Mathematical Problems in Rock Mechanics and Rock Engineering

With increasing requirements for energy, resources and space, rock engineering projects are being constructed more often and are operated in large-scale environments with complex geology. Meanwhile, rock failures and rock instabilities occur more frequently, and severely threaten the safety and stability of rock engineering projects. It is well-recognized that rock has multi-scale structures and involves multi-scale fracture processes. Meanwhile, rocks are commonly subjected simultaneously to complex static stress and strong dynamic disturbance, providing a hotbed for the occurrence of rock failures. In addition, there are many multi-physics coupling processes in a rock mass. It is still difficult to understand these rock mechanics and characterize rock behavior during complex stress conditions, multi-physics processes, and multi-scale changes. Therefore, our understanding of rock mechanics and the prevention and control of failure and instability in rock engineering needs to be furthered. The primary aim of this Special Issue “Mathematical Problems in Rock Mechanics and Rock Engineering” is to bring together original research discussing innovative efforts regarding in situ observations, laboratory experiments and theoretical, numerical, and big-data-based methods to overcome the mathematical problems related to rock mechanics and rock engineering. It includes 12 manuscripts that illustrate the valuable efforts for addressing mathematical problems in rock mechanics and rock engineering

Imaging of a fluid injection process using geophysical data - A didactic example

In many subsurface industrial applications, fluids are injected into or withdrawn from a geologic formation. It is of practical interest to quantify precisely where, when, and by how much the injected fluid alters the state of the subsurface. Routine geophysical monitoring of such processes attempts to image the way that geophysical properties, such as seismic velocities or electrical conductivity, change through time and space and to then make qualitative inferences as to where the injected fluid has migrated. The more rigorous formulation of the time-lapse geophysical inverse problem forecasts how the subsurface evolves during the course of a fluid-injection application. Using time-lapse geophysical signals as the data to be matched, the model unknowns to be estimated are the multiphysics forward-modeling parameters controlling the fluid-injection process. Properly reproducing the geophysical signature of the flow process, subsequent simulations can predict the fluid migration and alteration in the subsurface. The dynamic nature of fluid-injection processes renders imaging problems more complex than conventional geophysical imaging for static targets. This work intents to clarify the related hydrogeophysical parameter estimation concepts

Predicting and validating the load-settlement behavior of large-scale geosynthetic-reinforced soil abutments using hybrid intelligent modeling

Settlement prediction of geosynthetic-reinforced soil (GRS) abutments under service loading conditions is an arduous and challenging task for practicing geotechnical/civil engineers. Hence, in this paper, a novel hybrid artificial intelligence (AI)-based model was developed by the combination of artificial neural network (ANN) and Harris hawks’ optimisation (HHO), that is, ANN-HHO, to predict the settlement of the GRS abutments. Five other robust intelligent models such as support vector regression (SVR), Gaussian process regression (GPR), relevance vector machine (RVM), sequential minimal optimisation regression (SMOR), and least-median square regression (LMSR) were constructed and compared to the ANN-HHO model. The predictive strength, relalibility and robustness of the model were evaluated based on rigorous statistical testing, ranking criteria, multi-criteria approach, uncertainity analysis and sensitivity analysis (SA). Moreover, the predictive veracity of the model was also substantiated against several large-scale independent experimental studies on GRS abutments reported in the scientific literature. The acquired findings demonstrated that the ANN-HHO model predicted the settlement of GRS abutments with reasonable accuracy and yielded superior performance in comparison to counterpart models. Therefore, it becomes one of predictive tools employed by geotechnical/civil engineers in preliminary decision-making when investigating the in-service performance of GRS abutments. Finally, the model has been converted into a simple mathematical formulation for easy hand calculations, and it is proved cost-effective and less time-consuming in comparison to experimental tests and numerical simulations

Machine Learning-Based Rockfalls Detection with 3D Point Clouds, Example in the Montserrat Massif (Spain)

Rock slope monitoring using 3D point cloud data allows the creation of rockfall inventories, provided that an efficient methodology is available to quantify the activity. However, monitoring with high temporal and spatial resolution entails the processing of a great volume of data, which can become a problem for the processing system. The standard methodology for monitoring includes the steps of data capture, point cloud alignment, the measure of differences, clustering differences, and identification of rockfalls. In this article, we propose a new methodology adapted from existing algorithms (multiscale model to model cloud comparison and density-based spatial clustering of applications with noise algorithm) and machine learning techniques to facilitate the identification of rockfalls from compared temporary 3D point clouds, possibly the step with most user interpretation. Point clouds are processed to generate 33 new features related to the rock cliff differences, predominant differences, or orientation for classification with 11 machine learning models, combined with 2 undersampling and 13 oversampling methods. The proposed methodology is divided into two software packages: point cloud monitoring and cluster classification. The prediction model applied in two study cases in the Montserrat conglomeratic massif (Barcelona, Spain) reveal that a reduction of 98% in the initial number of clusters is sufficient to identify the totality of rockfalls in the first case study. The second case study requires a 96% reduction to identify 90% of the rockfalls, suggesting that the homogeneity of the rockfall characteristics is a key factor for the correct prediction of the machine learning models

Characterization of physical and mechanical properties of rocks from Otanmäki, Finland

Abstract. Physical and mechanical properties of rocks are important parameters for geological engineering and design of engineering structures, be it in the civil and/or mining sector. Rock physical properties include density, porosity, etc., and Young’s modulus, Poisson’s ratio and rock strength include some mechanical properties of rocks. These properties can be obtained by laboratory tests. This study aims at characterizing selected rock physical and mechanical properties to assist in predicting rock mass behavior when used in engineering structures, to discuss key rock petrographical features that affect strength and compare the prediction capacities of multiple linear regression and artificial neural network (ANN) models. The study investigates selected physical and mechanical properties from two igneous rock types, gabbro and granite, from the Otanmäki area, central Finland. The test results were used for the ANN and multiple regression models. In the analyses, a total of 25 cases from the two rocks were tested for uniaxial compression strength (UCS), Young’s modulus, Poisson’s ratio, Brazilian tensile strength (BTS), density, porosity and water content. Samples were also analyzed for petrographic and chemical compositions. Results from the analyses indicate the importance of adhering to testing standards because of inconsistencies and wide variations observed between nonstandardized as opposed to standardized specimens, and the need for large database for reliable predictive models. It presents ANN techniques as having a good generalization capacity for multi-variable nonlinear prediction