GC | Bearing capacity of shallow foundations in soil

c (kPa)

φ (⁰)

D_f (m)

B (m)

L (m)

θ (⁰)

γ(kN/m³)

GWT (m)

FS_st

FS_ss

F_st (kPa)

F_ss (kPa)

N_c, N_q, N_γ: Bearing Capacity Factors	S_c, S_q, S_γ: Shape Factors	d_c, d_q, d_γ: Depth Factors	i_c, i_q, i_γ: Inclination Factors

N_q=e^πtanφtan²(45+φ/2)
N_q=e^πtanφtan²(45+{{phi | round:0}}/2)
N_q={{nq | round:2}}

N_c=(N_q-1) cotφ
N_c=({{nq | round:2}}-1)cot{{phi | round:0}}
N_c={{nc | round:2}}

N_c=π+2
N_c={{nc | round:2}}

N_γ=(N_q-1)tan(1.4φ)
N_γ=({{nq | round:2}}-1)tan[(1.4)({{phi | round:0}})]
N_γ={{ngamma | round:2}}

K_p=tan²(45+φ/2)
K_p=tan²(45+{{phi | round:0}}/2)
K_p={{kp | round:2}}

s_c=1+(0.2)(K_p)(B/L)
s_c=1+(0.2)({{kp | round:2}})({{tg | round:1}}/{{tl | round:1}})
s_c={{sc | round:2}}

s_q=s_γ=1+(0.1)(K_p)(B/L)
s_q=s_γ=1+(0.1)({{kp | round:2}})({{tg | round:1}}/{{tl | round:1}})
s_q=s_γ={{sq | round:2}}

s_q=s_γ={{sq | round:2}}

K_p=tan²(45+φ/2)
K_p=tan²(45+{{phi | round:0}}/2)
K_p={{kp | round:2}}

d_c=1+(0.2)(K_p)^1/2(B/L)
d_c=1+(0.2)({{kp | round:2}})^1/2({{tg | round:1}}/{{tl | round:1}})
d_c={{dc | round:2}}

d_q=d_γ=1+(0.1)(K_p)^1/2(B/L)
d_q=d_γ=1+(0.1)({{kp | round:2}})^1/2({{tg | round:1}}/{{tl | round:1}})
d_q=d_γ={{dq | round:2}}

d_q=d_γ={{dq | round:2}}

i_c=i_q=1-(θ/90)²
i_c=i_q=1-({{theta | round:2}}/90)²
i_c=i_q={{ic | round:2}}

i_γ=1-(θ/φ)²
i_γ=1-({{theta | round:2}}/{{phi | round:2}})²
i_γ={{igamma | round:2}}

i_γ={{igamma | round:2}}

q_ult = c N_c s_c d_c + q N_q s_q d_q + 0.5 γ' B N_γ s_γ d_γ

q_ult = c N_c d_c i_c + q N_q d_q i_q + 0.5 γ B N_γ d_γ i_γ

q_ult = ({{kohezyon | round:2}})({{nc | round:2}})({{sc | round:2}})({{dc | round:2}}) + ({{efektifStres | round:2}})({{nq | round:2}})({{sq | round:2}})({{dq | round:2}}) + (0.5)({{gamma_effective | round:2}})({{tg | round:2}})({{ngamma | round:2}})({{sgamma | round:2}})({{dgamma | round:2}})

q_ult = ({{kohezyon | round:2}})({{nc | round:2}})({{dc | round:2}})({{ic | round:2}}) + ({{efektifStres | round:2}})({{nq | round:2}})({{dq | round:2}})({{iq | round:2}}) + (0.5)({{gamma_effective | round:2}})({{tg | round:2}})({{ngamma | round:2}})({{dgamma | round:2}})({{igamma | round:2}})

q_ult = {{qult | round:0}} kPa

q_{all - st} = q_ult / FS_st

q_{all - st} = {{qult | round:0}} / {{guvenlikSayisiSt | round:0}}

q_{all - st} = {{qallst | round:0}} kPa ≥ {{statikServisYuku | round:0}} kPa (✔) < {{statikServisYuku | round:0}} kPa (✘)

q_{all - ss} = q_ult / FS_ss

q_{all - ss} = {{qult | round:0}} / {{guvenlikSayisiSs | round:0}}

q_{all - ss} = {{qallss | round:0}} kPa ≥ {{sismikServisYuku | round:0}} kPa (✔) < {{sismikServisYuku | round:0}} kPa (✘)

