Chapter 8 Bearing Capacity Part 1 [地基承载力]
8.1 Introduction
A foundation is that part of a structure which transmits loads directly to the underlying soil. The 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: (1) the factor of safety against shear failure of the supporting soil must be adequate, a value between 2 and 3 normally being specified; (2) the settlement of the foundation should be tolerable and, in particular, differential settlement should not cause any unacceptable damage of the structure. The 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. [设计基础要满足两个要求: (1)地基达到剪切破坏的安全糸数要适当, 一般在2至3之间,(2)基础的沉降和沉降差必须在该建筑物所允许的范围之内, 地基的容许承载力定义为当上述两个要求满足时的基底最大压力]
8.2 Types of shear failure [剪切破坏的形式]
Three distinct modes of failure have been identified and these are illustrated in Fig. 8.1. In general shear failure, continuous failure surfaces develop between the edges of the footing and the ground surface. The state of plastic equilibrium is fully developed throughout the soil above the failure surfaces. Heaving of the ground surface occurs (see Fig.8.1a). This mode of failure is typical for soils of low compressibility (i.e. dense or stiff soils). The ultimate bearing capacity is well defined. [整体剪切破坏:当基底压力达到极限荷载时, 基础两侧地面向上隆起, 地基形成连续滑动面而破坏]
In local shear failure, there is significant compression of the soil under the footing and only partial development of the state of plastic equilibrium. The failure surfaces, therefore, do not reach the ground surface and only slight heaving occurs (see Fig.8.1b). This type of failure is associated with soils of high compressibility and is characterized by the occurrence of relatively large settlements. The ultimate bearing capacity is not well defined. [局部剪切破坏:当基底压力达到极限荷载时, 基础两侧地面只是微微隆起, 剪切破坏区限制在地基内部某一区域, 这种破坏型式的特征是出现相对大的沉降]
In punching shear failure, there is relatively high compression of the soil under the footing accompanied by shearing in the vertical direction around the edges of the footing. There is no heaving of the ground surface (see Fig.8.1c). Relatively large settlements are also a characteristic of this mode and the ultimate bearing capacity is not well defined. [冲剪破坏:当基底压力达到极限荷载时, 基础边缘下地基产生垂直剪切破坏, 基础两侧地面不出现隆起, 地基不出现连续滑动面, 这种破坏型式的特征是出现相对大的沉降]
8.3 Ultimate Bearing Capacity of Shallow Foundations [浅基础地基极限承载力]
The 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. The allowable bearing capacity (qa ) is defined as
q
a
=
q
u
F s
(8.1)
where F s is the factor of safety and its value is between 2 and 3. 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), the foundation is classified as shallow foundation. [地基的容许承载力定义为极限承载力除以一个安全糸数. 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]
8.3.1 Bearing capacity of foundations on weightless soils (Prandtl’s Method) [普朗特公式]
The failure mechanism for a strip footing is shown in Fig. 8.2. The footing of width b and infinite length carries a uniform pressure q on the surface of a mass of homogeneous, isotropic soil. The shear strength parameters for the soil are c and φ but the unit weight is assumed to be zero. The foundation is assumed to be smooth. In addition, a surcharge pressure q o acting on the soil surface is considered, otherwise if c = 0 the bearing capacity of a weightless soil would be zero. [图8.2代表一条形基础的假设滑动面. 基础宽度为b, 无限长度, 均布荷载q, 地基为均质土, 各性同向, 基底光滑, 基础两侧均布荷载匀q o ]
As the pressure becomes equal to the ultimate bearing capacity q c , the footing will have been pushed downwards into the soil mass, producing a state of plastic equilibrium, in the form of (i) an active Rankine zone ABC, (ii) zones of radial shear ACD and BCG. and (iii) passive Rankine zones ADE and BGF. A state of plastic equilibrium exists above the surface EDCGF.[当地基达到塑性极限平衡状态时,ABC 为朗肯主动区,ACD 与BCG 为径向剪切区,ADE 与BGF 为朗肯被动区]
The angles ∠ABC and ∠BAC are 45︒+φ/2. The angles ∠DAE, ∠DEA, ∠GBF and ∠GFB are 45︒-φ/2. The surfaces CD and CG are logarithmic spirals to which BC and ED, or AC and FG are tangential.
