2.2 Deformation and friction-slip behavior of the rough contact
surface
Sliding of geomaterials is a process of slow accumulation of internal
contact and friction, which is consistent with creep characteristics.
Therefore, we still describe the deformation of single contacting
asperities based on the velocity creep theory proposed by E. Aharonov
and C H. Scholz (2018), as follows
,
,
,
where, and are normal and tangential stresses on the contact asperities
interface. All parameters included in the equation are shown in Table 1.
Equations (2)-(4)
illustrate that the deformation of contact asperities is a creep process
that is related to temperature, creep activation energy, and creep
velocity. Further, the frictional force between individual contacting
asperities can be expressed as , where
is the real contact area between
individual contacting asperities.
The pressure on single contacting asperities is certain, which satisfies
, where is the nominal contact area of a single asperity and is the
normal stress acting on this nominal contact area. In addition, the sum
of the nominal contact areas () of all contacting asperities is equal to
the nominal contact area () of the entire contact surface at the time of
full contact, i.e., . Then, can be further expressed as
.
The frictional force at the rough contact surface can be considered to
be equal to the sum of the shear forces of each asperity (), as follows
.
The friction coefficient
of the rough contact surface can
be defined as the friction force divided by the positive pressureP i.e. , where positive pressure equals to . Therefore, the can
be expressed as
.
Equation (7) includes porosity , which is an
inherent structural property of the geomaterials. Their pores are
closely related to the seepage coefficient and fluid viscosity, which
are important factors affecting the friction-slip behavior. Based on the
hydraulic diffusivity ()
(Wibberley, 2002) and the specific
storage capacity m () (Renner and Steeb,
2014), we can obtain the expression for the
porosity as follows
,
where, k is the permeability, η is the fluid viscosity,m is the specific storage capacity, cf is
the compressibility of the pore fluid, and cpp is
the compressibility of the pore space. Substituting equation
(8) into equation
(7), the friction coefficient can be expressed
as
.
Further, based on the relationship between permeability coefficient and
saturation( K : hydraulic conductivity; WS :
degree of saturation; L , U : fitting parameters ) (Li ,
2021), the friction coefficientµs can be expressed as
Equation (10) describes the friction coefficient of the macroscopic
rough contact surface, which is based on the creep accumulation of
microscopic asperities and includes random contact processes. Previous
models considered the normal stress (or shear stress) to be the same
across the entire contact surface, which was an average treatment.
However, equation (10) only considers that the deformation mode of each
micro-contact asperity is the same, but the number of contact asperities
is random (in accordance with the exponential relationship), which is
closer to the real situation.