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Nc, Nq, Nγ: Bearing Capacity Factors Sc, Sq, Sγ: Shape Factors dc, dq, dγ: Depth Factors ic, iq, iγ: Inclination Factors
Nq=eπtanφtan2(45+φ/2)
Nq=eπtanφtan2(45+{{phi | round:0}}/2)
Nq={{nq | round:2}}

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

Nc=π+2
Nc={{nc | round:2}}

Nγ=(Nq-1)tan(1.4φ)
Nγ=({{nq | round:2}}-1)tan[(1.4)({{phi | round:0}})]
Nγ={{ngamma | round:2}}
Kp=tan2(45+φ/2)
Kp=tan2(45+{{phi | round:0}}/2)
Kp={{kp | round:2}}

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

sq=sγ=1+(0.1)(Kp)(B/L)
sq=sγ=1+(0.1)({{kp | round:2}})({{tg | round:1}}/{{tl | round:1}})
sq=sγ={{sq | round:2}}

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

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

dq=dγ=1+(0.1)(Kp)1/2(B/L)
dq=dγ=1+(0.1)({{kp | round:2}})1/2({{tg | round:1}}/{{tl | round:1}})
dq=dγ={{dq | round:2}}

dq=dγ={{dq | round:2}}
ic=iq=1-(θ/90)2
ic=iq=1-({{theta | round:2}}/90)2
ic=iq={{ic | round:2}}

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

iγ={{igamma | round:2}}


qult = c Nc sc dc + q Nq sq dq + 0.5 γ' B Nγ sγ dγ
qult = c Nc dc ic + q Nq dq iq + 0.5 γ B Nγ dγ iγ
qult = ({{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}})
qult = ({{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}})
qult = {{qult | round:0}} kPa
qall - st = qult / FSst
qall - st = {{qult | round:0}} / {{guvenlikSayisiSt | round:0}}
qall - st = {{qallst | round:0}} kPa ≥ {{statikServisYuku | round:0}} kPa (✔) < {{statikServisYuku | round:0}} kPa (✘)
qall - ss = qult / FSss
qall - ss = {{qult | round:0}} / {{guvenlikSayisiSs | round:0}}
qall - 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)

Df: 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)

FSst: Factor of safety - Static (-)

FSss: Factor of safety - Seismic (-)

Fst: Service load - Static (kPa)

Fss: 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 Nc, Nq and Nγ; 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, γe Term

The average effective unit weight of the soil (γe) considering the depth to water table below base of footing (dw) 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

$$ q_{all} = {q_{ult} \over FS} $$