Based on the mechanism described above, the following exact solution is obtained using plastic theory for the ultimate bearing capacity 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]
q
⎡π⋅tan
=c ⋅⎢e
⎣
φ
u
⋅tan
2
⎤φ⎫⎛
45︒+⎪-1⎥⋅cot φ+q
2⎭⎝⎦
o
⎡π⋅tan
⋅⎢e ⎣
φ
⋅tan
2
φ⎫⎤⎛
45︒+⎪⎥
2⎭⎦⎝
(8.2)
Equation (8.2) can be expressed in the following form:
q
u
=c ⋅N
c
+q
o
⋅N
q
(8.3)
where
N
q
=e
π⋅tan φ
⋅tan
2
φ⎫⎛
45︒+⎪
2⎭⎝
2
(8.4) (8.5)
N
c
⎡π⋅tan
=⎢e ⎣
φ
⋅tan
⎤φ⎫⎛
45︒+⎪-1⎥⋅cot φ=N
2⎭⎝⎦
(
q
-1⋅cot φ
)
N q and Nc are bearing capacity factors. Foundations are not normally located on the surface of a soil mass, as assumed in the above solutions, but at a depth d below the surface. In applying these solution in practice, it is assumed that the shear strength of the soil between the surface and depth d is neglected, this soil being considered only as a surcharge imposing a uniform pressure qo = γo ⋅d on the horizontal plane at foundation level, where d is depth of the foundation and γo ⋅is unit weight of soil above the base of the foundation. Equation (8.3) becomes [Nq 与N c 为承载力因素. 公式(8.3)中的均布荷载q o 可看
成基底以上两侧土体的重量, 因此q o = γ⋅d, d为基础的埋深]
q
u
=c ⋅N
c
+γo ⋅d ⋅N
q
(8.6)
8.3.2 Bearing capacity of foundations on soil having weight 1.
The ultimate bearing capacity derived from equation (8.6) does not take into account the weight of soil. No closed-form solutions have been obtained for the bearing capacity of foundations on soils which have weight. To simplify the calculations, we assume that the principle of superposition can be used in deriving the bearing capacity. As a result, the ultimate bearing capacity can be expressed in the following form:
q
u
Smooth Foundations [基底光滑]
=
12
γ⋅b ⋅N
γ
+c ⋅N
c
+γ
o
⋅d ⋅N
q
(8.7)
where N q and N c are values obtained for weightless soil (see equations (8.4) and (8.5)), and N γ is a coefficient defining the bearing capacity of a soil having weight but no cohesion or surcharge (c = qo = 0). We must remember that superposition cannot be validly applied when considering the behaviour of a plastic material. However the value of qu is under-estimated by this procedure. The values of Nγ are still not certainly known. One of the most widely used values for Nγ was obtained by Brinch Hansen (1986) and shown as follows: [当考虑地基重量时, 可应用叠加原埋, 公式8.7中的首项代表地基自重的贡献,N q 与N c 分别从公式8.4 and 8.5找出; 但公式8.7中的N γ 还是未知数, 一般可从经验公式8.8找出]
N
γ
=1. 8⋅N
c
⋅tan
2
φ
(8.8)
2.
If the foundation is rough, so that no slip takes place on AB (see Fig. 8.2), the zone ABC moves downwards as a rigid wedge with the foundation. Terzaghi (1943) assumed that the angles ∠ABC and ∠BAC in Fig. 8.2 were equal to φ, i.e. ABC is not considered to be an active Rankine zone. Terzaghi proposed the ultimate bearing capacity expressed in a form like equation (8.7) but the expressions for the Nq and Nc are obtained by modifying the Prandtl-Reisner’s solution. Nq , Nc and Nγ are functions of φ and the their relationships φ are shown in Fig.8.3. [当基底不光滑时,AB 不会滑动, 太沙基假设图8.2中∠ABC 与∠BAC 为φ, ABC再不是朗肯主动区, 太沙基公式与公式8.7一样, 但承载力因素N q , N c 与N γ可由图8.3查取] 3.
