Back Analysis Research Articles

Stress tensor similarity index based on Euclidean distance for numerical back analysis of in situ stress fields

Evaluating the similarity between measured and predicted stress states is critical for the numerical back analysis of three-dimensional in situ stress fields. However, conventional nontensor approaches process stress components or the magnitude and orientation of principal stresses separately, which may yield contradictory results among multiple indices. To address this issue, we propose the Euclidean distance similarity (EDS), which is a dimensionless single index based on spatial distance. As a case study, EDS was applied to a site with complex geological conditions for verification. EDS can be derived in the form of stress component or principal stress. EDS exhibited a positive correlation with the initial difference and magnitude error of principal stresses and changed periodically with the Euler angle of rotation around the principal stress. Moreover, three magnitude errors and three Euler angles had different effects on EDS. Finally, EDS can be classified into five levels (i.e., extremely high, high, normal, low, and very low) according to the magnitude errors of principal stresses and Euler angles, where the “normal” level is recommended as a general error standard. The thresholds of EDS differ according to the initial stress level. These results are a valuable contribution to the similarity evaluation of stress tensors.

Highly energetic rockfalls: back analysis of the 2015 event from the Mel de la Niva, Switzerland

Process-based rockfall simulation models attempt to better emulate rockfall dynamics to different degrees. As no model is perfect, their development is often accompanied and validated by the valuable collection of rockfall databases covering a range of site geometries, rock masses, velocities, and related energies that the models are designed for. Additionally, such rockfall data can serve as a base for assessing the model’s sensitivity to different parameters, evaluating their predictability and helping calibrate the model’s parameters from back calculation and analyses. As the involved rock volumes/masses increase, the complexity of conducting field-test experiments to build up rockfall databases increases to a point where such experiments become impracticable. To the author’s knowledge, none have reconstructed rockfall data in 3D from real events involving block fragments of approximately 500 metric tons. A back analysis of the 2015 Mel de la Niva rockfall event is performed in this paper, contributing to a novel documentation in terms of kinetic energy values, bounce heights, velocities, and 3D lateral deviations of these rare events involving block fragments of approximately 200 m3. Rockfall simulations are then performed on a “per-impact” basis to illustrate how the reconstructed data from the site can be used to validate results from simulation models.

Damage identification method on shield tunnel based on PLSR and equivalent damage analysis

Damage identification plays a critical role in the maintenance of the shield tunnel structure. This study proposes a damage identification method for shield tunnel lining based on back analysis, which lays emphasis on the mechanical responses of the structure. The connection between mechanical parameters and the structural response is extracted by the finite element model. With the employment of Partial Least Squares Regression (PLSR), the load on shield tunnel lining can be determined by the monitoring data, the variation of which before and after structural damage, regarded as damage index, is used to identify the damage position. The equivalent damage load is defined to establish the equations of the load, deformation and damage, which solves the problems induced by the randomness of damage position. To clarify the validation, the method is verified by previous experimental results. Involving the structural damage of various positions and intensities, this method is applied with the numerical models based on circular shield tunnel. The parametric study shows the accuracy of the method under different damage conditions. The effects of monitoring data of radial displacement and circumferential strain were also compared. As a result, the primary input from the circumferential strain has better sensitivity than that of the radial displacement.

Inversion Analysis of the In Situ Stress Field around Underground Caverns Based on Particle Swarm Optimization Optimized Back Propagation Neural Network

The in situ stress distribution is one of the driving factors for the design and construction of underground engineering. Numerical analysis methods based on artificial neural networks are the most common and effective methods for in situ stress inversion. However, conventional algorithms often have some drawbacks, such as slow convergence, overfitting, and the local minimum problem, which will directly affect the inversion results. An intelligent inverse method optimizing the back-propagation (BP) neural network with the particle swarm optimization algorithm (PSO) is applied to the back analysis of in situ stress. The PSO algorithm is used to optimize the initial parameters of the BP neural network, improving the stability and accuracy of the inversion results. The numerical simulation is utilized to calculate the stress field and generate training samples. In the application of the Shuangjiangkou Hydropower Station underground powerhouse, the average relative error decreases by about 3.45% by using the proposed method compared with the BP method. Subsequently, the in situ stress distribution shows the significant tectonic movement of the surrounding rock, with the first principal stress value of 20 to 26 MPa. The fault and the lamprophyre significantly influence the in situ stress, with 15–30% localized stress reduction in the rock mass within 10 m. The research results demonstrate the reliability and improvement of the proposed method and provide a reference for similar underground engineering.

