# Terzaghi Theory

Terzaghi’s Principle states that once a rock is subjected to pressure, it’s miles adversarial through the fluid strain of pores withinside the rock. analyzing that overall pressure is the same as the sum of powerful pressure and pore water strain.

## Assumption

(1) The soil is semi-infinite, homogeneous and
isotropic
(2) the problem is two-dimensional,(strip footing)
(3) the base of the footing is rough,
(4) the failure is by general shear,
(5) the load is vertical and symmetrical,
(6) the ground surface is horizontal,
(7) the overburden pressure at foundation level is equivalent to a surcharge load (shear resistance is ignored)
(8) the principle of superposition is valid,
(9) Coulomb’s law is strictly valid,

### Zone I of elastic equilibrium (cohesive resistance)⇒

the soil positioned right away below the bottom stays completely in a country of elastic equilibrium, and the soil positioned inside this primary Zone I behaves as though it had been part of the footing and sinks with the footing beneath neath the superimposed load. The intensity of this wedge-formed frame of soil ABC stays almost unchanged, but the footing sinks.  The sinking of Zone I creates zones of plastic equilibrium, II and III, on both aspects of the footing. It can be considered as Rankine Active zone. (settlement is necessary for mobilization of shear strength).

### Zones II of radial shear state⇒

Frictional resistance resulting from the surcharge from the q0 at the footing level. ∅ (curve shape is logarithmic spiral) Zone II is the radial shear zone whose remote boundaries bd and af meet the horizontal surface at angles (45° – Ø/2), whereas Zone III is a passive Rankine zone. The boundaries de and fg of these zones are straight lines and they meet the surface at angles of (45° – Ø/2).

### Zones III of Rankine passive state⟹

Frictional resistance resulting from the weight of soil within the failure zone. it touches the foundation level at an angel of (this zone is in plastic stage) Ultimate Bearing Capacity for shallow strip footing q= is overburden pressure. Zone III is a passive Rankine zone. The obstacles de and fg of these zones are immediately traces and that they meet the floor at angles of (45° – Ø/2).

#### Terzaghi’s Formula

Terzaghi’s Bearing Capacity Equations:-

• Strip Footings:-
• Square Footings:
• Circular Footings: