The Delft Sand, Clay & Rock Cutting Model, 2019a

The Delft Sand, Clay & Rock Cutting Model.
2.4.5. The Angle of Internal Friction.
Angle of internal friction for a given soil is the angle on the graph (Mohr's Circle) of the shear stress and normal
effective stresses at which shear failure occurs. Angle of Internal Friction, φ, can be determined in the laboratory
by the Direct Shear Test or the Triaxial Stress Test. Typical relationships for estimating the angle of internal
friction, φ, are as follows:
Table 2-7: Empirical values for φ, of granular soils based on the standard penetration number, (From
Bowels, Foundation Analysis).
SPT Penetration, N-Value (blows/ foot)
φ (degrees)
0 25 - 30
4 27 - 32
10 30 - 35
30 35 - 40
50 38 - 43
Table 2-8: Relationship between φ, and standard penetration number for sands,
(From Peck 1974, Foundation Engineering Handbook).
SPT Penetration, N-Value (blows/ foot) Density of Sand φ (degrees)
41
Table 2-9: Relationship between φ, and standard penetration number for sands,
(From Meyerhof 1956, Foundation Engineering Handbook).
SPT Penetration, N-Value (blows/ foot) Density of Sand φ (degrees)
45
Lambe & Whitman (1979), page 148 (Figure 2-23) give the relation between the SPT value and the angle of
internal friction, also in a graph. This graph is valid up to 12 m in dry soil. With respect to the internal friction, the
relation given in the graph has an accuracy of 3 degrees. A load of 12 m dry soil with a density of 1.67 ton/m 3
equals a hydrostatic pressure of 20 m.w.c. An absolute hydrostatic pressure of 20 m.w.c. equals 10 m of water
depth if cavitation is considered. Measured SPT values at any depth will have to be reduced to the value that would
occur at 10 m water depth. This can be accomplished with the following equation:
SPT
1
0.646 0.0354
z
10 z
SPT
(2-24)
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