Bearing Capacity of Shallow Foundation dr. isam jardaneh / foundation engineering / 2010
The load of the superstructure A foundation is required for distributing the loads of the superstructure on a large area. The design of foundations of structures such as buildings, bridges, dams, etc. generally requires a knowledge of such factors: The load of the superstructure The requirements of the local building code The behavior of stress –strain of soils The geological conditions dr. isam jardaneh / foundation engineering / 2010
To perform satisfactorily, shallow foundations should be designed with two main characteristics: a) They have to be safe against overall shear failure in the soil that supports them. b) They cannot go excessive settlement (settlement is within acceptable level) dr. isam jardaneh / foundation engineering / 2010
Foundation Engineering is a clever combination of soil mechanics, engineering geology and proper judgment derived from past experience. To a certain extent, it may be called and art. dr. isam jardaneh / foundation engineering / 2010
The aim of Geotechnical (Foundation) Engineer is to determine the most economical foundation type dr. isam jardaneh / foundation engineering / 2010
Shallow Foundation Deep Foundation The foundation types for structures have two main categories: Shallow Foundation Deep Foundation dr. isam jardaneh / foundation engineering / 2010
Shallow Foundation When Df / B ≤ 3 to 4 Ground Surface dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
Deep Foundation P I L E weak soil bed rock dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
Ultimate Bearing Capacity The load per unit area of the foundation at which shear failure in soil occurs. dr. isam jardaneh / foundation engineering / 2010
Modes of Failure of Soil under a Foundation General Concept Modes of Failure of Soil under a Foundation dr. isam jardaneh / foundation engineering / 2010
Modes of shear Failure : Vesic (1973) classified shear failure of soil under a foundation base into three categories depending on the type of soil & location of foundation. 1) General Shear failure. 2) Local Shear failure. 3) Punching Shear failure dr. isam jardaneh / foundation engineering / 2010
General Shear failure Strip footing resting on surface Load –settlement curve of dense sand or stiff clay The load - Settlement curve in case of footing resting on surface of dense sand or stiff clays shows pronounced peak & failure occurs at very small stain. A loaded base on such soils sinks or tilts suddenly in to the ground showing a surface heave of adjoining soil The shearing strength is fully mobilized all along the slip surface & hence failure planes are well defined. The failure occurs at very small vertical strains accompanied by large lateral strains. dr. isam jardaneh / foundation engineering / 2010
Local Shear failure Strip footing resting on surface Load –settlement curve Of Medium sand or Medium clay When load is equal to a certain value qu(1),The foundation movement is accompanied by sudden jerks. The failure surface gradually extend out wards from the foundation. The failure starts at localized spot beneath the foundation & migrates out ward part by part gradually leading to ultimate failure. The shear strength of soil is not fully mobilized along planes & hence failure planes are not defined clearly. The failure occurs at large vertical strain & very small lateral strains dr. isam jardaneh / foundation engineering / 2010
Punching Share failure The loaded base sinks into soil like a punch. The failure surface do not extend up to the ground surface. No heave is observed. Large vertical strains are involved with practically no lateral deformation. Failure planes are difficult to locate. dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
Terzaghi’s Bearing Capacity Theory for General Shear Failure Terzaghi (1943) analyzed a shallow continuous footing by making some assumptions dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
The failure zones do not extend above the horizontal plane passing through base of footing The failure occurs when the down ward pressure exerted by loads on the soil adjoining the inclined surfaces on soil wedge is equal to upward pressure. Downward forces are due to the load (=qu× B) & the weight of soil wedge (1/4 γB2 tanØ) Upward forces are the vertical components of resultant passive pressure (Pp) & the cohesion (c’) acting along the inclined surfaces. dr. isam jardaneh / foundation engineering / 2010
The failure area in the soil under the foundation can be divided into three major zones, they are: dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
For equilibrium: ΣFv = 0 1/4 γ B2tan ø + quxB = 2Pp +2C’ × Li sinø’ For equilibrium: ΣFv = 0 1/4 γ B2tan ø + quxB = 2Pp +2C’ × Li sinø’ where Li = length of inclined surface CB ( = B/2 /cosø’) Therefore, qu× B = 2Pp + BC’ tanø’ - ¼ γ B2tanø’ –------ (1) The resultant passive pressure (Pp) on the surface CB & CA constitutes three components i.e. (Pp)r, (Pp)c & (Pp) q, Thus, Pp = (Pp)r + (Pp)c + (Pp)q dr. isam jardaneh / foundation engineering / 2010
qu× B= 2[ (Pp)r +(Pp)c +(Pp)q ]+ Bc’tanø’-¼ γ B2 tanø’ Substituting; 2 (Pp)r - ¼rB2tanø1 = B × ½ γ BNr 2 (Pp)q = B × γ D Nq & 2 (Pp)c + Bc1 tanø1 = B × C1 Nc; We get, qu =C’Nc + γ Df Nq + 0.5 γ B N γ This is Terzaghi’s Bearing capacity equation for determining ultimate bearing capacity of strip footing. Where Nc, Nq & Nγ are Terzaghi’s bearing capacity factors & depends on angle of shearing resistance (ø) dr. isam jardaneh / foundation engineering / 2010
Ultimate Bearing Capacity Equation for Continuous Footing (General Shear Failure) dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
Terzaghi’s Bearing Capacity Theory for Local Shear Failure dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
Effect of water table on Bearing Capacity The equation for ultimate bearing capacity by Terzaghi has been developed based on assumption that water table is located at a great depth. If the water table is located close to foundation; the equation needs modification. dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
The General Bearing Capacity Equation Terzaghi’s bearing capacity equations have the following shortcomings: They don not address the case of rectangular foundations. They do not take into account the shearing resistance along the failure surface in the soil above the bottom of foundation. They do not take in account inclined load. dr. isam jardaneh / foundation engineering / 2010
Meyerhof (1963) suggested the general form of general capacity equation: dr. isam jardaneh / foundation engineering / 2010
Bearing Capacity Factors for General Bearing Capacity Equation dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
Effect of Soil Compressibility dr. isam jardaneh / foundation engineering / 2010
Gs = Es/2(1+μs dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
Bearing Capacity of Eccentrically Loaded Foundation dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
Ultimate Bearing Capacity under Eccentric Loading Meyerhof’s Theory In 1953, Meyerhof proposed a theory that is generally referred to as the effective area method. The following is a step – by – step procedure for determining the ultimate load that the soil can support: dr. isam jardaneh / foundation engineering / 2010
dr. isam jardaneh / foundation engineering / 2010
Homework # 2 Problem #2 Problem #3 Problem #1 dr. isam jardaneh / foundation engineering / 2010
Problem #5 Problem #6 Problem #4 dr. isam jardaneh / foundation engineering / 2010