius r and length L [圆心为O,半径为r,弧长为L]) is shown in Fig.7.4. The failure of slope is mainly due self-weight (W) of the soil. Consider the moment at point O, the disturbing moment of W is expressed as
(7.11)
where d is the moment arm of W from point O [d是W对滑弧圆心的力臂]. The forces resisting the rotation of the sliding soil mass are the shear forces (Tf) mobilised along the circular sliding surface. The resisting moment of Tf at point O is expressed as
(7.12)
where cu is undrained shear strength of the soil, L is length of the circular arc and r is radius of the circular arc. Then factor of safety (Fs) is given by
(7.13)
It is necessary to analyse the slope for a number of trial failure surfaces in order that the minimum factor of safety can be determined. If tension crack exists at the crest of the slope, the arc length L will be shortened. [当裂缝在坡顶出现,滑弧长度便会减小] The depth of the tension crack can be evaluated from the method presented in 土力学 p.196. [计算裂缝深度可参考土力学 p.196] If the crack is filled with water, a hydrostatic force will act normal to the crack. The additional moment of this hydrostatic force must be added to equation (7.11) for calculating the factor of safety of the slope. [当裂缝积水,计算安全糸数时公式(7.11)中必需考虑静水压力对滑弧圆心O的力矩]

Fig.7.1a Types of slope failures – translational slide

Fig.7.1b Types of slope failures – rotational slide

Fig.7.2 Plane Translational slide with no water table

Fig.7.3 Plane Translational slide with water table

Fig.7.4 Total stress analysis