Equation (8.7) is derived based on a strip foundation and a general shear failure mechanism. If the foundations are circular or square in shape, or are subjected to local shear failure, equation (8.7) has to be modified accordingly. [公式8.7应用于条形基础与整体剪切破坏, 当考虑圆形或矩形基础与局部剪切破坏时, 公式8.7必需作以下修改]
Correction factors for ultimate bearing capacity [修正因素] Rough Foundations(Terzaghi’s method) [基底粗糙]
A. Local shear failure [局部剪切破坏] Equation (8.7) is modified to
12
q
u
=γ⋅b ⋅N
*γ
+c
*
⋅N
*c
+γ
o
⋅d ⋅N
*q
(8.9)
where Nq *, Nc * and Nγ*are evaluated from φ* instead of φ
c
*
=
23
c
-1
(8.10) (8.11)
φ
*
=tan
⎛2⎫ tan φ⎪⎝3⎭
B. Shape of Foundation [基础形状]
Equation (8.7) becomes, for a square footing
q
u
=0. 4⋅γ⋅b ⋅N
γ
+1. 2⋅c ⋅N
c
+γo ⋅d ⋅N
q
(8.12)
for a circular footing
q
u
=0. 6⋅γ⋅R ⋅N
γ
+1. 2⋅c ⋅N
c
+γo ⋅d ⋅N
q
(8.13)
where R is radius of the circular footing.
8.3.3 Vesic’s Method [魏锡克公式]
Based on the work of Prandtl, Vesic assumed the foundation is subjected to general shear failure and the foundation is smooth. Vesic arrived the same expression (equation (8.7)) for the ultimate bearing capacity as proposed by Terzaghi. The expressions for Nq and Nc are the same as equations (8.4) and (8.5), but a new expression for Nγ is proposed [魏锡克公式中的N q 与N c 和公式8.4与8.5相同, 但建议用公式8.14找出N γ]
N
γ
=2⋅(N
q
+1) ⋅tan φ
(8.14)
Vesic also proposed a series of correction factors for the ultimate bearing capacity, equation (8.7) is modified as follows: [魏锡克亦建议下列修改因素]
q
u
=
12
γ⋅b ⋅N
γ
⋅S γ⋅d
q
γ
⋅i γ⋅g
γ
⋅ξγ⋅b
γ
+c ⋅N
c
⋅S c ⋅d c ⋅i c ⋅g c ⋅ξc ⋅b c
(8.15)
+γo ⋅d ⋅N ⋅S q ⋅d q ⋅i q ⋅g q ⋅ξq ⋅b q
where
S γ, S c , S q
are shape factors for foundation, [基础形状糸数] are depth factors, [深度糸数]
d γ, d c , d q
i γ, i c , i q
are inclination factors for surcharge, [荷载倾斜糸数] are inclination factors for foundation, [基础倾斜糸数] are soil compressibility factors, [土的压缩性影响糸数] are inclination factors for ground surface. [地面倾斜糸数]
g γ, g c , g q
ξγ, ξc , ξq
b γ, b c , b q
8.3.4 Ultimate bearing capacity for saturated soft clays (Skempton’s Method) [斯开普顿公式]
For saturated soft clays under undrained conditions (φu = 0), the failure surface is a circular arc instead of the one shown in Fig. 8.2. Skempton (1951) proposed the following expression for the ultimate bearing capacity of a footing:
q u =c u ⋅N c +γo ⋅d
(8.16)
where cu is undrained shear strength of the soil (the average value at depth 2/3 b below the bottom of the foundation is used), d is depth of the foundation, γo is unit weight of soil above base of the foundation and the factor Nc is a function of the shape of the footing and the depth/breadth ratio (d/b). Skempton ’s values of Nc are given in Fig.8.4. [因饱和软粘土在不排水状况下的滑动面为圆弧, 斯开普顿建议用公式8.16计算极限承载力. 公式8.16中cu 取基底下2/3 b深度的平均值, d为基础深度, γo 为基底以上土的重度, Nc 从图8.4查取]
(b)
(c)
Settlement
Fig.8.1 Types of failure: (a) general shear, (b) local shear, (c) punching shear
b
q o
q
u
q o
Fig.8.2 Failure mechanism under a strip loading
Chapter 8 Bearing Capacity Part 1 [地基承载力]
8.1 Introduction
A foundation is that part of a structure which transmits loads directly to the underlying soil. The 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: (1) the factor of safety against shear failure of the supporting soil must be adequate, a value between 2 and 3 normally being specified; (2) the settlement of the foundation should be tolerable and, in particular, differential settlement should not cause any unacceptable damage of the structure. The 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. [设计基础要满足两个要求: (1)地基达到剪切破坏的安全糸数要适当, 一般在2至3之间,(2)基础的沉降和沉降差必须在该建筑物所允许的范围之内, 地基的容许承载力定义为当上述两个要求满足时的基底最大压力]
