SLOPE STABILITY THEMED EDITION

 

Evaluating the triaxial strength of Misis fault breccia using artificial neural networks analysis

 

 

S. Kahraman^I; M. Alber^II; O. Gunaydin^III; M. Fener^IV

^IHacettepe University, Mining Engineering Department, Ankara, Türkiye. http://orcid.org/0000-0001-7903-143X
^IIRuhr University-Bochum , Applied Geology Department, Bochum, Germany. http://orcid.org/0000-0003-2488-7817
^IIIAdiyaman University, Civil Engineering Department, Adiyaman, Türkiye. http://orcid.org/0000-0002-0464-5194
^IVAnkara University, Geological Engineering Department, Ankara, Türkiye. http://orcid.org/0000-0001-7559-5684

Correspondence

 

 

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ABSTRACT

Falling into the weak rocks category, fault breccias have extremely poor engineering properties. These pebbles typically cause issues with slopes, subterranean construction, and building projects. Professionals will benefit from the creation of some predictive models for fault breccia triaxial strength, as smooth specimen preparation is typically challenging and time-consuming. The purpose of this study is to develop some predictive models for the differential stress (Δσ) based on physical and textural properties. Artificial neural networks were used to analyse data related to Misis fault breccia. Initially, models with moderate (noticeable, but not good) correlation coefficients were created using multiple regression analysis. After that, the regression models and three distinct artificial neuron network models were contrasted. Regression models are weaker and less trustworthy than artificial neuron network models, as demonstrated by this comparison. Pointed out is the practicality and ease of use of the artificial neuron network model with S-wave velocity and volumetric block proportion. Ultimately, it can be concluded that artificial neuron networks analysis provides a reliable indirect method for predicting the differential stress of Misis fault breccia.

Keywords: Misis fault breccia, triaxial strength, ultrasonic velocity, artificial neural networks

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Introduction

Non-linear multivariable problems are typical in the geosciences. Regression analysis and conventional expert systems can occasionally fail to provide satisfactory solutions for such issues. Artificial neural networks (ANNs) are therefore frequently employed in the geosciences (Yuanyou et al., 1997; Yang, Zhang, 1998; Singh et al., 2001; Kahraman et al., 2005; Sonmez et al., 2006; Zorlu et al., 2008; Gunaydin et al., 2010, Dagdelenler et al., Marais, Aldrich, 2011, Sayadi et al., 2013; Khoshjavan et al., 2013; Basarir et al., Kahraman, 2016, etc.). Numerous geoscience studies have used ANNs, and the results have shown that ANN models perform well when solving multivariable problems.

Typically, fault breccias cause issues in applications involving rock engineering since they belong to a weak rock group. In order to solve the issues that arise when carrying out projects, it is crucial to understand or estimate the geomechanical properties of fault breccias. To prepare smooth specimens for standard tests, on the other hand, requires a lot of time, effort, and money, and fault breccias are typically not suitable for this. Deriving a few predictive models for the geomechanical characteristics of fault breccias will be beneficial because of this. Many researchers (Chester, Logan, 1986; Medley, 1994; Medley, Goodman 1994; Lindquist, Goodman, 1994; Ehrbar, Pfenniger, 1999; Goodman, Ahlgren, 2000; Buergi et al., 1999; Medley, 2001; Medley, 2002; Habimana et al., 2002; Laws et al., 2003; Sonmez et al., 2004; Sonmez et al., 2006; Coli, 2011; Afifipour, Moaref, 2014; Mahdevari, Maarefvand, 2017; Lu et al., 2019; Festa et al., 2019; Avsar, 2020; Caselle et al., 2024; Gayathridevi, Ray, 2025) have studied the characteristics of geologically complex rocks such as melanges and fault rocks. On the Ahauser fault breccia (Germany), Kahraman and Alber (2006; 2008) as well as Alber and Kahraman (2009) conducted the first study on the geomechanical properties of fault breccias. Later on, Kahraman et al. (2008) and Slatalla et al. (2010) assessed the geomechanical characteristics of the breccia from the Misis fault. Kahraman et al. (2010) examined how well the Cerchar abrasivity index worked in predicting the uniaxial compressive strength (UCS) and Young's modulus € of the Misis fault breccia.

