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

2.12. Shear Strength versus Friction.
Basic Soil Mechanics.
To avoid confusion between cohesion and adhesion on one side and internal and external friction on the other side,
internal and external friction, also named Coulomb friction, depend linearly on normal stresses, internal friction
depends on the normal stress between the sand grains and external friction on the normal stress between the sand
grains and another material, for example steel. In civil engineering internal and external friction are denoted by
the angle of internal friction and the angle of external friction, also named the soil/interface friction angle. In
mechanical engineering the internal and external friction angles are denoted by the internal and external friction
coefficient. If there is no normal stress, there is no shear stress resulting from normal stress, so the friction is zero.
Adhesion and cohesion are considered to be the sticky effect between two surfaces. Cohesion is the sticky effect
between two surfaces of the same material before any failure has occurred and adhesion is the sticky effect between
two different materials, for example adhesive tape. Adhesion and cohesion could be named the external and
internal shear strength which are independent from normal stresses. The equations for the resulting shear stresses
are:
in c in tan( )
or in c in in
(2-122)
tan( )
or (2-123)
ex a ex ex a ex ex
Or
in c in tan( ) or in c in in
(2-124)
a tan( ) or a (2-125)
With:
ex ex ex ex ex
in tan( )
(2-126)
ex tan( )
(2-127)
The values of the internal friction angle φ and the external friction angle δ not only depend on the soil properties
like the density and the shape of the particles, but may also depend on the deformation history.
100.00
K a & K p vs. Angle of Internal Friction φ
10.00
Ka
K a & K p (-)
1.00
0.10
Kp
0.01
20 25 30 35 40 45 50 55 60
Angle of Internal Friction φ (Degrees)
© S.A.M.
Figure 2-59: The coefficients of active and passive soil failure Ka & Kp.
Figure 2-59, Figure 2-60 and Figure 2-61 show the Ka and Kp coefficients as a function of the internal friction
angle.
Copyright © Dr.ir. S.A. Miedema TOC Page 71 of 454