8.2 Types of shear failure [剪切破坏的形式]
Three distinct modes of failure have been identified and these are illustrated in Fig. 8.1. In general shear failure, continuous failure surfaces develop between the edges of the footing and the ground surface. The state of plastic equilibrium is fully developed throughout the soil above the failure surfaces. Heaving of the ground surface occurs (see Fig.8.1a). This mode of failure is typical for soils of low compressibility (i.e. dense or stiff soils). The ultimate bearing capacity is well defined. [整体剪切破坏:当基底压力达到极限荷载时, 基础两侧地面向上隆起, 地基形成连续滑动面而破坏]
In local shear failure, there is significant compression of the soil under the footing and only partial development of the state of plastic equilibrium. The failure surfaces, therefore, do not reach the ground surface and only slight heaving occurs (see Fig.8.1b). This type of failure is associated with soils of high compressibility and is characterized by the occurrence of relatively large settlements. The ultimate bearing capacity is not well defined. [局部剪切破坏:当基底压力达到极限荷载时, 基础两侧地面只是微微隆起, 剪切破坏区限制在地基内部某一区域, 这种破坏型式的特征是出现相对大的沉降]
In punching shear failure, there is relatively high compression of the soil under the footing accompanied by shearing in the vertical direction around the edges of the footing. There is no heaving of the ground surface (see Fig.8.1c). Relatively large settlements are also a characteristic of this mode and the ultimate bearing capacity is not well defined. [冲剪破坏:当基底压力达到极限荷载时, 基础边缘下地基产生垂直剪切破坏, 基础两侧地面不出现隆起, 地基不出现连续滑动面, 这种破坏型式的特征是出现相对大的沉降]
8.3 Ultimate Bearing Capacity of Shallow Foundations [浅基础地基极限承载力]
The 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. The allowable bearing capacity (qa ) is defined as
q
a
=
q
u
F s
(8.1)
where F s is the factor of safety and its value is between 2 and 3. 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), the foundation is classified as shallow foundation. [地基的容许承载力定义为极限承载力除以一个安全糸数. 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]
8.3.1 Bearing capacity of foundations on weightless soils (Prandtl’s Method) [普朗特公式]
The failure mechanism for a strip footing is shown in Fig. 8.2. The footing of width b and infinite length carries a uniform pressure q on the surface of a mass of homogeneous, isotropic soil. The shear strength parameters for the soil are c and φ but the unit weight is assumed to be zero. The foundation is assumed to be smooth. In addition, a surcharge pressure q o acting on the soil surface is considered, otherwise if c = 0 the bearing capacity of a weightless soil would be zero. [图8.2代表一条形基础的假设滑动面. 基础宽度为b, 无限长度, 均布荷载q, 地基为均质土, 各性同向, 基底光滑, 基础两侧均布荷载匀q o ]
As the pressure becomes equal to the ultimate bearing capacity q c , the footing will have been pushed downwards into the soil mass, producing a state of plastic equilibrium, in the form of (i) an active Rankine zone ABC, (ii) zones of radial shear ACD and BCG. and (iii) passive Rankine zones ADE and BGF. A state of plastic equilibrium exists above the surface EDCGF.[当地基达到塑性极限平衡状态时,ABC 为朗肯主动区,ACD 与BCG 为径向剪切区,ADE 与BGF 为朗肯被动区]
The angles ∠ABC and ∠BAC are 45︒+φ/2. The angles ∠DAE, ∠DEA, ∠GBF and ∠GFB are 45︒-φ/2. The surfaces CD and CG are logarithmic spirals to which BC and ED, or AC and FG are tangential.
