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Foundation – Stability Analysis

The maximum load that can be sustained by shallow foundation elements due to the bearing capacity is a function of the cohesion and friction angle of bearing soils as well as the width B and shape of the foundation. The net bearing capacity per unit area, qu, of a long footing is expressed as:

where
(alpha)f= 1.0 for strip footings and 1.3 for circular and square footings
cu= Un-drained shear strength of soil
(sigma) vo = effective vertical shear stress in soil at level of bottom of footing
(beta)f = 0.5 for strip footings, 0.4 for square footings, and 0.6 for circular footings
gamma =unit weight of soil
B=width of footing for square and rectangular footings and radius of footing for circular footings
Nc, Nq, N=bearing-capacity factors, functions of angle of internal friction (phi)

Groups of Piles

Group of piles means when we have more than 1 pile in a row. Many factors influence the pile group stability. The major factors are Geometry of the group, soil conditions and direction of loads.

The efficiency factor Eg is defined as the ratio of the ultimate group capacity to the sum of the ultimate capacity of each pile in the group. It is this factor which is mostly used to express the ultimate load considerations.

In case of piles being driven in cohesive soils, the ultimate load is alculated by using the followinf formula

Qbu=Abq=AbNccu

where
Ab = End bearing area of pile
q= bearing capacity of soil
Nt =bearing capacity factor
cu= Un-drained shear strength of soil within zone 1 pile diameter above and 2 diameters below pile tip

The value of Nc varies from 8-12 but normally we take the value to by 9

For Cohesionless soils
In case of cohesionless soils, the toe resistance q is calculated as
q=NNq (sigma)’vo<=qt

For Piles driven in Sand
ql=0.5Nq tan(phi)

where
phi= friction angle of the bearing soils below the critical depth.

When ever we are studying about a vertical pile, we need to understand that the flexural stiffness of the shaft and stiffness of the bearing soil in the upper 4D to 6D length of shaft are the two main factors on which the resistance to lateral loads of vertical pile depends.

Nondimensional solutions of Reese and Matlock help us plot the lateral-load vs. pile-head deflection relationship but the basic assumption with this is that the soil modulus K increases linearly with depth z

K= nhz
where nh coefficient of horizontal subgrade reaction.

A characteristic pile length T is given by
T=(EI/nh)1/2
where
EI= pile stiffness.

The most commonly used formula to determine the allowable static load on a pile is the Engineering News formula.

Case-1 The allowable load for piles driven by a drop hammer
Pa=(2WH)/(p+1)

Case-2 The allowable load for piles driven by a steam hammer
Pa=(2WH)/(p+0.1)

where