Numerical Back-analysis Research Articles

Parameter determination of Johnson–Holmquist–Cook constitutive model and calibration for Indiana Limestone

In this study, a comprehensive parameter determination procedure for the Johnson–Holmquist–Cook (JHC) constitutive model is introduced, including calibration and validation processes for Indiana Limestone rocks. The procedure is conducted utilizing the existing physical and mechanical properties of Indiana Limestone. To obtain an accurate set of parameters for the JHC model for Indiana Limestone, an extensive dataset comprising mechanical and physical properties of Indiana Limestone rocks was initially compiled. The static mechanical tests incorporated uniaxial compression, triaxial compression, direct tensile, and uniaxial strain data, while the dynamic mechanical test data was primarily derived from the Split Hopkinson Pressure Bar experiments. Subsequently, the JHC constitutive model parameters were determined using existing literature data, employing statistical analysis, theoretical derivation, and numerical back analysis techniques. One of the damage parameters was determined through numerical post-peak behavior calibration of triaxial compression strength test results on experimental data. Finally, the accuracy of the determined parameters was validated by comparing the numerical and experimental results of both static and dynamic tests. This study effectively addresses the challenges associated with the numerical method using the JHC material model, such as the complex parameter determination process and the costly required tests, thereby preserving the efficiency and applicability of the numerical method.

Numerical back analysis of an underground bulk mining operation using distributed optical fiber sensors for model calibration

Numerical back analysis of an underground bulk mining operation using distributed optical fiber sensors for model calibration

A new experimental setup to investigate the cyclic response of soft soils under induced earthquakes

Energy technologies, which work by extracting or injecting fluids in the ground, such as geothermal energy systems or underground liquefied gas storage, may induce seismic events, see e.g., [1]. In the Netherlands, induced earthquakes are continuously recorded from the Groningen gas field, with the largest magnitude ever recorded of ML 3.6 at Huizinge. Even though the magnitude of these events is not high, compared to natural earthquakes, damage to the built environment is still caused because of the shallow depth of the events and site amplification, especially where soft soils are encountered [2]. Proper quantification of the induced seismic risk requires better understanding of the response of soft soils to these repeated short events, covering a range of frequencies from 1 to about 20 Hz. This motivated the development of a new advanced dynamic equipment to experimentally investigate the coupled response of soft organic clays and peats from the typical deltaic areas of the Netherlands.
 Direct simple shear (DSS) apparatuses are preferred usually to investigate the soil behaviour under cyclic and dynamic loading. Among them, a number of multi-directional DSS setups have been developed to investigate the soil behaviour under multidirectional loading [3, 4, 5, 6, 7, 8]. Applying multi-directional loading to soil specimens in the laboratory is a keystone for elucidating the cyclic and dynamic soil response, as several studies have shown that the cyclic and post-cyclic response of soils is affected by multiple loading directions [6, 9, 10, 11, 12]. However, traditional DSS devices have a number of shortcomings, which are inherited by multi-directional DSS devices. The main deficiency of the DSS device is that the shear stress acting on the lateral side of the specimen cannot be controlled, and hence, a homogeneous stress state cannot be achieved, in spite of the common assumptions. Lateral stresses cannot be measured either in traditional setups, which leaves a knowledge gap on the stress state and the stress path of the sample.
 In addition, the majority of laboratory element tests are performed by imposing “slow” undrained cyclic loads, to try to guarantee uniform water pressure distribution within the sample, for the sake of interpretation and modelling. However, seismic events encompass much higher loading frequencies than typically available, with loading rate effects playing a key role in the response of soft soils such as organic clays and peats. In order to fully understand the cyclic behaviour of soft soils, “fast” cyclic tests are crucial.
 The innovative multidirectional shear device, developed in the section of Geoengineering at TU Delft (Cyclic-Dynamic shear simulator for Organic Soft Soils, CYC-DOSS), was designed to overcome some limitations of previous equipment. The underlying idea is to abandon the homogenous stress-strain state assumption and monitor the response with local sensors, which allows conditioning a numerical back-analysis of the test data. The new device shown in Figure 1 is characterised by (1) servo-hydraulic control; (2) multi-directional loading in 3 axes; (3) bender elements to measure both P-wave and S-wave velocity; (4) fully controlled cell pressure and back-pressure; and (5) possibility to reproduce the full acceleration time history of seismic events. The device is capable to apply loading frequencies up to 25Hz and a wide variety of multidirectional cyclic loading patterns. The apparatus is equipped with advanced sensors, also developed at TU Delft, including local pressure, displacements, and accelerations devices. The sensors are installed to reduce a priori assumptions on the soil response, better interpret the experimental results as a small-scale physical model and further investigate in depth the soil response under a variety of cyclic loading histories. The experimental information from the setup will be used to develop and calibrate an advanced bounding surface constitutive model for soft organic soils.

