## 5 Comparative Analysis: Mechanical vs. Petrographic Properties
### Correlation Between Mechanical Properties and Petrographic Characteristics  
The mechanical properties of rock materials are related to textural characteristics. [PERSON] et al. [96] (2017) outline the relationship between mechanical properties and textural characteristics of rocks which have been widely studied through experimental tests. These studies often use single- and multiple-variable regression analysis to examine how mechanical properties relate to textural features [95]. Textural characteristics, such as mineral composition, grain size, shape, spatial distribution, porosity, and the presence of microcracks, significantly influence the mechanical behavior of rock materials [97].  
The study by [PERSON] and [PERSON] [98] (1995) established statistical relationships between mechanical rock properties and texture. Strong correlations with certain rock types such as granite were discovered. The ratio of quartz to feldspar (QFR) was found to cause a linear rise in both uniaxial compressive strength and tensile strength [99]. Thus, rocks with a higher QFR generally exhibit higher strength values.  
The relationship between mechanical properties and QFR were investigated by different researchers such as [PERSON] and [PERSON] [100] (1999), [PERSON] [101] (2013), and [PERSON] and [PERSON] [99] (2016). These researchers focused on the linear regression relationships between mechanical properties and the QFR, using regression equations to derive a conclusion about the relations. The literature provides a few examples on linear regression, which are expressed as  
\[\sigma_{c}=121.02\times QFR+115,\ R^{2}=0.792 \tag{10}\]  
\[\sigma_{c}=-437.67\times QFR+384.82,\ R^{2}=0.54 \tag{11}\]  
\[\sigma_{t}=-0.959\times QFR+7.685,\ R^{2}=0.54=0.039 \tag{12}\]  
where \(\sigma_{c}\) is the unconfined compressive strength in MPa, \(\sigma_{t}\) is the tensile strength in MPa, and QFR is the quartz-to-feldspar ratio.  
Since the 1960s, [PERSON] [50] has shown that rocks with finer mineral grains exhibit higher mechanical strength, suggesting that grain size plays a significant role in determining the mechanical properties of a rock. [PERSON] and [PERSON] [102] (1969) further supported this by reporting that the ultimate strength of a rock and the direction of crack propagation are influenced by factors such as mineral cleavage, microfractures, and grain boundaries. This is because finer mineral grains have smaller surface areas, and as the grain size decreases, the length-to-width ratio of microcracks also decreases [103,104].  
The feldspar framework first regulates the behavior of coarse-grained plagioclase rocks, including equigranular leuconorite to leucogabbro with a fine- to medium-grained subophilic texture, supporting stress even under high-grade settings [105]. Deformation weakens rock due to grain size reduction and weaker mineral phases, such as plagioclase-porphyrin leuconorite to anorthosite, forming interconnected networks and reducing its strength during deformation [105].  
Generally, petrographic features such as mineralogy, grain size, texture, porosity, and alteration significantly influence the brittleness and mechanical properties of rock materials. Rocks with fine grains, a high quartz content, and tightly interlocked textures tend to display greater strength and brittleness [106]. In contrast, rocks containing altered minerals, or those with high porosity and microcracks, often show reduced strength, lower brittleness, and increased deformability. These features impact key parameters such as the uniaxial compressive strength (UCS), tensile strength, and elastic modulus by affecting how stress is distributed and how fractures are initiated within the rock [39].  
The altered minerals also influence the brittleness of a rock, and the alteration processes that occur in a rock can weaken the original minerals. For example, the transformationof feldspar to clay minerals decreases the grain cohesion and increases the porosity and microcracking of a rock [32].