Finite Element Analysis of Stress Distribution in Underground Galleries with Varying Dimensions

The data of the rock material considered in the created field model are provided in Table 1. The underground quarry under investigation in this study is located 70 km east of İzmir and 15 km northwest of Bayındır.

Table 1. Data related to rock material [7]

During the creation of the field model, a depth of 90 meters from the surface was considered for excavating the galleries. In the subsequent stage, using the rock material properties provided in Table 1 and considering the depth, the parameters related to the rock mass were calculated using RocData software [8]. The process of obtaining the rock mass data is illustrated in Figure 1.

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Figure 1. Obtaining rock mass data

The data related to the rock mass calculated using the RocData software are provided in Table 2.

Table 2. Rock mass data used in the model

The horizontal and vertical stress values that will occur at a working depth of 90 meters under the selected rock mass conditions, considering the Poisson's ratio of the dominant rock structure in the field, have been calculated using the following equations [9]:

$\sigma \mathrm{h}=\mathrm{k} . \sigma \mathrm{v}$            (1)

$\mathrm{k}=0,25+7 . \mathrm{E} .(0,001+1 / \mathrm{z})$            (2)

Here is a brief explanation of the variables: σv: Vertical stress in megapascals (MPa); σh: Horizontal stress in megapascals (MPa); k: Ratio of horizontal stress to vertical stress (no units); E: Average modulus of elasticity of the rock mass in the vertical direction up to the working depth in gigapascals (GPa); z: Working depth in meters (m).

The vertical stress at a working depth of 90 m was calculated as 2.33 MPa using Eq. (1). Considering the rock mass properties given in Table 2 and the calculated coefficient k as 0.84 based on the rock mass ’s modulus of elasticity and depth (Eq. (2)), the expected horizontal stress in the field was calculated as 1.96 MPa. The calculated coefficient k was incorporated into the field model, ensuring an accurate representation of stress conditions within the rock mass environment where the galleries will be excavated. Field models with dimensions of 4×4 meters and 5×5 meters were created using Phase2D software [10]. A visual representation of the models is provided in Figure 2.

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Figure 2. Different gallery size models

After entering the data the models, the models were run, and normal and horizontal stresses around the galleries were calculated for different gallery sizes. The stresses around the galleries with gallery sizes of 4×4 and 5×5 meters in the same rock mass environment are shown in Figure 3.

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Figure 3. Normal stresses occurring around galleries of different sizes

The calculated stress values are detailed in Table 3. Normal stresses occurring immediately above the gallery were measured along an approximately 14-meter line. The horizontal stress values on the right and left walls were recorded by measurements along an approximately 4-meter line. The measurements were conducted using measurement lines placed on models established within the software. These measurement lines are structures permitted to be generated by the software, allowing the user to obtain results of their desired intervals and types in the regions they pass through. The measurements were taken just above the gallery and on the side walls.

Table 3. Normal and horizontal stresses occurring around galleries of different sizes

In the scope of this study, vertical stresses expected to occur around galleries of different sizes were calculated through two different stress analyzes in the first stage, the vertical and horizontal stresses that would affect the galleries were calculated using the Phase2D program. In the second stage, the ANSYS stress analysis software was used to measure the vertical stress values around the gallery and the deformation and vertical stress values that would occur in the third dimension within the galleries. Because of the stress analyzes conducted in the first stage, it can be observed from the values given in Table 3 that the stresses increase linearly from the base region of the gallery toward the upper region of the gallery. They decrease slightly, stabilizing, and are influenced by the pressure arch formed on the gallery's upper portion. This situation has also been explained in detailed scientific studies on the subject [13-20]. It is noted that the vertical stresses occurring in the 4×4 meter and 5×5 meter gallery sizes are very close to each other, but the vertical stresses on the gallery's upper portion are particularly lower in the 4×4 meter gallery size.

Looking at the average horizontal stress values around the gallery given in Table 3 because of the first-stage stress analysis, it is observed that the stresses on the left and right walls of the 4×4 meter and 5×5 meter gallery sizes are very close to each other. The lowest average vertical stress value was observed in the upper region of the 4×4 meter gallery size.

Because of the two-stage stress analyzes it was determined that the horizontal stress values occurring in the left and right regions of the gallery are very close to each other. However, especially in the graphical representation shown in Figure 11, it is evident that the normal stresses occurring on the gallery and analyzed in the second and third dimensions are lower in the 4×4 meter gallery size. In addition, it allows for less deformation. Therefore, it has been determined that designing the gallery sizes to be opened in the working area as 4×4 meters would be suitable in terms of both work efficiency and health.