Contents 内容
SYNOPSIS 概要

FAILURE SURFACES AND PLASTICITY… 13
失效表面和可塑性...13

SMOOTH WALLS 光滑的墙壁

Passive condition without cohesion … 22
没有内聚力的被动条件 ...22

Passive condition with cohesion … 28
具有内聚力的被动条件 ...28
Active condition with surcharge (uniformly distributed)… 31
有效状态，需加收（均匀分配）...31

Rough walls, battered back face & sloping backfill - Coulomb equations …
粗糙的墙壁，破损的背面和倾斜的回填 - 库仑方程...
Sensitivity of Coulomb’s earth pressure coefficient to input parameters… 37
库仑土压力系数对输入参数的敏感性...37
AT REST CONDITION $$$$qquad\qquad
AT REST CONDITION （静止状态） $$$$qquad\qquad

The problem of retaining soil and the lateral earth pressures therein is one the oldest in the geotechnical engineering; some of the earliest and most fundamental principles of soil mechanics were developed to allow rational design of retaining walls. Many approaches to soil retention have been developed and used successfully. In the recent years, the development of metallic, polymer, and geotextile reinforcement has also led to the development of many innovative types of mechanically stabilized earth retention system.
挡土和其中的侧向土压力问题是岩土工程中最古老的问题之一;土力学的一些最早和最基本的原理是为了允许合理设计挡土墙而开发的。许多土壤保持方法已经被开发并成功使用。近年来，金属、聚合物和土工布加固的发展也导致了许多创新类型的机械稳定固土系统的发展。

Lateral earth pressure: what is it?
侧向土压力：它是什么？
When earth lies against or is retained by a wall or other structure, like a bridge abutment, quay wall or braced excavation, the earth exerts a (lateral) pressure on the structure.
当泥土靠墙或其他结构（如桥台、码头墙或支撑开挖）或被墙或其他结构挡住时，泥土会对结构施加（横向）压力。

Lateral pressure from retained earth can push over a ‘light’ retaining wall or cause it to slide
来自滞留泥土的侧向压力可以推过“轻型”挡土墙或导致其滑动

Types of retaining wall 挡土墙的种类
Retaining walls can be categorized in terms of their mass, flexibility and anchorage conditions. This gives rise to: gravity, cantilever and braced walls. We will spend most of our time investigating gravity walls but first let us consider the differences of gravity vs cantilever walls.
挡土墙可以根据其质量、柔韧性和锚固条件进行分类。这产生了：重力、悬臂和支撑墙。我们将花费大部分时间研究重力墙，但首先让我们考虑重力墙与悬臂墙的差异。

A gravity wall relies on its mass to stabilize the retained earth. It does not bend in service.
重力墙依靠其质量来稳定保留的土壤。它在服务中不会弯曲。

A cantilever wall or embedded wall, is relatively light by comparison to a gravity wall. It relies on earth pressures both behind and in front of the structure to stabilise the retained earth. Stiffness of the wall is important.
与重力墙相比，悬臂墙或嵌入式墙相对较轻。它依靠结构前后的土压来稳定保留的土。墙的刚度很重要。

Some retaining wall design sections to manage earth pressures.
一些挡土墙设计截面用于管理土压力。

Failure of Retaining Walls
挡土墙失效
To design any structure it is necessary to understand its mode(s) of failure. A properly design wall with achieve equilibrium of the forces acting upon it
要设计任何结构，都必须了解其失效模式。设计合理的墙体，使作用在其上的力达到平衡

Gravity walls fail by rigid body mechanisms such as sliding (case (a) below) or overturning (b). There is also the possibility of global instability © but this is not directly an earth pressure problem, more a slope stability problem.
重力墙因刚体机制而失效，例如滑动（下面的情况 （a））或翻转 （b）。也有可能出现全局不稳定©，但这并不是直接的土压力问题，而是边坡稳定性问题。

(a) （一）

(b) （二）

©

Kramer (1996) 克莱默 （1996）

Sliding is a matter of force equilibrium. Overturning occurs when moment equilibrium is not satisfied.
滑动是一个力平衡问题。当力矩平衡不满足时，就会发生倾覆。