Probabilistic back analysis of rainfall-induced slope failure considering slope survival records from past rainfall events

Many rainfall-induced landslides occur on slopes that have limited, or even no, site investigation data before failure. Probabilistic back analysis of slope failure provides an effective tool to back analyze possible pre-failure soil parameters, thus gaining insights into the mechanism of slope failure. For a slope failure induced by rainfall, the actual factor of safety (FS) is time-variant when time-variant rainfall and infiltration are explicitly modeled. This study proposes a novel probabilistic back analysis method that models explicitly the rainfall triggering mechanism for a rainfall-induced slope failure. Unlike existing methods that are based on a constant FS = 1, the proposed method utilizes FS inequality information for probabilistic back analysis, including slope failure record with FS < 1 and slope survival records from past rainfall events with FS > 1. The proposed method is suitable for high-dimensional problems when soil hydraulic properties are also back analyzed. The proposed method converges to the conventional methods with FS = 1 when the time span of slope failure is narrowed down to a few hours and slope survival records are ignored. Incorporating both slope failure and survival records effectively reduces uncertainties in soil strength and hydraulic parameters.

Rainfall Infiltration Impact on Road Embankment Stability

This study evaluates the stability of a widened road embankment slope by considering the effect of rain infiltration, which is often ignored in practical design. Rainfall infiltrates the soil and alters pore water pressure, reducing its shear strength and potentially causing slope failure. The Phi Index method is used to determine rain infiltration values, using rainfall data from four nearby rain stations over 10 years. The changes in pore water pressure resulting from rain infiltration are incorporated into the slope stability analysis by the limit equilibrium concept using the Spencer method. Back analysis is used to determine the soil shear strength parameters since the CPT test results provide a correlation with values within a certain range. Soil parameters resulting in a safety factor value close to 1.25 (critical condition) were considered representative field conditions. The analysis shows a decrease in the safety factor from 1.50 to 1.31 (12%). These findings emphasize the importance of accounting for rain infiltration in road embankment stability analyses, particularly in areas with high rainfall where the safety factor may fall below the minimum required by Indonesian geotechnical code. When an infiltration effect analysis is not conducted, the safety factor should be increased at least 12% from normal conditions.

Pseudo-discontinuum model to simulate hard-rock mine pillars

In this study, the pseudo-discontinuum modeling technique, called continuum Voronoi block model (CVBM), was applied to represent the behavior of hard-rock pillars from underground mines subjected to high field stresses. The CVBM’s ability to produce numerical results consistent with the observed behavior of pillars is demonstrated through the numerical analysis of a hypothetical case and a back analysis of the Creighton mine pillar. The results show that the model can capture convergence displacements and explicitly show the formation of macro-fractures parallel to excavation walls, intact rock slabs, and V-shaped notches. These components are characteristics of brittle failure induced by highly stressed ground conditions. The studies presented in this work confirm the CVBM as a convenient tool for the numerical modeling of intact rock pillars excavated in deep underground mines.

An effective method for real-time estimation of slope stability with numerical back analysis based on particle swarm optimization

Abstract The purpose of this article is to provide an effective approach to evaluate slope stability in real-time in a reservoir area, which is significant for carrying out risk management for landslide disaster prevention in various engineering practices. A comprehensive idea for stability estimation of bank slope under the influence of rainfall or the reservoir water level is presented in this work. Slope stability analysis and back analysis of soil parameters are both included based on numerical simulation. The mechanical parameters of the bank slope were first back-analyzed using particle swarm optimization (PSO), and real-time stability analysis with high accuracy and efficiency was then established based on multiple continuously monitored displacements. Two case studies were carried out in this study. The results show that (1) based on the real-time monitored displacement and numerical simulation, the mechanical parameters of the slope can be reasonably retrieved through PSO; and (2) based on the inverse mechanical parameters, the safety factors of the slope can be numerically obtained, so that the real-time estimation of slope stability can be realized.

