CIVIL ENGINEERING FORMULAS

188 CHAPTER EIGHT

INTERNAL FRICTION AND COHESION

The angle of internal frictionfor a soil is expressed by

(8.12)

where angle of internal friction
tancoefficient of internal friction
normal force on given plane in cohesionless soil mass
!shearing force on same plane when sliding on plane is
impending

For medium and coarse sands, the angle of internal friction is about 30° to 35°.
The angle of internal friction for clays ranges from practically 0° to 20°.
Thecohesionof a soil is the shearing strength that the soil possesses by
virtue of its intrinsic pressure. The value of the ultimate cohesive resis-
tance of a soil is usually designated by c. Average values for care given in
Table 8.2.

VERTICAL PRESSURES IN SOILS

The vertical stress in a soil caused by a vertical, concentratedsurface load may
be determined with a fair degree of accuracy by the use of elastic theory. Two
equations are in common use, the Boussinesq and the Westergaard. The Boussi-
nesq equation applies to an elastic, isotropic, and homogeneous mass that
extends infinitely in all directions from a level surface. The vertical stress at a
point in the mass is

z (8.13)

3 P

2

 z^2 

1 

r

z

2



5/2

tan

!



TABLE 8.2 Cohesive Resistance of Various Soil Types

Cohesionc

General soil type lb/ft^2 (kPa)

Almost-liquid clay 100 (4.8)

Very soft clay 200 (9.6)

Soft clay 400 (19.1)

Medium clay 1000 (47.8)

Damp, muddy sand 400 (19.1)