The Procedure and Formulations for Meyerhof (1963) Bearing Capacity Calculations

Input Parameters

c: Cohesion (kPa)

φ: Internal friction angle (^o)

D_f: Foundation depth (m)

B: Foundation width (m)

L: Foundation length (m)

θ: Angle of force (^o)

γ: Natural unit weight (kN/m³)

GWT: Ground water table depth (m)

FS_st: Factor of safety - Static (-)

FS_ss: Factor of safety - Seismic (-)

F_st: Service load - Static (kPa)

F_ss: Service load - Seismic (kPa)

The calculation tool given above for calculating bearing capacity of a shallow foundation follows the procedure given in "Foundation Analysis and Design, 5th Edition (Joseph E. Bowles) - Chapter 4. The details of the Meyerhof (1963) method for calculating bearing capacity of shallow foundations is given below.

Ultimate Bearing Capacity

The bearing capacity is calculated according to the following equations for Meyerhof (1963) method.

In case of a vertical load (θ=0);

$$q_{ult} = c N_{c} s_{c} d_{c} + \overline{q} N_{q} s_{q} d_{q} + 0.5 \gamma_{e} B N_{\gamma} s_{\gamma} d_{\gamma}$$

In case of a inclined load (θ>0);

$$q_{ult} = c N_{c} d_{c} i_{c} + \overline{q} N_{q} d_{q} i_{q} + 0.5 \gamma_{e} B N_{\gamma} d_{\gamma} i_{\gamma}$$

Bearing Capacity Factors

The bearing capacity factors N_c, N_q and N_γ; are calculated as follows:

$$N_{q} = e^{\pi tan \phi}tan^2 \left(45 + {\phi \over 2} \right) $$

$$N_{c} = (N_{q}-1)cot\phi$$

$$N_{\gamma} = (N_{q}-1)tan(1.4\phi)$$

Shape, Depth and Inclination Factors

Shape Factors:

$$ s_c = 1 + 0.2K_p(B/L) \ for \ any \ \phi$$

$$ s_q = s_{\gamma} = 1 + 0.1K_p(B/L) \ for \ \phi > 10^o$$

$$ s_q = s_{\gamma} = 1 \ for \ \phi = 0^o$$

Depth Factors:

$$ d_c = 1 + 0.2 \sqrt{K_p} {D \over B} \ for \ any \ \phi$$

$$ d_q = d_{\gamma} = 1 + 0.1 \sqrt{K_p} {D \over B} \ for \ \phi > 10^o$$

$$ d_q = d_{\gamma} = 1 \ for \ \phi = 0^o$$

Inclination Factors:

$$ i_c = i_q = \left(1 -{\theta \over 90^o}\right)^2 \ for \ any \ \phi$$

$$ i_{\gamma} = \left(1 -{\theta \over \phi}\right)^2 \ for \ \phi > 10^o$$

$$ i_{\gamma} = 0 \ for \ \theta > 0^o \ and \ \phi=0$$

Where,

$$ K_{p} = tan^2 \left(45 + {\phi \over 2} \right)$$

Effect of Water table, γ_e Term

The average effective unit weight of the soil (γ_e) considering the depth to water table below base of footing (d_w) and the depth of wedge zone (H) is calculated as follows;

$$ \gamma_e = (2H-d_w){d_w \over H^2}\gamma_{wet} + {\gamma' \over H^2}(H-d_w)^2 $$

Where,

$$ H = 0.5 B tan(45+\phi/2)$$

Allowable Bearing Capacity