Kahraman et al. (2008), investigated the triaxial strength of Misis fault breccia and developed an estimation equation for the differential stress (Δσ) using multiple regression analysis. However, the correlation coefficient for this relationship was weak. In this work, artificial neural networks (ANNs) were utilised to analyse the triaxial strength of Misis fault breccia with the goal of creating more robust models. Fifty specimens were added to this study in addition to the eighteen from the previous investigation.

 

Sampling

For the experimental investigations, large blocks were taken from the Misis fault breccia (Ceyhan-Adana, Türkiye). The Misis fault's location map is displayed in Figure 1. Dolomitic limestone blocks embedded in a finely grained matrix of red claystone containing clay rich in iron make up the Misis fault breccia. From the large blocks in the lab, 68 test samples in total were cored. The test samples have a 61 mm diameter and a 2-2.5 length-to-diameter ratio (Figure 2).

 

 

 

 

Determination of textural properties

Each core sample's circumferential surface was scanned with the DMT CoreScan II to produce digital images. Using image analysis software, the volumetric block proportion (VBP), average block diameter (ABD), aspect ratio, and roundness of the blocks were calculated from the scanned images of the cores.

Estimation of volumetric block proportion

The volume of block partition (VBP) is calculated by dividing the volume of blocks or grains by the volume of rock mass. A few researchers have explained the VBP prediction methods and the uncertainties in predicting three-dimensional block size distributions from one- or two-dimensional measurements (Medley, Goodman, 1994; Goodman, Ahlgren, 2000; Medley, 1997; Medley, 2002; Haneberg, 2004). Blocks from the matrix are typically very difficult to separate, even though sieve analysis is the best technique. This is why it is common practice to estimate VBP using one- or two-dimensional methods like scanlines, geological mapping, and image analysis, or drill core/block intersection lengths. The circumferential surface scan images of the cores were processed and used to estimate VBP in this study. Figure 3 displays a sample's raw and processed images.

 

 

Average block diameter

The length of the line that passes through each block's 2° centroid was used to estimate the two-dimensional diameter, which was assumed to be the same as the three-dimensional diameter (Figure 4). ABD values were then calculated by averaging these lines.

 

 

Aspect ratio of blocks

The length of the major and minor axes of an ellipse with an area equal to that of the block is called the aspect ratio, which characterises the elongation of blocks. Every block in the sample had its aspect ratio measured, and the average value was determined.

Roundness of blocks

Form factor is another way to define roundness. For a perfect circle, roundness equals 1. The roundness decreases as the shape moves away from circularity. Each block's roundness value in the sample was found, and the average value was computed. This is the roundness formula.

where R is roundness, A is the area of shape (mm²), and p is the perimeter of shape (mm).

 

Experimental studies

Prior to conducting triaxial compressive strength tests, each core sample underwent a density test and an ultrasonic test.

Density test

Density was calculated using samples of smooth core. Averaging multiple calliper readings allowed for the calculation of the specimen volume. A balance that could weigh the specimens precisely to within 0 points of the sample mass was used to determine their mass. The specimen mass to volume ratio was used to calculate the density values.

Ultrasonic test

To test the samples' elastic qualities, the USG 40 ultrasonic generator, made in Pirna, Germany, by Geotron GmbH, was employed. For the measurements, a 250 kHz ultrasonic transducer was employed. The ultrasonic tests yielded P- and S-wave velocities.

Triaxial compressive strength test

A stiff testing machine was used to perform the triaxial compression tests on smooth core specimens. The tests used confining pressures ranging from 1 MPa to 10 MPa. The triaxial cell of the Hoek-Franklin type has a capacity of about 70 MPa, while the load frame has a capacity of 4600 kN. Tests involved constant observation of the axial load and axial displacement. Two extensometers are used to measure axial deformation. Using an MTS Teststar IIm controller, the servo-hydraulics are controlled at high speed and in closed loop to operate the testing system. It is possible to use computed signals, such as stress or strain, or variable feedback signals, such as force or displacement, as control modes with this closed-loop control. However, this feature of the system has not been used in this study. The sample is loaded in axial strain control at a rate of 10^-5 mm/ mm/s beyond peak strength after being simultaneously loaded laterally and axially to the selected confining stress level.

