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1、Chapter 2 Bearing capacity of foundation,In lesson of soil mechanics, weve learned Types of foundation failures (基础破坏的类型) Ultimate bearing capacity of shallow Foundations (浅基础地基极限承载力) Prandtls method: smooth foundation and weightless soil (普朗特公式:基底光滑与土无重量) Terzaghis method: rough foundation (太沙基公式:基
2、底粗糙),2.1 Introduction (前言),Ultimate bearing capacity (qu) is defined as the pressure which would cause shear failure of the supporting soil immediately below and adjacent to a foundation. (当基底压力增大到极限承载力时,地基出现剪切破坏) A foundation must satisfy two fundamental requirements: (设计基础要满足两个要求 ) the factor of s
3、afety Fs against shear failure of the supporting soil must be adequate, a value between 2 and 3 normally being specified (地基达到剪切破坏的安全糸数 Fs 要适当,一般在2至3之间 ),2.1 Introduction (前言),the settlement of the foundation should be tolerable and, in particular, differential settlement should not cause any unacce
4、ptable damage of the structure (基础的沉降和沉降差必须在该建筑物所允许的范围之内) Allowable bearing capacity (qa) is defined as the maximum pressure which may be applied to the soil such that the above two requirements are satisfied. From first requirement, qa is defined as: (地基的容许承载力 qa 定义为当上述两个条件满足时的基底最大压力.当条件一满足时qa 定义如下
5、),2.2 Types of foundation failures (基础破坏类型),(i) General shear failure (整体剪切破坏 ),State of plastic equilibrium is fully developed throughout the soil above the failure surfaces (地基形成连续滑动面而破坏) Heaving of the ground surface occurs (基础两侧地面向上隆起) Typical failure mode for soils of low compressibility, i.e.
6、dense or stiff soils (紧砂或硬粘土的典型破坏模式),2.2 Types of foundation failures (基础破坏类型),(ii) Local shear failure (局部剪切破坏),Partial development of the state of plastic equilibrium (剪切破坏区限制在地基内部某一区域) Slight heaving occurs (基础两侧地面只是微微隆起) It is characterized by the occurrence of relatively large settlements (这种破坏
7、型式的特征是出现相对大的沉降 ),2.2 Types of foundation failures (基础破坏类型),(iii) Punching shear failure (冲剪破坏),There is relatively high compression of the soil under the foundation accompanied by shearing in the vertical direction around the edges of the foundation (基础边缘下地基产生垂直剪切破坏 ) No heaving of the ground surfac
8、e (基础两侧地面不出现隆起 ),2.3 Ultimate bearing capacity of shallow foundations (浅基础极限承载力),Foundations can be classified as shallow and deep foundations. In general, if the depth of a foundation (D) is smaller than or equal to its breadth (B), i.e. D/B 1, the foundation is classified as shallow foundation. (一
9、般认为,当基础的埋深D小于或等于基础宽度B时,称为浅基础),2.3 Ultimate bearing capacity of shallow foundations (浅基础极限承载力),The following figure shows a strip foundation of width b and infinite length carries a uniform pressure q on the surface of a homogeneous and isotropic soil. In addition, an additional surcharge pressure qo
10、 acts on the soil surface (下图代表一条形基础:基础宽度为b,无限长度,均布荷载q,地基为均质土和各性同向,基础两侧均布荷载为qo),2.3.1 Prandtls method (普朗特公式),Assumption: the base of the foundation is smooth and the soil is weightless. (假设基底光滑与土体无重) The failure mechanism for a strip foundation is shown in following figure. (下图代表条形基础的假设滑动面),2.3.1 P
11、randtls method (普朗特公式),Plastic equilibrium exists above the assumed failure surface EDCGF such that: (在滑动面EDCGF以上土体达到朔性平衡状态) ABC is active Rankine zone (ABC为朗肯主动区) ACD and BCG are radial shear zones (ACD与BCG为径向剪切区 ) ADE and BGF are passive Rankine zones ADE and BGF (ADE与BGF为朗肯被动区 ),2.3.1 Prandtls me
12、thod (普朗特公式),ABC and BAC are 45+/2 DAE, DEA, GBF and GFB are 45-/2 The surfaces CD and CG are logarithmic spirals to which BC and ED, or AC and FG are tangential (ED与FG为直线),2.3.1 Prandtls method (普朗特公式),Using plastic theory, the following exact solution is obtained for the ultimate bearing capacity
13、qu of a strip footing on the surface of a weightless soil. (根据塑性理论, 条形基础在无重量地基上的极限承载力为以下公式),2.3.1 Prandtls method (普朗特公式),The ultimate bearing capacity equation is simplified to the following expression: (极限承载力公式可以简化为以下公式),where d is depth of foundation, o is unit weight of soil above the base of th