Numerical back analysis method of three-dimensional in situ stress fields considering complex surface topography and variable collinearity

Numerical back analysis based on incomplete in situ stress measurements is widely used to estimate the three-dimensional (3D) in situ stress fields of large deep underground caverns. However, the variable collinearity caused by complex geological environments has rarely been considered. This paper proposes a numerical back analysis method for 3D in situ stress fields based on stepwise regression (BSSR). In BSSR, the collinearity between independent variables is associated with the surface topography, and insignificant variables caused by variable collinearity are eliminated through stepwise regression. BSSR was applied to the underground powerhouse of a hydropower station for validation, and the results showed that it can reliably estimate the 3D in situ stress field despite the complex geological environments. Multidimensional mathematical models of in situ stress fields were established with the improved predictive ability and clear physical meaning, which can quantify the contributions of six geological actions and three stress sources. The findings of this study can help with understanding the formation mechanism of in situ stress fields for large, deep underground caverns in complex geological environments and provide a useful reference for optimizing excavation schemes and support designs.

Transition from rock mass creep to progressive failure for rockslide initiation at Mt. Conero (Italy)

The full description of rock mass behaviour involved in slope deformation, through its onset and progression until ultimate failure, is still a challenge in numerical simulations. The slope deformation that involved the coastal sector of Mt. Conero (Italy), leading to the rock avalanche of Portonovo, is an impressive example of a multistage creep evolution involving a jointed rock mass towards general failure. A landslide mass for the last event up to 5 Mm3 has previously been estimated from geomorphological analysis. This volume is not consistent with the size of the scar or the landslide deposit, suggesting a history of failures. Moreover, field evidence of pre-failure strain suggests progressive failure of the slope leading up to failure. In this study, a numerical back-analysis was set up using the finite difference method in a stress–strain approach, which applied an uncoupled solution to simulate the creep process and the progressive failure of the slope, as well as the accumulation of damage. The modelling outputs support the hypothesis that the landslide event was marked by two distinct episodes, each with volumes of approximately 20 Mm3, at 56 and 16 ka, which is consistent with the relative dating constraints. Additionally, a numerical back-analysis of the rock mass viscosity was calibrated and validated on the size of the scar area of the Portonovo landslide and on the morphological and structural evidence. The adopted strain-softening models caused significant differences in strain distribution and slope failure evolution. The proposed modelling demonstrated the importance of the creep process in controlling slope evolution and the reliability of the tested analytical approach for the analysis of progressive brittle rock failure, including the three-stage evolution of time-dependent viscous processes.

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.

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.

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.

The Dynamic Simulation and Potential Hazards Analysis of the Yigong Landslide in Tibet, China

High-altitude and long-runout landslides, commonly forming chains of secondary disasters, frequently occur in the Yigong Zangbo Basin, which has a complex geologic background. Identifying the potential hazards posed by disaster chains plays a vital role in assessing geohazards. Analysis of the potential hazards related to a landslide that occurred on 9 April 2000, in Tibet, China, known as the Yigong landslide, is studied using remote sensing technology and numerical simulations. Due to the warming of the climate, more extreme dry–wet cycles, and frequent earthquakes, the Yigong landslide area became extremely fragile and more sensitive to perturbations. Based on multiphase optical remote sensing and InSAR (Interferometric Synthetic Aperture Radar) technology, risk monitoring and identification of the Yigong landslide was conducted. The results show that there are two displacement deformation areas. These areas have a maximum displacement deformation rate of 60 mm/year and a maximum accumulative displacement of 160 mm and are likely to reoccur. Additionally, the risks of deformation areas collapsing and blocking the river, which would likely form a disaster chain, were analyzed by prediction simulation based on the numerical back-analysis associated with the 2000 Yigong landslide. The results show that if only one displacement deformation area collapses, the maximum accumulation height would reach 76 m; if the displacement deformation areas both collapse, the maximum accumulation height would reach 106 m. Both conditions would set off disaster chains resulting in river blockages and subsequent flood disasters. Therefore, this work demonstrates that prediction analysis based on remote sensing technology and numerical simulations are effective methods for identifying potential geohazards.