 

Assessment of the results

Table 1 provides the textural characteristics of the tested samples along with statistical analyses. The values of VBP vary from 3.05 per cent to 80.93 per cent. The values of ABD vary from 2.15 per cent to 10.22 per cent. Blocks have aspect ratios ranging from 1.54 to 2.22. Blocks range in roundness from 0.53 to 0.85. Table 2 provides descriptive statistics of the physico-mechanical test results. The differential stress readings fall between 26.40 and 131.20 MPa. The density values are between 2.35 and 2.64 g/cm³. The values of P-wave velocity span from 3:71 km/s to 5:88 km/s. The range of values for S-wave velocity is 1.69 km/s to 3.26 km/s.

 

 

 

 

The triaxial compressive test results were used to plot the Mohr stress circles. As illustrated in Figure 5, the stress circles are not uniform, and the failure envelope derived from these circles will not be trustworthy. Normally, as the confining stress increases (σ₃), the vertical stress (σ₁) increases steadily, and the Mohr circles shift to the right. Such unconformities frequently occur in geologically complex materials such as fault breccias. The inconsistent trend is expected, given the varying textural characteristics of the samples. In geologically complex materials such as breccias, the differential stress (Δσ = σ₁-σ₃) at failure can be a useful tool for determining the triple strength. This is why the failure envelope was not used in the analysis; instead, the Δσ was used.

 

 

Regression analysis

The intercorrelations between the test results and the textural characteristics are displayed in a correlation matrix. There are no significant correlations between the independent parameters and the dependent parameter (Δσ), as Table 3 illustrates. This suggests that there is more than one parameter that influences the Δσ. According to a prior investigation (Kahraman et al., 2008), the strength range of block and matrix values is wide. This could be the cause of the absence of associations. The varying textures of the samples could be another factor. Therefore, in order to derive strong correlations, multivariable analysis is required.

Alternative prediction models for the Δσ were examined using stepwise regression analysis. The software was used to create the following four models.

where, Δσ is differential stress (MPa), Vs is S-wave velocity (km/s), VBP is volumetric block proportion (%), ρ is density (g/cm³), and ABD is average block diameter (mm).

The first model (Equation 2) has a weak correlation coefficient. The other models (Equations 3-5) have moderate correlation coefficients.

Artificial neural network analysis

Artificial neural networks (ANNs) are extremely simplified models of the human brain's nervous system. The basic processing components of these models are interconnected assemblies of neurons arranged in layers. As can be seen in Figure 5, every neuron in one layer is connected to the neurons in the layer below it, and so forth. W_ij stands for 'weights,' and it describes the connection between the i^th and j^th layers. The potent tool for estimation and classification is provided by these connections between the layers. In order to minimise a predetermined cost function, these connections are optimised during the learning phase. The activation of a neuron is determined by its activation function, which is shown in Figure 6 as (f), and the weighted sum of its inputs is calculated to determine the neuron's output.

 

 

Multi layered perception (MLP) neural networks are the kind utilised in this investigation. In Figure 7, an MLP neural network is displayed. An input layer, one or more hidden layers, and an output layer make up MLP networks. There are many processing units (neurons) in each layer, and each unit is fully connected to units in the layer below it via weighted connections. The MLP uses nonlinear mapping functions to convert i inputs into k outputs.

 

 

Some investigators (Kumar, 2005; Altun et al., 2007) demonstrated that when data is highly skewed, ANN models do not always perform well in predictions. In order to minimise skewness in the data, a transformation such as power transformation can be applied prior to neural network analysis. The degree of symmetry of the normal distribution is gauged by its skewness. A symmetric distribution (one that is not skewed) is indicated by a skewness coefficient of 0. When a distribution is positively skew, it is skewed to the right; when it is negatively skew, it is skewed to the left. As demonstrated by Tables 1 and 2, the parameters' skewness values are typically low. Consequently, there is no need to transform or handle the data.

For the ANNs analysis, data from 68 rock samples were used. The network was trained, and several ANN models were developed using the data of the first group of 48. Ten of the data points were used for testing, and the other ten were used for validation.

