## 1 Introduction  
Geotechnical evaluation of wellbores, which is crucial for hydraulic fracturing design, sand production management and prediction, fault stability, reactivation analysis, and wellbore stability, requires accurate and comprehensive knowledge of the mechanical properties of rocks [1]. The uniaxial compressive strength (UCS) of rocks is a fundamental measure of drillability in geostechnical engineering, particularly in the oil and gas sectors. UCS quantifies the maximum axial load a rock can endure before failure, reflecting the rock's resistance to compressive forces. In drilling applications, higher UCS values signal harder formations, which demand increased energy and precise adjustments to drilling parameters--such as bit type, weight on bit, and rotary speed--to achieve efficient penetration. Accurately estimating UCS enables engineers to anticipate the energy requirements and bit wear, aiding in optimal drilling parameter selection and cost reduction. UCS significantly influences the rate of penetration (ROP) in drilling. Rocks with lower UCS allow for higher ROP, facilitating faster drilling and minimizing tool wear, while those with higher UCS reduce ROP, requiring adjustments to drilling methods and equipment. Therefore, reliable UCS prediction models are vital for enhancing drillability assessments, proactively managing wellbore stability and improving drilling efficiency in complex geological formations. One commonly used method to evaluate these properties is through the measurement of UCS in the laboratory [2]. However, this method can be highly sensitive to the loading process of the core sample and is destructive in nature [3]. As an alternative, log-based methods that indirectly measure rock strength have been proposed, but their precision and accuracy have not been fully validated by reliable data [4]. Given the challenges and expenses associated with standard laboratory tests, indirect methods are more promising for practical use [2]. Sonic travel time is a physical property of rocks that is utilized for studying rock mechanics and reservoir evaluation. This property varies based on the lithology, rock textures, fluid content, and porosity of the rock [5]. In cases where limited core samples are available, sonic and neutron logs can be used to estimate the rock properties. Researchers have developed six experimental equations related to carbonate rock strength for measuring geophysical properties, which are listed in Table 1[6; 7; 8; 9; 10]. Another approach for predicting rock strength is to use drilling data based on ROP models [11; 12]. These models can be used with all types of bits, although tri-cone bits (TCBs) are preferred due to their wide range of use [13]. [PERSON] et al. [14] developed a method for determining the UCS of rock formations using Genetic Programming (GP). This approach utilized parameters such as total formation porosity, Bulk Density, and water saturation obtained from various logging techniques, including sonic, neutron, gamma ray, and electric logs. The elastic moduli were derived from compressional and shear sonic logs using mathematical correlations, and the rock UCS was estimated using empirical correlations by [PERSON] and [PERSON]. The study involved analyzing approximately 5000 data points from three wells in an Iranian oil field to develop the GP model for UCS prediction. The model was fine-tuned using UCS data from core samples and validated with two separate datasets. The estimated UCS values from the GP model closely matched those obtained from analytical methods based on well-log data [14]. [PERSON] and colleagues [15] introduced an ANN modelling approach for predicting the UCS of oil well cement, specifically class \"H\". This research analyzed 195 cement samples, incorporating varying concentrations of pre-dispersed nanoparticles, including nanosilica (nano-SiO\({}_{2}\)), nanoalumina (nano-Al\({}_{2}\)O\({}_{3}\)), and nanoitanium dioxide (nano-TiO\({}_{2}\)), across different temperature conditions.