Physical overloading test for 3D printed caverns: Failure performance and supporting effect

Excavation of a large underground cavern often induces the unstable behavior of the surrounding rock due to intensive stress redistribution; thus, reasonable supporting measurements are necessary. A new 3D print-based physical overloading test method is presented for exposing the failure performance of caverns and the reinforcing effect of supported structures. Taking the Yingliangbao underground caverns as an engineering background, a physical model and supporting elements for the cavern groups are manufactured first by 3D printing (3DP) technology, including a multi-cavern 3DP sand model, 3DP polymer lining and metal bolt. Further overloading tests for the printed physical models are carried out, and the progressive failure performances are exposed, including crack extension, model loading evolution, local strain development, etc., which indicate that shear failure often appears on the mid-wall. Moreover, the overloading test for the supported cavern model also quantitatively reveals the reinforcing role of the 3DP polymer lining and metal bolt, such as increasing the bearing capacity by more than 10%. A corresponding numerical back analysis is further applied to certify the progressive failure process of multiple caverns under overloading conditions, which provides some cures for the supported bolt position and depth in multiple caverns. This method can enrich the physical model test and guide the support design for underground engineering construction.

Challenges associated with numerical back analysis in rock mechanics

Numerical back analysis is a valuable tool available to rock mechanics researchers and practitioners. Recent studies related to back analysis methods focused primarily on applications of increasingly sophisticated optimization algorithms (primarily machine learning algorithms) to rock mechanics problems. These methods have typically been applied to relatively simple problems; however, more complex back analyses continue to be conducted primarily through ad hoc manual trial-and-error processes. This paper provides a review of the basic concepts and recent developments in the field of numerical back analysis for rock mechanics, as well as some discussion of the relationship between back analysis and more broadly established frameworks for numerical modelling. The challenges of flexible constraints, non-uniqueness, material model limitations, and disparate data sources are considered, and representative case studies are presented to illustrate their impacts on back analyses. The role of back analysis (or “model calibration”) in bonded particle modelling (BPM), bonded block modelling (BBM), and synthetic rock mass (SRM) modelling is also considered, and suggestions are made for further studies on this topic.

In-situ Primary Stress Detection Based on Seismic Tomography Measurements and Numerical Back-analysis for an Underground Radwaste Repository

In order to understand how the in-situ primary stress state has evolved with subsidence and uplift in a granitic rock mass for anticipated of a radioactive waste repository in Hungary, the authors investigated the applicability of seismic tomography as an interpretive tool. Very high P wave velocity (Vp) values were obtained during the tomographic scanning of the study area of the repository, and these were compared with existing findings of in-situ and laboratory seismic measurements.Apart from seismic tomographic survey, dynamic FEM numerical modelling, empirical calculations of residual stresses, laboratory measurements of compression wave (ultrasonic) velocities on intact rock cores, in-situ primary stress measurements as well as site geological model were integrated to evaluate the use of seismic tomography for identifying possible in-situ stress increases around the excavation.A detailed calibration modelling was carried out based on the site seismic tomography measurements and during the large-scale modelling. It was observed that the increasing Vp is directly related to simulated increasing directional loadings on the rock mass. Using a measured wave raypath it was possible to check the different in-situ stress parametrizations which resulted in the best approximation to the measured Vp values.It was concluded that the rock mass under investigation to extend the repository must have higher in-situ stress values than the area of the constructed deposition chambers nearby. The results of this research indicated that seismic tomography is a useful tool for determining relative stress around and within the vicinity of underground excavation.

An Integrated Approach for the Determination of Young’s Modulus of a Cantilever Beam Using Finite Element Analysis and the Digital Image Correlation (DIC) Technique

This paper is an extended paper from the 24th International Conference on Mechatronics Technology, ICMT 2021. The basic mechanical characteristic that gauges the stiffness of a solid material is known as the Young’s modulus. To evaluate the Young’s modulus, destructive material testing is frequently used. This paper describes how to determine a material’s dynamic Young’s modulus using Digital Image Correlation (DIC) in conjunction with numerical back-analysis. Three different materials (brass, aluminum, and steel) were examined for their static and dynamic reactions. A static transverse displacement was first applied at the free end of the beam before it was released and the beam was allowed to vibrate freely. The resulting vibrations at the free end were monitored using the DIC method, following which the natural frequencies of the beam were derived by applying the Fast Fourier Transform (FFT) to the DIC measured time history. The Young’s modulus corresponding to the fundamental natural frequency of the beam was then obtained via modal back-analysis using the finite element program Ansys 2022 R1. In this way, the Young’s modulus of the material may be calculated using a combination of numerical and DIC techniques, thus allowing for the non-contact evaluation of the structural integrity without subjecting the material to destructive testing. Potential applications of this method include bridge and building assessments, and structural health monitoring (SHM).