14、e foundation, Nc and Nq are bearing capacity factors (d为基础的埋深, o基底以上两侧土体的重度,Nq与Nc为承载力因素),2.3.2 Soil with weight (考虑土体重量),Assumption: the principle of superposition can be used in deriving the ultimate bearing capacity equation. The ultimate bearing capacity can be expressed in the following form: (当
15、考虑地基重量时,可应用叠加原埋,以下公式中的首项代表地基自重的贡献,Nq与Nc分别从普朗特公式找出 ),(i) Smooth foundation (基底光滑),and,2.3.2 Soil with weight (考虑土体重量),If the foundation is rough, so that no slip takes place on AB, ABC is not considered to be an active Rankine zone (ABC不是朗肯主动区) Assumption: ABC and BAC equal to ,(ii) Rough foundation
16、Terzaghis method (基底粗糙-太沙基公式),2.3.2 Soil with weight (考虑土体重量),The ultimate bearing capacity equation is shown as follows:,(ii) Rough foundation Terzaghis method (基底粗糙-太沙基公式),The ultimate bearing factors are shown in the next graph.,Ultimate bearing capacity factors (极限承载力因素),Chapter 2 Bearing capaci
17、ty of foundation (基础承载力),In lesson of soil mechanics, weve learned Allowable bearing capacity of shallow foundations based on depth of plastic zone (从塑性区的深度计算浅基础地基容许承载力) Design value of bearing capacity (地基承载力的设计值),2.4 Allowable bearing capacity of shallow foundations (浅基础容许承载力),The following figure
18、 shows a strip foundation of width b and infinite length carries a uniform pressure q on the surface of a homogeneous and isotropic soil. In addition, an additional surcharge pressure qo acts on the soil surface (下图代表一条形基础:基础宽度为b,无限长度,均布荷载q,地基为均质土和各性同向,基础两侧均布荷载为qo),2.4 Allowable bearing capacity of
19、shallow foundations,From elastic theory, the increases in principal stresses at a given point M are shown as follows (地基中任意点M的附加大,小主应力可从弹性理论找出),b,2.4 Allowable bearing capacity of shallow foundations,Assume the coefficient of earth pressure at-rest (Ko) is 1, the increments in principal stresses can
20、 be superimposed to the principal stresses. The final principal stresses at depth z are (假设静止土压力系数Ko=1,这样自重应力与附加应力可以在任意方向叠加,地基中任意点M的大小主应力可从以下公式找出 ),2.4 Allowable bearing capacity of shallow foundations,When the stresses in point M reach the limiting equilibrium, 1 and 3 at failure are related by the
21、 following expression from Mohr-Coulomb failure criteria (当M点达到极限平衡状态时,大小主应力必需满足以下公式),z is depth of the plastic zone and is expressed as a function of (z为塑性区深度,是的函数),2.4 Allowable bearing capacity of shallow foundations,Differentiate z with respect to , the maximum value of z can be determined by eq
22、uating dz/d to 0 (z最大值从设导数dz/d为零找出 ),Rearrange the above expression into the following form:,2.4 Allowable bearing capacity of shallow foundations,The bearing capacity equation is better to express into the following form:,or,where is unit weight of soil below the base of the foundation, o is unit w
23、eight of soil above the base of the foundation,2.4 Allowable bearing capacity of shallow foundations,If zmax is chosen as b/3,If zmax is chosen as b/4,If zmax is chosen as 0,q1/3, q1/4 and qc are allowable bearing capacities of the foundation (q1/3, q1/4 and qc 为地基容许承载力),2.5 Design values of bearing
24、 capacity (地基承载力的设计值),Determine the ultimate bearing capacity qu from theory likes plastic theory (从理论公式如塑性理论计算极限承载力qu) Calculate allowable bearing capacity qa from dividing qu by a factor of safety Fs (极限承载力qu除以一个安全糸数作为容许承载力qa),If qa also satisfies the settlement criteria, qa will be the design val
25、ue of bearing capacity (当基底压力为qa时, 沉降小于所允许的范围之内, qa 为承载力的设计值),(i) Theoretical Methods (理论公式),2.5 Design value of bearing capacity (地基承载力的设计值),从承载力表,可依据原位标准贯入击数 (SPT N values) 查取承载力标准值 fk 从承载力表,可依据室内试验指标查取承载力基本值fo,然后将fo乘以回归修正糸数f得到fk 当基础宽度小于或等于3m,基础埋深小于或等于0.5m, fk 为承载力的设计值 (design value of bearing capacity) 当基础宽度与埋深超出以上范围时,须经深宽修正得到承载力的设计值,(ii) Codes of practice (规范查表方法),