Three regression models (Equations 3-5) mentioned in the aforementioned exhibit moderate correlation coefficient values. In order to evaluate these regression models against ANNs models, three distinct types of neural network structures were implemented in the MATLAB environment for the purpose of predicting the Δσ. The structures of the ANN models, i.e., the quantity of input layer neurons, hidden layer neurons, and output layer neurons are provided in Table 4. Table 4 also displays the training parameters and the algorithm used during the training phase.

A neural network with the structure 2-2-1 (Model I in Table 4) is used in the first trial. Using this structure, a model is built that illustrates the nonlinear relationship between the independent variables and the Δσ value. The model I is

A neural network is built in the second trial using the structure 3-5-1 (Model II in Table 4). The model II is

The third trial involves the construction of a neural network with the structure 4-6-1 (Model III in Table 4). The model III is

where, Δσ is difierential stress (MPa), Vs is S-wave velocity (km/s), VBP is volumetric block proportion (%), ρ is density (g/cm³), and ABD is average block diameter (mm).

Scatter plots indicating measured and predicted values can be used to display how well the derived models estimate values. When comparing estimated and observed data, a plotted data set should ideally have its points distributed around the 1:1 diagonal straight line. An accurate estimate is shown by a point that is on the line. Indicating non-linearity in one or more parameters, a systematic departure from this line can, for instance, show that larger errors typically go hand in hand with larger estimations. Plots of estimated Δσ versus observed Δσ are shown in Figures 8-10 for Models I, II, and III, respectively. The plots exhibit uniform point scattering around the diagonal line, indicating the plausibility of the models.

 

 

 

 

 

 

Comparison of regression and ANNs models

The correlation coefficients and standard error of estimates were used to compare the models produced by regression analysis and ANNs. Table 5 illustrates the moderate correlation coefficients of the regression models (Equations 3-5). Corresponding ANN models, however, have high correlation coefficients (Equations 6-8). Table 5 also provides the standard error of estimate values. ANN models exhibit lower standard error of estimates values in comparison to regression models. Comparison results reveal that ANNs models are strong and reliable for predicting the Δσ of fault breccia compared to the regression models.

 

 

Discussion

The correlations between Δσ and breccia characteristics such as S-wave velocity, VBP and average aspect ratio of blocks are examined, but these are weak, as shown in Table 3. The fact that the strengths of both the matrix and the blocks have wide ranges and the specimens have different textures is likely the cause of weak correlations. It is clear that the triaxial strength of the Misis fault breccia does not depend on one rock property. Multiple regression analyses were performed in anticipation of developing strong models. However, the models derived from the multiple regression analysis show moderate correlation coefficients. An ANN analysis was then performed using the independent variables included in the regression models with moderate correlation coefficients. The developed ANN models were shown to be strong and reliable. The three ANNs models can be used to estimate the Δσ of the Misis fault breccia or similar breccias. Model I (Equation 6) is practical and easy to use because it has only two independent variables (S-wave velocity and VBP). Measuring S-wave speed is very simple. Determining VBP is quite difficult and time-consuming. Alternatively, VBP can be easily estimated from density as there is a good correlation between VBP and density, as shown in Table 3. The correlation equation is:

where, VBP is volumetric block proportion (%) and ρ is density (g/cm³).

 

Conclusions

The predictability of the Δσ of the Misis fault breccia from physical and structural properties was examined using regression and ANN analysis. It was seen that there were no significant correlations between Δσ and independent variables. Some models with moderate correlation coefficients were derived through multiple regression analysis. Three different ANN models were constructed and compared with the regression models. Comparing the ANNs models with the regression models revealed that the ANNs models are stronger and more reliable than the regression models. The ANNs model (Equation 6) including S-wave velocity and VBP is practical and easy to use. A final note is that the Δσ of the Misis fault breccia can be reliably predicted from indirect methods using ANN analysis.

 

Acknowledgement

This study was supported by the Alexander von Humboldt Foundation.

 

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Correspondence:
S. Kahraman
Email: sairkahraman@yahoo.com

Received: 24 Mar. 2024
Revised: 19 May 2025
Accepted: 16 July 2025
Published: August 2025