Numerical Back-analysis of Caisson Quay Walls in the Yeong-il Bay Port during the 2017 Pohang Earthquake

The performance of nonlinear response history analysis was analyzed based on the historic case of the 2017 Pohang earthquake in Korea. The Yeong-il bay container terminal stopped operations for a period after the Pohang earthquake and intensive site and hazard investigations were conducted. Nonlinear response history analyses using various soil constitutive models, including sophisticated liquefaction models, were performed on the caisson quay wall under two-dimensional plane strain condition. The results of analysis were compared to the hazard investigation results. The analysis results exhibit reasonable agreement with the field measurement data for the earthquake-induced permanent displacement of the quay wall and quay crane rails.

An investigation of the combined effect of rainfall and road cut on landsliding

The reduction of soil suction and consequent loss of shear strength due to infiltration is known to trigger shallow landslides during periods of concentrated rainfall. In the mountainous terrain of Nepal, the risk of shallow rainfall-induced landsliding is further exacerbated by non-engineered hillslope excavation for local roads construction. To better understand the combined effect of rainfall and road cutting on landsliding, a detailed investigation of a shallow landslide was conducted, on a site with a steep road cut that failed due to rainfall infiltration in July 2018. An integrated investigation approach was adopted, combining field and laboratory testing and field monitoring with a series of coupled hydro-mechanical analyses with the finite element code PLAXIS 2D. The field and laboratory tests were performed to characterise the subsoil condition and determine the soil parameters for the hydro-mechanical analyses. The field monitoring program was set up to obtain real-time measurements of rainfall and volumetric water content of the soil. The monitored data was used to calibrate the numerical model and assess the reliability of its predictions. Results of the numerical back-analysis suggest that the investigated landslide was triggered by rainfall infiltration causing a gradual reduction of soil suction at shallow depths of ≤1.7 m and the presence of the steep road cut promoted slope failure by allowing larger displacements to occur in the hillslope. Without the road cut, the slope was found to have ~35% greater initial factor of safety and under the landslide-triggering rainfall, the undisturbed slope was found to remain stable with ~170% greater factor of safety than that in the slope with the road cut. This indicates that the presence of a road cut increases the likelihood of landslide during rainfall and lowers the minimum level of rainfall needed for landslide initiation. Hence, rainfall-induced roadside slope failures could become more frequent and extensive if roads continue to be built by informal slope excavation, without adopting suitable interventions, some examples of which are presented in this study.

Reliability and Efficiency of Metamodel for Numerical Back Analysis of Tunnel Excavation

During tunnel construction, the ground properties, initially evaluated, are continuously assessed and verified through back analysis. This procedure generally requires many numerical analyses, so a metamodel based on artificial neural networks has been used to reduce the number of analyses. More datasets can be used to create more reliable metamodels. However, there are no established rules regarding the optimum number of datasets for a reliable metamodel. Metamodels predicting the vertical displacement of the tunnel crown using five ground parameters (unit weight (γ), uniaxial compressive strength (UCS), material constant mi, geological strength index (GSI), and coefficient of lateral pressure (K)), with 3, 4, 6, 8, and 10 values per property, were created to confirm the reliability of the metamodel based on the number of datasets in this study. Metamodels using 6 and 8 values for each property showed 5% and 1% mean absolute percent errors, respectively. These numbers of each of the properties would be appropriate for developing the metamodel. Among the five parameters, only the results of the global sensitivity analyses of GSI and K are higher than 0.9. According to these results, it is verified that assessments based only on these parameters are sufficient in the back analysis.

