# Influence of Drilling Along Pilot Holes on Drilling Performance and Effective Rock Strength +
## 5 Evaluating the Influence of Pilot Hole Diameter on Effective  
### Rock Strength  
The modified [PERSON] (1962) model is a useful tool for determining the effective rock strength (S) based on the drilling rate (ROP) data obtained under different pilot hole diameters [18]. The calibrated model can be used in Equation (3) to estimate effective rock strength (S) for other pilot hole diameters. \[ROP=\frac{K}{S^{2}}\frac{\left(WOB-WOB_{o}\right)^{n}}{{D_{O}}^{2}-{D_{I}}^{2}}N \tag{3}\]  
Figure 11: (**a**) is the MSE results (Mpa) for HO-1.5 configurations. (**b**) Illustrates the MSE results (Mpa) for HO-1.0 configurations for gabbro rock. Figure 12: (**a**) the MSE results (Mpa) for HO-0.5 configurations. (**b**) the MSE results (Mpa) for FF-FF configurations for gabbro rock. Plotting Rate of Penetration (ROP) data against Weight on Bit (WOB) for every pilot hole diameter is the first step in the process. Next, the data are fitted to the modified Maurer equation, holding K and in constant, and only S is varied to determine the best fit. The S value for each diameter represents the effective rock strength for a given pilot hole size. The equation relates ROP to these factors, showing that drilling performance depends on the balance between the force applied to the drill bit and the rock's resistance. Experimental data are first calibrated at a specific pilot hole diameter to use the model, allowing for determining the calibration constants K and n, and the effective rock strength for that scenario. Using the modified Maurer model with a WOB exponent n = 1 and the calibration constant K = 3.15 \(\ast\) 10\({}^{-6}\), simplifies the relationship between the rate of penetration (ROP) and the other variables, such as the weight on bit (WOB), effective rock strength (S), and bit diameters (Do and Di). The value n = 1 suggests a linear relationship between the WOB and ROP, as shown in Figure 13, meaning that increasing the weight on the bit directly increases the penetration rate in a straightforward, proportional manner. Meanwhile, the calibration constant K = 3.15 asterisk operator 10 to the minus six ends superscripts derived from experimental data helps adjust the model to match the specific conditions of the studied drilling scenario. With these values, the model becomes more practical, assuming that no complex nonlinear scaling of the WOB is needed and that calibration constant (K) provides the necessary correction factor for the rock type and drilling conditions under investigation. This allows for the effective estimation of rock strength and performance for different pilot hole diameters with reasonable accuracy, especially when using the same drilling setup or similar rock formations. Overall, the modified Maurer model provides valuable insights into drilling performance but must be applied carefully, considering its limitations. The drill ability strength of the rock is shown in Figures 14 and 15, along with Weight on Bit (WOB) and Rate of Penetration (ROP) results (in N-m) for various configurations (HO-1.5, HO-1.0, HO-0.5, and full-face (FF) in gabbro rock. Figure 14 shows that the drill ability strength decreases with increasing WOB for both gabbro. The full-face bit exhibits the steepest decline, indicating lower drilling efficiency. Larger pilot holes, like 1.5 and 1 inches, maintain greater drilling efficiency, which shows less abrupt drops. The 1.5-inch pilot hole lowers resistance and guarantees more steady and reliable drilling. In both types of rock, Figure 15 demonstrates that larger pilot holes are correlated with higher ROP, with the full-face configuration showing the lowest ROP. With the highest ROP, the  
Figure 13: Calibrate the experimental dataset at the specific pilot hole. 1.5-inch pilot hole configuration makes it easier to penetrate the rock, uses less energy, and improves drilling performance overall.