Chapter 2 Bearing capacity of foundation In lesson of soil mechanics,we've 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 Prandtl's method: :smooth foundation and weightless soil(普朗特公式：基底光滑与 润 尤重量 Terzaghi's method:rough foundation(太沙基 公式：基底粗糙 超
Chapter 2 Bearing capacity of foundation In lesson of soil mechanics, we’ve 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) ▪ Prandtl’s method: smooth foundation and weightless soil (普朗特公式:基底光滑与土 无重量) ▪ Terzaghi’s method: rough foundation (太沙基 公式:基底粗糙)
2.1 Introduction(前言) Ultimate bearing capacity (q)is defined as the pressure which would cause shear failure of the supporting soil immediately below and adjacent to a foundation. 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: 计基础要两足两个婆求) the factor of safety Fs against shear failure of the supporting soil must be adequate,a value between 2 通 and3 normally being specified(地基达到剪切破坏的 全系数F。要适当， 般在2至3乙间 超
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 safety 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 unacceptable damage of the structure(基础的沉降和元 降差必须在该建筑物所允许的范围之内)「 Allowable bearing capacity (q)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q定义为当上述两 亲件满足时的基底最大压力.当条件满是时9。定义 如下 qu qa
2.1 Introduction (前言) ▪ the settlement of the foundation should be tolerable and, in particular, differential settlement should not cause any unacceptable 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) s u a F q q =
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 实滑动围而破场 Heaving of the ground surface occurs(甚础两侧地面向L隆起 Typical failure mode for soils of low compressibility,i.e.dense or stiff soils(紧砂或硬粘士的典型破坏模式 图 Pressure Ground surface (地面) Sliding surface (滑动面)
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. dense or stiff soils (紧砂或硬粘土的典型破坏模式) Pressure Settlement Sliding surface (滑动面) Ground surface (地面)
2.2 Types of foundation failures(基础破坏类型) (i)Local shear failure(局部剪切破坏) Partial development of the state of plastic equilibrium 破坏区限制在地基内部某一区域 Slight heaving occurs(基础两侧地i只是微微隆起) It is characterized by the occurrence of relatively large settlements(这种破坏型式的情征是出现相对木的沉降 Pressure I Ground surface (地面) Sliding surface (滑动面)
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 (这种破坏型式的特征是出现相对大的沉降 ) Pressure Settlement Sliding surface (滑动面) Ground surface (地面)
2.2 Types of foundation failures(基础破坏类型) (ii)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(基边缘下地基产生 切被环 No heaving of the ground surface(基础内侧地面不出现隆 Pressure 通 Ground surface (地面) Sliding surface (滑动面) 阔
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 surface (基础两侧地面不出现隆 起 ) Pressure Settlement Sliding surface (滑动面) Ground surface (地面)
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 s 1,the foundation is classified as shallow foundation. 股认为，当基础的理深D 或 于基础宽度B时称为浅基础 Ground Surface 蘭 B (a)Shallow B (b)Deep
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 do acts on the soil surface 下图代表条形基：基宽度为b,无限长度，均布荷 唐4，地基为均质士和各性同向，岳础两侧均布有载为9 Ground surface Ground surface
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 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 ) Ground surface q b qo Ground surface q b d o
2.3.1 Prandtl's method(普朗特公式) Assumption:the base of the foundation is smooth and the soil is weightless.(假设基底光滑与士体无重 The failure mechanism for a strip foundation is shown in following figure.下图代表条形基础的假设情动面 qo 45°+ 是 阔
2.3.1 Prandtl’s 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) qu qo qo b
2.3.1 Prandtl's method(普朗特公式) Plastic equilibrium exists above the assumed failure surface EDCGF such that:(在动[面EDCGF以上土 本大 ABC is active Rankine zoneABG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 和 育动区 45-号 r=r。e9-tanp
2.3.1 Prandtl’s 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 ) qu qo qo b = tan o r r e