Numerical Investigation of Impact Characteristics of Rigid Retaining Wall for Blocking Landslides: A Case Study of the Shum Wan Road Landslide

Landslides pose a serious threat to the downstream infrastructure and personnel safety. For situations where the location of possible landslides is difficult to determine, or the potential landslides areas are widely distributed and scattered, passive protective structural measures need to be adopted to relieve the threat of landslides. Taking the Shum Wan Road landslide as an example, the discrete element method was used to reproduce and analyze the landslide movement. On this basis, this study conducts a further numerical investigation on the impact characteristics of the rigid retaining wall used to block landslides. The results show that the numerical back analysis can well represent the evolution of the landslide, and the numerical results are in good agreement with the actual situation, thus confirming its correctness and effectiveness. Under the condition of setting a rigid retaining wall, the landslide can be effectively blocked and form a final deposition behind the retaining wall. The impact on the rigid retaining wall varies with time, and the distribution of the impact in space is also uneven. Through the statistical analysis of the contact forces on the retaining wall, the distributions of static and peak stresses on the retaining wall can be obtained. Compared with the static stability, the spatial distribution of dynamic impact is more difficult to predict, especially the area of the peak impact has a significant influence on the design. Numerical investigation can efficiently and reliably provide abundant information of static stress and dynamic impact on the rigid retaining wall, which can provide important reference for the optimal design of the rigid retaining wall structure.

Shear failure process of rectangular tunnel: Physical experimental test and numerical back-analysis

Shear failure is a typical failure mode in underground engineering and has resulted in a large number of instability issues. To study the shear failure mechanism, physical shearing tests for rectangular tunnel of sandstone, including single rectangular tunnel (SRT) and double rectangular tunnels (DRT) specimens, were carried out under three normal stress states. During the shearing tests, the internal failure process and the external cracks evolution of tunnel specimens were recorded by video camera, and the acoustic emission (AE) events of specimens were also monitored for exposing the mesoscopic failure characteristics. In addition, the discrete element method was also applied to analyze the corresponding shear experiment of rectangular-tunnel specimens. The tested results showed that the shear strength, shear modulus of the samples were positively correlated with the normal stress. For example, the shear strength, and shear modulus of SRT increased from 5.18 MPa to 8.70 MPa, and 1.02GPa to 1.88GPa, respectively when the normal stress increased from 2.0 MPa to 5.0 MPa. More importantly, the shear failure of rectangular tunnel model can be generally divided into four stages: (i) Shearing compression stage characterized by loading contacting and compressing; (ii) Shearing micro-crack propagation stage dominated by inner particles ejection of tunnel, tensile crack initiation and shear crack propagation of specimen; (iii) Shearing fracture stage dominated by the specimen’s crack propagation, coalescence, penetration, and corresponding rock ejection; (iv) Shearing friction stage dominated by shear damage of tunnel specimen. Corresponding back analysis by numerical simulation and scanning electron microscope results indicated that the shear failure of rectangular-tunnel specimen can be classified as tensile-shear mixed failure mode. The research results provide a new cures for shear prevention and support design of rectangular tunnels in underground engineering.

Determining the cause of tunnel damages during tunneling in silty clay

This paper presents a case study of investigating the cause of tunnel damages during tunneling in silty clay, in which the damages are existed in both ground surface and tunnel lining. The study is implemented by field investigation and numerical back analysis to determine the cause of tunnel damages, in which the field observed funnel-shaped surface subsidence of ground and surrounding soil moving to the tunnel are considered as softening soil body from ground surface until surrounding rocks in the numerical model, and the material parameters of the field monitored softening soil body are respectively taken as 0.8 times and 0.6 times of the original ones. This work confirms that the field observed tunnel damages during tunneling in silty clay can be numerically simulated, which is significantly influenced by the field monitored softening soil body from ground surface until surrounding rocks.

Experimental study on load sharing characteristics of long-short CFG pile composite foundation adjacent to rigid retaining wall rotating about its base

Practicing geoengineers and researchers generally consider the load sharing behavior in multi-type pile composite foundation as an important design aspect. On the other hand, due to urbanization, such foundation system in cities will inevitably appear next to supported excavation. This paper discusses the result from relatively large-scale indoor experiment conducted to investigate the load sharing behavior of loaded long-short CFG pile composite foundation behind a neighboring rigid retaining wall undergoing rotation around the bottom. It was found that with progression of wall movement, the hidden load from soil displacement was borne by the piles with marked reduction in soil load sharing. At the end of wall rotation, the percentage of long piles’ head load increment needed to arrive at a new static equilibrium was about 12.57~32.22% while the end bearing increased by more than 97%. The consequences on the short piles, however, were manifested with an increasing pile head (13.42%) and toe (28.9%) load for the pile far from the wall whereas the closest one experienced a certain increment up to 15×10-4rad wall rotation and finally the head load and end bearing decreased to 8.28% and 12.63%, respectively. The 3D numerical back analysis conducted using FE software ABAQUS yielded the pile – soil stress ratio lower than the value obtained from the experiment but provided great insight into pile settlement characteristics during wall rotation.