BEARING CAPACITY OF SOILS

General Bearing Capacity Theory

Bearing Capacity of Soils

General Bearing Capacity Theory

Extensive research work and numerous methods proposed by researchers including Meyerhof (1963), DeBeer (1970), Hansen (1970), Vesic (1973, 1975), and Hanna and Meyerhof (1981) led to the formulation of general bearing capacity theory. Originally proposed by Meyerhof (1963), the general bearing capacity theory takes into consideration factors such as rectangular footings, inclined loads, shear resistance due to the soil above the footing etc. which were not considered in Terzaghi's bearing capacity theory.

The ultimate bearing capacity is expressed as per the following equation;

$q_{u l t} = c^{'} N_{c} F_{c s} F_{c d} F_{c i} + q N_{q} F_{q s} F_{q d} F_{q i} + \frac{1}{2} γ B N_{γ} F_{γ s} F_{γ d} F_{γ i}$

where:
c^'=effective cohesion of the soil beneath the foundation,
𝛾=unit weight of the homogeneous soil,
B= width of foundation (or diameter in the case of circular foundation),
q=effective stress at the bottom of the foundation (due to the soil above the foundation and surcharge (if any) at the ground surface).
If no surcharge is present at the ground surface, then:

q = γ D_{f}

where:
D_f=embedment depth of foundation,
𝛾=unit weight of the homogeneous soil,

Bearing Capacity Factors:
The bearing capacity factors, N_c, N_q, and N_𝛾 , are expressed as per the following equations;

N_{q} = \tan^{2} (45 + \frac{ϕ^{'}}{2}) e^{π \tan ϕ^{'}}

N_{c} = \frac{N_{q} - 1}{\tan ϕ^{'}} for ϕ^{'} > 0

N_{c} = 5.14 for ϕ^{'} = 0

N_{γ} = 2 (N_{q} + 1) \tan ϕ^{'}

Shape Factors:
To account for the broad range of footing shapes, the following shape factors were proposed by DeBeer (1970):

F_{c s} = 1 + (\frac{B}{L}) (\frac{N_{q}}{N_{c}})

F_{q s} = 1 + (\frac{B}{L}) \tan ϕ^{'}

F_{γ s} = 1 - 0.4 (\frac{B}{L})

Depth Factors:
Depth factors that take into account the contribution of foundation embedment to the bearing capacity. Hansen (1970) proposed the following equations for the depth factors:

F_{c d} = 1 + 0.4 (\frac{D_{f}}{B}) ......... for \frac{D_{f}}{B} \leq 1

F_{c d} = 1 + 0.4 \tan^{- 1} (\frac{D_{f}}{B}) ......... for \frac{D_{f}}{B} > 1

F_{q d} = 1 + 2 \tan ϕ^{'} {(1 - \sin ϕ^{'})}^{2} (\frac{D_{f}}{B}) ......... for \frac{D_{f}}{B} \leq 1

F_{q d} = 1 + 2 \tan ϕ^{'} {(1 - \sin ϕ^{'})}^{2} \tan^{- 1} (\frac{D_{f}}{B}) ......... for \frac{D_{f}}{B} > 1

F_{γ d} = 1

Load Inclination Factors:
Load inclination factors that take into account the reduction of bearing capacity due to inclined loads. Meyerhof (1963) proposed the following equations for the load inclination factors:

F_{c i} = F_{q i} = {(1 - \frac{β^{°}}{90^{°}})}^{2}

F_{γ i} = {(1 - \frac{β^{°}}{ϕ^{'}})}^{2}

where:
φ^' = Effective internal frictional angle of the foundation soil,
β = Inclination of the load (Q) on the foundation with respect to the vertical.

Ground Water Table above Footing Level

Ground Water Table below Footing Level

Ground Water Table below Footing Level (D_w-D_f>B)

General Bearing Capacity - Inputs

Effective Cohesion of soil beneath the foundation (c'), KN/m² Effective Internal Friction Angle of the foundation soil (Φ') Unit Weight of the homogenous soil (γ) KN/m³ Saturated Unit Weight of soil (γ_sat) KN/m³ Inclination of Load on the Foundation with respect to Vertical (β) Width of Foundation/Diameter of Circular Foundation (B), m Length of Foundation (L), m Depth of Foundation (D_f), m Depth to Water Table (D_w), m

Bearing Capacity of Soils - Results

INPUTS:

Effective Cohesion of soil beneath the foundation (c'), KN/m²:

Effective Internal Friction Angle of the foundation soil (Φ'):

Unit Weight of the homogenous soil (γ) KN/m³

Saturated Unit Weight of soil (γ_sat) KN/m³

Inclination of Load on the Foundation with respect to Vertical (β)

Width/Diameter of Foundation (B), m:

Length of Foundation (L), m:

Depth of Foundation (D_f), m:

Depth to Water Table (D_w), m:

OUTPUT:

Bearing Capacity Factors:

N_c:

N_q:

N_γ:

Ultimate Bearing Capacity:

Effective Stress, KN/m²:

Ultimate Bearing Capacity, KN/m²:

REPORT SECTION

TRANSCALC TOOLS

AASHTO Soil Classification

AASHTO M 145: Classification of Soils and Soil Aggregate Mixtures for Highway Construction

ASTM Soil Classification

ASTM D 2487:Classification of Soils For Engineering Purposes(Unified Soil Classification System)

Stresses on Soils

Vertical Stress Increase Caused by Vertical Strip Load of Finite Width and Infinite Length on the surface of a semi-infinite soil mass

Specific Gravity of Soils

AASHTO T 100-15/ASTM D 854-00:Specific Gravity of Soils

< >

To advertise, please contact connect@transcalc.com .

CONTENT DISCLAIMER

The information and calculation tools provided on www.transcalc.com website (the "Service") is for general information purposes only. TransCalc assumes no responsibility for errors or omissions in the contents on the Service.In no event shall TransCalc be liable for any special, direct, indirect, consequential, or incidental damages or any damages whatsoever, whether in an action of contract, negligence or other arising out of or in connection with the use of the Service or the contents of the Service. TransCalc reserves the right to make additions, deletions, or modification to the contents on the Service at any time without prior notice.

BEARING CAPACITY OF SOILS

General Bearing Capacity Theory