Back analysis of geomechanical parameters for rock mass under complex geological conditions using a novel algorithm

Geomechanical properties of rock mass are of vital importance for design optimization and stability evaluation in geotechnical engineering. Traditionally, they are estimated by laboratory experiments, in situ tests, and empirical classification, which ignore the scale effect, and may be not representative, leading to uncertainties of parameters. Back analysis method based on the monitoring displacement data provides the state-of-the-art tool for the estimation of geomechanical parameters. This paper proposed a novel back analysis method, which combined the optimized particle swarm optimization (OPSO) algorithm with the support vector machine (SVM) algorithm. And then, we cooperate the method with finite element method (FEM) forming the comprehensive method named OPSO-SVM-ABAQUS. This method has developed the standard PSO algorithm from two aspects for more powerful optimization capability and higher optimization precision. The OPSO algorithm is then used for the estimation of the SVM hyperparameters and the optimal values of geomechanical parameters. Furthermore, the performance of the proposed algorithm is compared with other six algorithms. Finally, the geomechanical parameters of the interlayered soft and hard rocks are calculated accurately, with the average error between the back-analyzed and assumed actual parameters to be 0.91 %. And the parametric investigations are implemented with the trained model. It dominates that the proposed algorithm is feasible for reasonable parameters in geotechnical engineering under complex geological conditions.

Instantaneous limit equilibrium back analyses of major rockslides triggered during the 2016–2017 central Italy seismic sequence

Abstract. Among the almost 1400 landslides triggered by the shocks of the 2016–2017 central Italy seismic sequence, only a limited number, all classifiable as rockslides, involved volumes larger than 1000 m3. Four of these failures, including the three largest among the documented landslides, were described in terms of structural and geomechanical investigations in a previous paper. In this study, the estimated acceleration time histories at the rockslide sites were evaluated through a 2D simplified numerical model accounting for the attenuation phenomena and for the topographic effect of the rock cliffs from which the slide detached. Instantaneous stability analyses were carried out to obtain insights into the variability of the instantaneous margin of safety along the motion, over the entire spectrum of mechanisms that could be activated. Finally, some general suggestions on the pseudo-static verification method for 3D cases are proposed, which represent useful indications to hazard evaluation at local and regional scales.

Two- and Three-dimensional Numerical Back-analysis of Deep Excavation Case Studies from Budapest, Hungary

In this paper, the numerical back analyses of four, typical, monitored deep excavations completed in Budapest are presented. The typical excavation solution in Budapest city center, down to 15–18 m excavation depth, is a diaphragm wall embedded in the clay bedrock and supported by prestressed anchors embedded in the sedimentary soils above the clay. In these case studies this solution is analyzed with traditional Winkler type and more complex PLAXIS 2D and 3D finite element models. The focus of the study was to compare the measured wall deformations with the calculated ones derived by the listed methods. As the clay bedrock is a deterministic layer for the wall behavior, several different FEM models were prepared to analyze the appropriateness of the potential constitutive models for its proper characterization. As a conclusion, practical proposals were made for practitioners for future excavations.

Study of a Method for Drivability of Monopile in Complex Stratified Soil

At present, there is no commonly used method for predicting soil resistance to the driving (SRD) of monopiles, because all available methods are developed based on an installed offshore pile with a diameter of 2–3 m. In addition, due to the complexity of soil profiles in situ, the accuracy of methods used is often not stable under different soil conditions. Based on two typical stratified soil conditions of offshore wind farms in the East China Sea, which are clay-interlayered sand and sand-interlayered clay where, according to the pile driving records of the monopiles in sites, the SRD is obtained by back analysis using the method of the wave equation. At the same time, SRD is also calculated using Steven and Alm methods and compared with that of the back analysis. The results show that the SRDs from the Steven and Alm methods are basically consistent with that of the back analysis, but the predicted SRD of the clay layer is higher than that of back analysis, while the predicted SRD of the sand layer is lower. Based on the characteristics of SRD in different soil layers, a modified method for calculating unit friction in clay and the unit end resistance in sand is proposed for stratified soil, and the error between SRD of the proposed method and of the back analysis was approximately 20%. It could be helpful to improve the accuracy of the monopile drivability analysis in stratified soil.