Cantilever walls present a greater design challenge because in addition to sliding and overturning, we must also consider flexural failure. Lateral earth pressures create bending moments in the retaining wall. Wall stiffness must then be checked. Figure below shows a distribution of (a) earth pressures and (b) bending moments with © showing flexural failure.
悬臂墙提出了更大的设计挑战，因为除了滑动和倾覆之外，我们还必须考虑弯曲失效。侧向土压力会在挡土墙中产生弯矩。然后必须检查墙刚度。下图显示了 （a） 土压力和 （b） 弯矩的分布，©显示了弯曲破坏。

Calculating lateral earth pressures
计算横向土压力

Some common types of retaining wall and modes of failure
挡土墙的一些常见类型和破坏模式

How much is it? How do we calculate lateral earth pressures?
它是多少？我们如何计算横向土压力？
Consider a cohesionless soil in which lateral earth pressure is a simple function of vertical stress, i.e.
考虑一个无粘性土壤，其中横向土压力是垂直应力的简单函数，即
${\sigma }_{\mathrm{H}}=\mathrm{K}{\sigma }_{\mathrm{V}}$${\sigma }_{\mathrm{H}}=\mathrm{K}{\sigma }_{\mathrm{V}}$sigma_(H)=Ksigma_(V)\sigma_{\mathrm{H}}=\mathrm{K} \sigma_{\mathrm{V}}
Remember ${\sigma }_V=\gamma z$${\sigma }_V=\gamma z$sigma_(V)=gamma z\sigma_{V}=\gamma z so lateral earth pressure increases with depth
请记住 ${\sigma }_V=\gamma z$${\sigma }_V=\gamma z$sigma_(V)=gamma z\sigma_{V}=\gamma z ，横向土压力会随着深度的增加而增加
$K$$K$KK is an earth pressure coefficient. In the analysis and design of retaining walls, particular soil states or conditions are identified. For example, the active condition: in this case, the (lateral) earth pressure coefficient is ${\mathrm{K}}_{\mathrm{A}}$${\mathrm{K}}_{\mathrm{A}}$K_(A)\mathrm{K}_{\mathrm{A}}, where
$K$$K$KK 是土压力系数。在挡土墙的分析和设计中，确定了特定的土壤状态或条件。例如，活动条件：在本例中，（横向）土压力系数为 ${\mathrm{K}}_{\mathrm{A}}$${\mathrm{K}}_{\mathrm{A}}$K_(A)\mathrm{K}_{\mathrm{A}} ，其中
$K_A=\frac{1-\sin {\varphi }^{\prime }}{1+\sin {\varphi }^{\prime }}$$K_A=\frac{1-\sin {\varphi }^{\prime }}{1+\sin {\varphi }^{\prime }}$K_(A)=(1-sin phi^('))/(1+sin phi^('))K_{A}=\frac{1-\sin \phi^{\prime}}{1+\sin \phi^{\prime}}
This and other stress states are covered in much more detail below.
下面将更详细地介绍这种状态和其他应力状态。

Since lateral earth pressure is a fixed function of vertical stress, it increases linearly with depth. Its distribution on a wall is triangular with zero pressure at ground surface. At the base of the wall it is equal to
由于横向土压力是竖向应力的固定函数，因此它随深度线性增加。它在墙上的分布是三角形的，地表压力为零。在墙的底部，它等于
${\sigma }_H=K_A\gamma H$${\sigma }_H=K_A\gamma H$sigma_(H)=K_(A)gamma H\sigma_{H}=K_{A} \gamma H

Pressure distribution is converted to an equivalent force, equal in magnitude to the area of the triangle,
压力分布转换为等效力，其大小等于三角形的面积
$F_A=\frac{1}{2}{K}_A\gamma H^2$$F_A=\frac{1}{2}{K}_A\gamma H^2$F_(A)=(1)/(2)K_(A)gammaH^(2)F_{A}=\frac{1}{2} K_{A} \gamma H^{2}

The line of action, or point at which the equivalent force acts, is important in design. This is easily found by taking the moment of the area of the pressure distribution and making it equivalent to the sum of the moments of all ‘elements’ of the pressure distribution about a given axis.
作用线或等效力作用的点在设计中很重要。这很容易找到，方法是取压力分布面积的力矩，并使其等于围绕给定轴的压力分布的所有“元件”的力矩之和。