Based on the mechanism described above, the following exact solution is obtained using plastic theory for the ultimate bearing capacity 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]
q
⎡π⋅tan
=c ⋅⎢e
⎣
φ
u
⋅tan
2
⎤φ⎫⎛
45︒+⎪-1⎥⋅cot φ+q
2⎭⎝⎦
o
⎡π⋅tan
⋅⎢e ⎣
φ
⋅tan
2
φ⎫⎤⎛
45︒+⎪⎥
2⎭⎦⎝
(8.2)
Equation (8.2) can be expressed in the following form:
q
u
=c ⋅N
c
+q
o
⋅N
q
(8.3)
where
N
q
=e
π⋅tan φ
⋅tan
2
φ⎫⎛
45︒+⎪
2⎭⎝
2
(8.4) (8.5)
N
c
⎡π⋅tan
=⎢e ⎣
φ
⋅tan
⎤φ⎫⎛
45︒+⎪-1⎥⋅cot φ=N
2⎭⎝⎦
(
q
-1⋅cot φ
)
N q and Nc are bearing capacity factors. Foundations are not normally located on the surface of a soil mass, as assumed in the above solutions, but at a depth d below the surface. In applying these solution in practice, it is assumed that the shear strength of the soil between the surface and depth d is neglected, this soil being considered only as a surcharge imposing a uniform pressure qo = γo ⋅d on the horizontal plane at foundation level, where d is depth of the foundation and γo ⋅is unit weight of soil above the base of the foundation. Equation (8.3) becomes [Nq 与N c 为承载力因素. 公式(8.3)中的均布荷载q o 可看
成基底以上两侧土体的重量, 因此q o = γ⋅d, d为基础的埋深]
q
u
=c ⋅N
c
+γo ⋅d ⋅N
q
(8.6)
8.3.2 Bearing capacity of foundations on soil having weight 1.
The ultimate bearing capacity derived from equation (8.6) does not take into account the weight of soil. No closed-form solutions have been obtained for the bearing capacity of foundations on soils which have weight. To simplify the calculations, we assume that the principle of superposition can be used in deriving the bearing capacity. As a result, the ultimate bearing capacity can be expressed in the following form:
q
u
Smooth Foundations [基底光滑]
=
12
γ⋅b ⋅N
γ
+c ⋅N
c
+γ
o
⋅d ⋅N
q
(8.7)
where N q and N c are values obtained for weightless soil (see equations (8.4) and (8.5)), and N γ is a coefficient defining the bearing capacity of a soil having weight but no cohesion or surcharge (c = qo = 0). We must remember that superposition cannot be validly applied when considering the behaviour of a plastic material. However the value of qu is under-estimated by this procedure. The values of Nγ are still not certainly known. One of the most widely used values for Nγ was obtained by Brinch Hansen (1986) and shown as follows: [当考虑地基重量时, 可应用叠加原埋, 公式8.7中的首项代表地基自重的贡献,N q 与N c 分别从公式8.4 and 8.5找出; 但公式8.7中的N γ 还是未知数, 一般可从经验公式8.8找出]
N
γ
=1. 8⋅N
c
⋅tan
2
φ
(8.8)
2.
If the foundation is rough, so that no slip takes place on AB (see Fig. 8.2), the zone ABC moves downwards as a rigid wedge with the foundation. Terzaghi (1943) assumed that the angles ∠ABC and ∠BAC in Fig. 8.2 were equal to φ, i.e. ABC is not considered to be an active Rankine zone. Terzaghi proposed the ultimate bearing capacity expressed in a form like equation (8.7) but the expressions for the Nq and Nc are obtained by modifying the Prandtl-Reisner’s solution. Nq , Nc and Nγ are functions of φ and the their relationships φ are shown in Fig.8.3. [当基底不光滑时,AB 不会滑动, 太沙基假设图8.2中∠ABC 与∠BAC 为φ, ABC再不是朗肯主动区, 太沙基公式与公式8.7一样, 但承载力因素N q , N c 与N γ可由图8.3查取] 3.
