Page 254 - Civil Engineering Formulas

188 CHAPTER EIGHT

INTERNAL FRICTION AND COHESION

The angle of internal friction for a soil is expressed by
!
tan (8.12)

where angle of internal friction
tan coefficient 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°.
The cohesion of 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 c are given in
Table 8.2.

VERTICAL PRESSURES IN SOILS

The vertical stress in a soil caused by a vertical, concentrated surface 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

3P r 2 5/2
z 2 (8.13)
1
2
z z

TABLE 8.2 Cohesive Resistance of Various Soil Types
Cohesion c
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)