|
|
| Line 1: |
Line 1: |
| In [[geotechnical engineering]], '''bearing capacity''' is the capacity of [[soil]] to support the [[structural load|loads]] applied to the ground. The bearing capacity of soil is the maximum average contact [[pressure]] between the [[foundation (architecture)|foundation]] and the soil which should not produce [[shear strength (soil)|shear]] failure in the soil. ''Ultimate bearing capacity'' is the theoretical maximum pressure which can be supported without failure; ''allowable bearing capacity'' is the ultimate bearing capacity divided by a factor of safety. Sometimes, on soft soil sites, large settlements may occur under loaded foundations without actual shear failure occurring; in such cases, the allowable bearing capacity is based on the maximum allowable settlement.
| | Yoshiko is her name but she doesn't like when people use her complete title. Playing croquet is something I will by no means give up. Managing individuals is what I do in my working day job. Kansas is where her house is but she requirements to move because of her family.<br><br>Also visit my blog :: [http://www.Thehubermangroup.com/ActivityFeed/MyProfile/tabid/60/userId/24292/Default.aspx car warranty] |
| | |
| There are three modes of failure that limit bearing capacity: general shear failure, local shear failure, and punching shear failure.
| |
| | |
| == Introduction ==
| |
| A foundation is the part of a structure which transmits the weight of the structure to the ground. All structures constructed on land are supported on foundations. A foundation is, therefore, a connecting link between the structure proper and the ground which supports it.
| |
| | |
| == General shear failure ==
| |
| The general shear failure case is the one normally analyzed. Prevention against other failure modes is accounted for implicitly in settlement calculations.<ref name=coduto>{{Citation|surname=Coduto|given=Donald|author-link=|year=2001|title=Foundation Design|Place=|publisher=Prentice-Hall|isbn=0-13-589706-8|url=}}</ref> There are many different methods for computing when this failure will occur.
| |
| | |
| == Terzaghi's Bearing Capacity Theory ==
| |
| [[Karl von Terzaghi]] was the first to present a comprehensive theory for the evaluation of the ultimate bearing capacity of rough shallow foundations. This theory states that a foundation is shallow if its depth is less than or equal to its width.<ref name=Das>{{Citation|surname=Das|given=Braja|author-link=|edition=6th|year=2007|title=Principles of Foundation Engineering|place=Stamford, CT|publisher=Cengage Publisher|id=}}</ref> Later investigations, however, have suggested that foundations with a depth, measured from the ground surface, equal to 3 to 4 times their width may be defined as shallow foundations(Das, 2007).
| |
| | |
| Terzaghi developed a method for determining bearing capacity for the general shear failure case in 1943. The equations are given below.
| |
| | |
| For square foundations:
| |
| :<math> q_{ult} = 1.3 c' N_c + \sigma '_{zD} N_q + 0.4 \gamma ' B N_\gamma \ </math>
| |
| | |
| For continuous foundations:
| |
| :<math> q_{ult} = c' N_c + \sigma '_{zD} N_q + 0.5 \gamma ' B N_\gamma \ </math>
| |
| | |
| For circular foundations:
| |
| :<math> q_{ult} = 1.3 c' N_c + \sigma '_{zD} N_q + 0.3 \gamma ' B N_\gamma \ </math> | |
| | |
| where
| |
| :<math> N_q = \frac{ e ^{ 2 \pi \left( 0.75 - \phi '/360 \right) \tan \phi ' } }{2 \cos ^2 \left( 45 + \phi '/2 \right) } </math> | |
| :<math> N_c = 5.7 \ </math> for φ' = 0
| |
| :<math> N_c = \frac{ N_q - 1 }{ \tan \phi '} </math> for φ' > 0
| |
| :<math> N_\gamma = \frac{ \tan \phi ' }{2} \left( \frac{ K_{p \gamma} }{ \cos ^2 \phi ' } - 1 \right) </math>
| |
| :''c''′ is the effective [[cohesion (geology)|cohesion]].
| |
| :''σ<sub>zD</sub>''′ is the vertical [[effective stress]] at the depth the foundation is laid. | |
| :γ''′ is the effective unit weight when saturated or the total unit weight when not fully saturated.
| |
| :''B'' is the width or the diameter of the foundation.
| |
| :''φ''′ is the effective internal [[friction#ange of friction|angle of friction]].
| |
| :''K<sub>pγ</sub>'' is obtained graphically. Simplifications have been made to eliminate the need for ''K<sub>pγ</sub>''. One such was done by Coduto, given below, and it is accurate to within 10%.<ref name=coduto/>
| |
| :<math> N_\gamma = \frac{ 2 \left( N_q + 1 \right) \tan \phi ' }{1 + 0.4 \sin 4 \phi ' }</math>
| |
| | |
| For foundations that exhibit the local shear failure mode in soils, Terzaghi suggested the following modifications to the previous equations. The equations are given below.
| |
| | |
| For square foundations:
| |
| :<math> q_{ult} = 0.867 c' N '_c + \sigma '_{zD} N '_q + 0.4 \gamma ' B N '_\gamma \ </math>
| |
| | |
| For continuous foundations:
| |
| :<math> q_{ult} = \frac{2}{3} c' N '_c + \sigma '_{zD} N '_q + 0.5 \gamma ' B N '_\gamma \ </math>
| |
| | |
| For circular foundations:
| |
| :<math> q_{ult} = 0.867 c' N '_c + \sigma '_{zD} N '_q + 0.3 \gamma ' B N '_\gamma \ </math>
| |
| | |
| <math> N '_c, N '_q and N '_y </math>, the modified bearing capacity factors, can be calculated by using the bearing capacity factors equations(for <math> N_c, N_q, and N_y</math>, respectively) by replacing the effective internal angle of friction<math>(\phi ')</math> by a value equal to <math> : tan^{-1}\, (\frac{2}{3} tan \phi ') </math> <ref name=Das>{{Citation|surname=Das|given=Braja|author-link=|edition=6th|year=2007|title=Principles of Foundation Engineering|place=Stamford, CT|publisher=Cengage Publisher|id=}}</ref>
| |
| | |
| == Factor of Safety ==
| |
| Calculating the gross allowable-load bearing capacity of shallow foundations requires the application of a factor of safety(FS) to the gross ultimate bearing capacity, or:
| |
| | |
| <math> q_{all} = \frac{q_{ult}}{FS} </math> <ref name=Das>{{Citation|surname=Das|given=Braja|author-link=|year=2007|title=Principles of Foundation Engineering|place=Stamford, CT|publisher=Cengage Publisher|id=}}</ref>
| |
| | |
| == Meyerhofs's Bearing Capacity theory ==
| |
| In 1951, Meyerhof published a bearing capacity theory which could be applied to rough shallow and deep foundations.<ref name=Das2>{{|publisher=CRC Press LLC|id=|}}</ref>
| |
| | |
| ==See also==
| |
| *[[Geotechnical engineering]]
| |
| *[[Foundation (architecture)]]
| |
| *[[Soil mechanics]]
| |
| | |
| ==References==
| |
| {{reflist}}
| |
| | |
| ==External links==
| |
| *[http://www.geotechnicalinfo.com/bearing_capacity_factors.html Bearing Capacity Factors related to the angle of internal friction]
| |
| {{Geotechnical engineering}}
| |
| | |
| [[Category:Soil mechanics]]
| |
| | |
| [[nl:Draagkracht (constructie)]]
| |
Yoshiko is her name but she doesn't like when people use her complete title. Playing croquet is something I will by no means give up. Managing individuals is what I do in my working day job. Kansas is where her house is but she requirements to move because of her family.
Also visit my blog :: car warranty