Equation (8.7) is derived based on a strip foundation and a general shear failure mechanism. If the foundations are circular or square in shape, or are subjected to local shear failure, equation (8.7) has to be modified accordingly. [公式8.7应用于条形基础与整体剪切破坏, 当考虑圆形或矩形基础与局部剪切破坏时, 公式8.7必需作以下修改]
Correction factors for ultimate bearing capacity [修正因素] Rough Foundations(Terzaghi’s method) [基底粗糙]
A. Local shear failure [局部剪切破坏] Equation (8.7) is modified to
12
q
u
=γ⋅b ⋅N
*γ
+c
*
⋅N
*c
+γ
o
⋅d ⋅N
*q
(8.9)
where Nq *, Nc * and Nγ*are evaluated from φ* instead of φ
c
*
=
23
c
-1
(8.10) (8.11)
φ
*
=tan
⎛2⎫ tan φ⎪⎝3⎭
B. Shape of Foundation [基础形状]
Equation (8.7) becomes, for a square footing
q
u
=0. 4⋅γ⋅b ⋅N
γ
+1. 2⋅c ⋅N
c
+γo ⋅d ⋅N
q
(8.12)
for a circular footing
q
u
=0. 6⋅γ⋅R ⋅N
γ
+1. 2⋅c ⋅N
c
+γo ⋅d ⋅N
q
(8.13)
where R is radius of the circular footing.
8.3.3 Vesic’s Method [魏锡克公式]
Based on the work of Prandtl, Vesic assumed the foundation is subjected to general shear failure and the foundation is smooth. Vesic arrived the same expression (equation (8.7)) for the ultimate bearing capacity as proposed by Terzaghi. The expressions for Nq and Nc are the same as equations (8.4) and (8.5), but a new expression for Nγ is proposed [魏锡克公式中的N q 与N c 和公式8.4与8.5相同, 但建议用公式8.14找出N γ]
N
γ
=2⋅(N
q
+1) ⋅tan φ
(8.14)
Vesic also proposed a series of correction factors for the ultimate bearing capacity, equation (8.7) is modified as follows: [魏锡克亦建议下列修改因素]
q
u
=
12
γ⋅b ⋅N
γ
⋅S γ⋅d
q
γ
⋅i γ⋅g
γ
⋅ξγ⋅b
γ
+c ⋅N
c
⋅S c ⋅d c ⋅i c ⋅g c ⋅ξc ⋅b c
(8.15)
+γo ⋅d ⋅N ⋅S q ⋅d q ⋅i q ⋅g q ⋅ξq ⋅b q
where
S γ, S c , S q
are shape factors for foundation, [基础形状糸数] are depth factors, [深度糸数]
d γ, d c , d q
i γ, i c , i q
are inclination factors for surcharge, [荷载倾斜糸数] are inclination factors for foundation, [基础倾斜糸数] are soil compressibility factors, [土的压缩性影响糸数] are inclination factors for ground surface. [地面倾斜糸数]
g γ, g c , g q
ξγ, ξc , ξq
b γ, b c , b q
8.3.4 Ultimate bearing capacity for saturated soft clays (Skempton’s Method) [斯开普顿公式]
For saturated soft clays under undrained conditions (φu = 0), the failure surface is a circular arc instead of the one shown in Fig. 8.2. Skempton (1951) proposed the following expression for the ultimate bearing capacity of a footing:
q u =c u ⋅N c +γo ⋅d
(8.16)
where cu is undrained shear strength of the soil (the average value at depth 2/3 b below the bottom of the foundation is used), d is depth of the foundation, γo is unit weight of soil above base of the foundation and the factor Nc is a function of the shape of the footing and the depth/breadth ratio (d/b). Skempton ’s values of Nc are given in Fig.8.4. [因饱和软粘土在不排水状况下的滑动面为圆弧, 斯开普顿建议用公式8.16计算极限承载力. 公式8.16中cu 取基底下2/3 b深度的平均值, d为基础深度, γo 为基底以上土的重度, Nc 从图8.4查取]
(b)
(c)
Settlement
Fig.8.1 Types of failure: (a) general shear, (b) local shear, (c) punching shear
b
q o
q
u
q o
Fig.8.2 Failure mechanism under a strip loading