Predicting settlement of embankments built on PVD-improved soil using Bayesian back analysis and elasto-viscoplastic modelling

In this study, an implicit finite difference program, 1DFDM, based on the fully coupled one dimensional elasto-viscoplastic (1D EVP) model combining radial and vertical drainage is developed to perform consolidation analysis of embankments constructed on soft soils. Class A prediction (prior prediction) is performed by using 1DFDM for the embankment constructed on soft clay in Ballina, Australia. However, the prediction deviates significantly from the measurements, and the model parameters need to be calibrated. Bayesian back analysis is thus combined with 1DFDM in this study to do Class C prediction. Three updating schemes (using monitoring settlement only, using monitoring pore water pressure only, and using both monitoring settlement and pore water pressure) are employed to shed light on the effects of the monitoring data types on settlement prediction. The results show that the long-term settlement and pore water pressure predictions could be further improved if both the monitoring settlement and pore water pressure data are incorporated. The coupling effects in the constitutive model can reduce the fluctuations in the updated optimum parameters. A stable and physically reasonable parameter set could be obtained if enough monitoring data is incorporated into the Bayesian back analysis.

Development of a methodology for predicting landslide hazards at a regional scale

Landslide risk analysis is a common geotechnical evaluation and it aims to protect life and infrastructure. In the case of sensitive clay zones, landslides can affect large areas and are difficult to predict. Here we propose a methodology to determine the landslide hazard across a large territory, and we apply our approach to the Saint-Jean-Vianney area, Quebec, Canada. The initial step consists of creating a 3D model of the surficial deposits of the target area. After creating a chart of the material electrical resistivity adapted for eastern Canada, we applied electric induction to interpret the regional soil. We transposed parameter values obtained from the laboratory to a larger scale, that is to a regional slope using the results of a back analysis undertaken earlier, on a smaller slide within the same area. The regional 3D model of deposits is then used to develop a zonation map of slopes that are at risk and their respective constraint areas with the study region. This approach allowed us to target specific areas where a more precise stability analysis would be required. Our methodology offers an effective tool for stability analysis in territories characterized by the presence of sensitive clays.

Influence of Load–Settlement Relationship of Intermediate Foundation Pile Group on Numerical Analysis of a Skyscraper under Construction

Slab and pile foundations are one of the most popular solutions for transferring building loads to the ground. This is due to the combination of the advantages of direct and indirect foundations. Unfortunately, the lack of studies on this type of foundation that present the theoretical and practical dimensions of this approach is apparent. This article presents the theoretical background of this issue, capturing the advantages and disadvantages of this solution. The authors lean into the theoretical derivation by demonstrating various computational approaches. Thanks to the theoretical derivation and the citation of various computational approaches, it is possible to correctly determine the bearing capacity of the slab itself or the piles themselves in a slab–pile foundation. In addition, the authors have prepared numerical calculations based on theoretical considerations. The numerical analysis method shows the convergence of the selected theoretical method, which confirms the uniqueness of this computational approach through back analysis and validation of numerical models with Robot Structural Analysis software. The numerical consideration confirms the correct distribution of pile- and slab-bearing capacities; thus, it is possible to design the slab–pile foundation economically. With this verification, the design method of this type of foundation can be correctly determined.

Monitoring Displacements and Damage Detection through Satellite MT-InSAR Techniques: A New Methodology and Application to a Case Study in Rome (Italy)

Satellite interferometry has recently developed as a powerful tool for monitoring displacements on structures for structural health monitoring (SHM), as it allows obtaining information on past deformation and performing back analysis on structural behavior. Despite the increasing literature on this subject, the lack of protocols for applying and interpreting interferometric data for structural assessment prevents these techniques from being employed alongside conventional SHM. This paper proposes a methodology for exploiting satellite interferometric data aiming at remotely detecting displacements and buildings’ criticalities at different levels of analysis, i.e., urban scale and single-building scale. Moreover, this research exploits the capability of satellite monitoring for damage diagnosis, comparing the millimeter scale displacements to information derived from on-site inspections. Different data-driven algorithms were applied to detect seasonal and irreversible components of displacements, such as statistical models for damage identification derived from traditional on-site monitoring. Thus, the proposed methodology was applied to a XVI-century case study located in the city center of Rome (Italy), Palazzo Primoli, and two stocks of COSMO-SkyMed (CSK) images processed through the Small BAseline Subset Differential Interferometry (SBAS-DInSAR) technique were used to assess displacements for an eight-year-long (between 2011 and 2019) monitoring period.

