Characterizing Spatial Variability in Heterogeneous Soft Rock Using Advanced Statistical Models

 

1. Introduction

Understanding the spatial variability of thermodynamic properties in heterogeneous soft rock is essential for accurate geotechnical design and risk assessment. Natural rock formations exhibit significant randomness due to mineral composition, weathering, and structural discontinuities. This research introduces a probabilistic framework combining Random Field Theory and Copula statistical methods to capture spatial uncertainty and dependency structures, offering a more realistic representation of subsurface conditions.

2. Spatial Variability in Heterogeneous Soft Rock

Heterogeneous soft rock exhibits complex spatial variability due to geological processes such as sedimentation, diagenesis, and tectonic activity. This variability directly influences mechanical and thermodynamic behavior, making deterministic approaches insufficient. Spatial modeling allows researchers to quantify randomness and understand how material properties change across a rock mass.

3. Application of Random Field Theory

Random Field Theory provides a mathematical framework to model spatially distributed rock properties as stochastic processes. By incorporating correlation lengths and variance structures, this method captures realistic spatial fluctuations, enabling more reliable predictions for engineering analysis and design in uncertain geological environments.

4. Role of Copula Statistical Methods

Copula methods are powerful tools for modeling dependency between multiple thermodynamic properties without assuming identical probability distributions. In soft rock analysis, copulas allow researchers to describe nonlinear and complex correlations, improving joint probability assessment and uncertainty quantification.

5. Engineering and Energy Applications

Accurate characterization of spatial variability is critical for tunneling, slope stability, underground energy storage, geothermal systems, and sustainable infrastructure projects. Probabilistic models enhance safety, optimize design parameters, and reduce economic risks associated with unexpected subsurface behavior.

6. Future Research Directions

Future research may integrate machine learning, real-time sensor data, and multi-scale modeling with Random Field and Copula approaches. Such advancements will further enhance predictive accuracy and support resilient, data-driven decision-making in geotechnical and energy-related engineering projects.


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