Soil bearing earth pressure theory assumes that upon exceeding a certain
stress condition, rupture surfaces are formed in the soil mass. Thus, the
stress causing the formation of these rupture surfaces may be considered
as the Ultimate Bearing Capacity of the soil.
Based on the above assumption, the bearing capacity can be determined from:
1- The relationships of the principal stresses. The pertinent theories are those by Pauker, Rankine, Bell, Cassagrande and Fadum, Terzaghi and others (most common).
2- The shape of rupture surfaces, such as broken planes, circular, and logarithmic spiral.
3- The mode of expulsion of the ruptured soil mass from underneath the base of the footing, i.e. one-side and two sides.
** One the oldest methods for determining bearing capacity of soil.Where su= Ultimate Bearing Capacity
** Developed based on Coulomb earth pressure theory (1776).
** It is used for sandy soils only.
** The bearing capacity increases linearly with the depth Z
** This formula is valid only when Z > 0 why ???????
Because the weight of the soil wedges below the footing are not included.
** When f = 0 ......
** No consideration for the cohesion of the soil (c).
** This equation does not consider the width of the footing
** The angle of internal friction at the vertical plane, A-A1, is not included.
where = major principal stress = ultimate bearing capacity
= unit weight of the soil
Z = critical depth of the foundation
f = angle of internal friction
1 - sin tan(45 -/2) = = tan2(45-f/2) 1 + sin tan(45 +/2)
** Prandtl studied the process of penetration of hard bodies such as metal punchers into another soft homogenous isotropic rigid material.
** He assumed a rigid plastic body in his system where deformations have no effect on the level od stresses in the limit equilibrium analysis.
** He decided that at failure the material beneath the load could be divided into five regions consisting of Rankin's zones and fans. The fans are sections of logarithmic spirales
** From Mohr's stress theory, and using Airy's stress function, Prandtl obtained a differential equation of a second order. The solution gives the analytical expression of the ultimate bearing capacity of soil
1- Cost (affordable)
2- Construction Procedure (simple)
3- Materials (mostly concrete)
4- Labor (does not need expertise)
2- Limit Capacity * Soil * Structure
3- Irregular ground surface (slope, retaining wall)
4- Foundation subjected to pullout, torsion, moment.
1- Rectangular Combined Footing
2- Trapezoidal Combined Footing
3- Cantilever Footing
4- Mat Foundation
1- Flat plate ---- The mat is of uniform thickness
2- Flat plate thickened under columns
3- Beams and slabs
4- Slab with basement walls
1- Determine the bearing capacity of the foundationFrom Step (4)
2- Determine the settlement of the foundation
3- Determine the differential settlement
4- Determine the stress distribution beneath the foundation
5- Design the structural components of the mat foundation using the stress distribution obtained from (4).
a- The mat foundation is assumed to be a rigid foundationSupport Method.
b- The mat foundation is assumed to be a Flexible Foundation; here use Beam on Elastic
Bearing Capacity of MAt Foundations:
The gross ultimate bearing capacity of a mat foundation is
same as for shallow foundations:
qu = CNc F F F + q Nq F F F + 0.5 B N F F FThe net ultimate capacity is
qult,net= qult - q