A novel short pile foundation system bonded to highly cemented layers for settlement control

While design methods of deep foundations are mainly developed for homogenous soil deposits, the presence of highly cemented layers could lead to underestimation of resistance and overestimation of settlement of pile foundations. This study presents a novel approach using competent caliche layers bonded to the top and bottom of a continuous flight auger (CFA) pile as a new composite foundation system named caliche stiffened pile (CSP). The key objective is to optimize the required pile length in a cost-effective approach without ameliorating soil properties. Settlements of the CSP foundation for a high-rise building were monitored and full-scale tests were conducted to measure piles’ capacity. Finite element back analyses were performed to avoid adverse effect of sample disturbance in settlement calculations. A back calculation of a test fill embankment was performed to determine soil stiffness parameters by simulating an unscheduled imposed load to the structure. Impacts of the CSP on controlling the settlement of pile foundation and optimizing the required pile length are investigated using finite element analysis and a parametric study. The proposed CSP foundation can reduce the CFA pile settlement significantly in the presence of caliche layers with thickness equal or greater than a pile diameter at CFA pile head and toe, where the CSP is located.

An Experimental Study of Industrial Site and Shaft Pillar Mining at Jinggezhuang Coal Mine

Engineering site and shaft pillars are excavated to prolong the life of collieries and excavate more underground coal. The Jinggezhuang colliery (‘JGZ’) is a resource-exhausted coal mine in eastern China. It was determined that the industrial site and shaft pillar of JGZ would be extracted in 2008. This study excavated an experimental panel to examine the effect of pillar excavation on surface buildings in complicated geological conditions. A new pillar design was proposed based on surface monitoring to increase the recovery ratio. To maintain the safety of the shaft and engineering facilities, panel 0091 was mined and surface deformation was monitored during the experiment. The deformation characteristics and parameters were obtained using a back analysis method. A new pillar was designed using the parameters measured from panel 0091. The design maintained the safety of the shaft but relaxed the restriction of the influence of constructions at the engineering site. The prediction results of the surface subsidence and the deformation of the main building were analyzed. The maximum subsidence of the surface was 7419 mm, but the surface subsidence of the shafts was less than 10 mm. The shafts were weakly influenced by the pillar excavation. The prediction results can be used as basic information for the monitoring and maintenance of buildings in the future. Using the new pillar design, 2.54 million tons of coal resources were mined. This study provides an engineering example and a reference for shaft pillar excavation in the future.

Engineering Safety Evaluation of the High Rock Slope of a Hydropower Project: A Case Study of 684 m-High Slope Related to Lianghekou Hydropower Project at Yalong River

The stability of the slope is a very important topic in the construction of hydropower projects, especially the slope engineering in the dam area, as its stability will directly affect the safety of engineering. Taking the inlet slope of the flood discharge structure of Lianghekou Hydropower Project as the research object, based on the analysis and exploration of the geological condition of the slope and the field monitoring data, GA-LSSVM is used to establish the non-linear mapping relationship, and the BP neural network is used to establish the mechanical parameters back analysis of the slope at different water impoundment stages. A numerical simulation model is also established to set up different reservoir impoundments to study the stability and sensibility of the slope and provide guidance for slope operation. This case study shows that there is a hysteresis in the response of slope deformation to reservoir impoundment. At the same time, the mechanical parameters of the slope will be weakened by the seepage. In the process of water level changes, the stability of the slope decreases due to the decrease in mechanical parameters. The study will be practically useful for engineering applications.

Seasonal Variability in Fine Particulate Matter Water Content and Estimated pH over a Coastal Region in the Northeast Arabian Sea

The acidity of atmospheric particles can promote specific chemical processes that result in the production of extra condensed phases from lesser volatile species (secondary fine particulate matter), change the optical and water absorption characteristics of particles, and enhance trace metal solubility that can function as essential nutrients in nutrient-limited environments. In this study, we present an estimated pH of fine particulate matter (FPM) through a thermodynamic model and assess its temporal variability over a coastal location in the northeast Arabian Sea. Here, we have used the chemical composition of FPM (PM2.5) collected during the period between 2017–2019. Chemical composition data showed large variability in water-soluble ionic concentrations (WSIC; range: 2.3–39.9 μg m−3) with higher and lower average values during the winter and summer months, respectively. SO42− ions were predominant among anions, while NH4+ was a major contributor among cations throughout the season. The estimated pH of FPM from the forward and reverse modes exhibits a moderate correlation for winter and summer samples. The estimated pH of FPM is largely regulated by SO42− content and strongly depends on the relative ambient humidity, particularly in the forward mode. Major sources of FPM assessed based on Positive matrix factorization (PMF) and air-mass back trajectory analyses demonstrate the dominance of natural sources (sea salt and dust) during summer months, anthropogenic sources in winter months and mixed sources during the post-monsoon season.