Weak Rocks and IGMs
For weak rock layers or IGMs (intermediate geomaterials), some simple methods for the estimation of the shaft friction and the tip resistance are presented in the following sections.
Shaft Friction in Weak Rocks and IGMs
The shaft friction along the part of the pile socketed in weak rock or IGMs can be approximated by:
Many experiments were performed on weak rocks and IGMs in order to determine the adhesion factor in equation \((\ref{eq:unitshaftresistanceigm1})\). The experimental data and the line of best fit are shown in Figure 1.
Figure 1. Relationship between the factor of adhesion and the unconfined compressive strength of rock (after Wyllie, 1999; after Williams and Pells, 1981).
For practical purposes, the equation of the best fit line in Figure 1 is used for estimating the shaft friction of weak rocks and IGMs:
General notes for shaft friction in weak rocks and IGMs
 Reference for equations \((\ref{eq:unitshaftresistanceigm1})\) and \((\ref{eq:unitshaftresistanceigm2})\), and Figure 1: Wyllie (1999), pp.258263.
 Ultimate unit skin friction \(q_s\) has a limiting value of around 10 MPa or 1450 psi since the adhesion factor converges to 0.10 for an extreme unconfined strength of 100 MPa as illustrated in Figure 1 for weak rocks and IGMs.
Tip Resistance in Weak Rocks and IGMs
The tip resistance of a pile socketed in weak rock or IGMs can be approximated with the following formula which uses a wide range of field test data (Figure 2).
Figure 2. Relationship between the ultimate unit tip resistance and the compressive strength of weak rock (after Zhang, 2004)
General notes for tip resistance in weak rocks and IGMs

Reference for equation \((\ref{eq:unittipresistanceigm3})\) and Figure 2: Zhang (2004), p. 219.

Ultimate unit tip resistance \(q_b\) has a limiting value of 50 MPa or 7250 psi for weak rocks and IGMs as suggested by Figure 2. But the ultimate bearing capacity of rock sockets are generally limited by the compressive strength of the reinforcedconcrete material inside the shaft.
We strongly recommend not to rely only on these simple approximations for pile bearing capacity in rocks, since there are many other methods which incorporate other crucial rock parameters such as the RQD, shaft roughness and the fracture structure at the rock socket, etc.
Diameter Reduction Coefficient in Weak Rocks and IGMs
For pile drilling in rocks or in stiff soil deposits like IGMs, the diameter of the pile body might be reduced due to the temporary pile casing being terminated above the level of these stratum leaving only the drill lead (auger, bucket etc.) penetrating into these hard base materials (Figure 3).
Figure 3. Typical pile tip drilling in rock (Tomlinson and Woodward, 2008)
To calculate the reduction in surface areas of the pile shaft and the tip, we have introduced a coefficient called Diameter Reduction \(( \phi_\text{red} )\), which is the ratio of the pile diameter in rock or IGM layer (without casing), to the diameter in the rest of pile body (with casing). The maximum value for this parameter is 0.99≈1.