Calibration Of Model Parameters Research Articles

Understanding Climate Change by Modeling the Earth's Atmosphere as a Well‐Stirred Tank

AbstractComing to terms with climate change by understanding climate processes and their policy implications is essential not only for climate scientists and policymakers, but also for the general public, for industrial practitioners, and for engineers, including process system engineers. We have developed a simplified linear climate model (SLCM) to enable non‐specialists to explore the essential physical and chemical processes caused by greenhouse gas emissions. Trading‐off simplicity and accuracy, achieved by calibrating model parameters using established simple climate models, the SLCM allows (i) determining the climate impact of given past and future emissions, (ii) determining the amounts of CO2 removal needed to compensate for any unavoidable emissions of CH4 and N2O from agriculture, and (iii) back‐calculating emission pathways to meet specified global warming targets.

Combining Biology-based and MRI Data-driven Modeling to Predict Response to Neoadjuvant Chemotherapy in Patients with Triple-Negative Breast Cancer.

"Just Accepted" papers have undergone full peer review and have been accepted for publication in Radiology: Artificial Intelligence. This article will undergo copyediting, layout, and proof review before it is published in its final version. Please note that during production of the final copyedited article, errors may be discovered which could affect the content. Purpose To combine deep learning and biology-based modeling to predict the response of locally advanced, triple negative breast cancer before initiating neoadjuvant chemotherapy (NAC). Materials and Methods In this retrospective study, a biology-based mathematical model of tumor response to NAC was constructed and calibrated on a patient-specific basis using imaging data from patients enrolled in the MD Anderson ARTEMIS trial (ClinicalTrials.gov, NCT02276443) between April 2018 and May 2021. To relate the calibrated parameters in the biology-based model and pretreatment MRI data, a convolutional neural network (CNN) was employed. The CNN predictions of the calibrated model parameters were used to estimate tumor response at the end of NAC. CNN performance in the estimations of total tumor volume (TTV), total tumor cellularity (TTC), and tumor status was evaluated. Model-predicted TTC and TTV measurements were compared with MRI-based measurements using the concordance correlation coefficient (CCC), and area under the receiver operating characteristic curve (for predicting pathologic complete response at the end of NAC). Results The study included 118 female patients (median age, 51 [range, 29-78] years). For comparison of CNN predicted to measured change in TTC and TTV over the course of NAC, the CCCs were 0.95 (95% CI: 0.90-0.98) and 0.94 (95% CI: 0.87-0.97), respectively. CNN-predicted TTC and TTV had an AUC of 0.72 (95% CI: 0.34-0.94) and 0.72 (95% CI: 0.40-0.95) for predicting tumor status at the time of surgery, respectively. Conclusion Deep learning integrated with a biology-based mathematical model showed good performance in predicting the spatial and temporal evolution of a patient's tumor during NAC using only pre-NAC MRI data. ©RSNA, 2024.

Comparison of synergy extrapolation and static optimization for estimating multiple unmeasured muscle activations during walking

BackgroundCalibrated electromyography (EMG)-driven musculoskeletal models can provide insight into internal quantities (e.g., muscle forces) that are difficult or impossible to measure experimentally. However, the need for EMG data from all involved muscles presents a significant barrier to the widespread application of EMG-driven modeling methods. Synergy extrapolation (SynX) is a computational method that can estimate a single missing EMG signal with reasonable accuracy during the EMG-driven model calibration process, yet its performance in estimating a larger number of missing EMG signals remains unknown.MethodsThis study assessed the accuracy with which SynX can use eight measured EMG signals to estimate muscle activations and forces associated with eight missing EMG signals in the same leg during walking while simultaneously performing EMG-driven model calibration. Experimental gait data collected from two individuals post-stroke, including 16 channels of EMG data per leg, were used to calibrate an EMG-driven musculoskeletal model, providing “gold standard” muscle activations and forces for evaluation purposes. SynX was then used to predict the muscle activations and forces associated with the eight missing EMG signals while simultaneously calibrating EMG-driven model parameter values. Due to its widespread use, static optimization (SO) applied to a scaled generic musculoskeletal model was also utilized to estimate the same muscle activations and forces. Estimation accuracy for SynX and SO was evaluated using root mean square errors (RMSE) to quantify amplitude errors and correlation coefficient r values to quantify shape similarity, each calculated with respect to “gold standard” muscle activations and forces.ResultsOn average, compared to SO, SynX with simultaneous model calibration produced significantly more accurate amplitude and shape estimates for unmeasured muscle activations (RMSE 0.08 vs. 0.15, r value 0.55 vs. 0.12) and forces (RMSE 101.3 N vs. 174.4 N, r value 0.53 vs. 0.07). SynX yielded calibrated Hill-type muscle–tendon model parameter values for all muscles and activation dynamics model parameter values for measured muscles that were similar to “gold standard” calibrated model parameter values.ConclusionsThese findings suggest that SynX could make it possible to calibrate EMG-driven musculoskeletal models for all important lower-extremity muscles with as few as eight carefully chosen EMG signals and eventually contribute to the design of personalized rehabilitation and surgical interventions for mobility impairments.

Assessment of the Choked Flow Model of RELAP5 for Application of Inverse Quantification Methods

In the framework of deterministic safety analysis, best estimate plus uncertainty methodologies can provide a more informative detailed analysis of transients than conservative approaches. However, one important step in the application of such methodologies is derivation of uncertainty of the physical models. Probability density functions of the physical model parameters are obtained by applying inverse uncertainty quantification (IUQ) methods to experimental data. The present work deals with evaluation of the experimental database and assessment of the simulation model, which are required steps prior to the application of IUQ methods. The U.S. Nuclear Regulatory Commission system code RELAP5 has been applied for simulation of three experimental databases on choked/critical flow: Sozzi-Sutherland, Super MobyDick, and Marviken Critical Flow Tests. First, the adequacy of the experimental data to the specific target domain is carried out, to then proceed to calibration of the input model parameters by combining the use of Gaussian Process metamodels and optimization schemes. The assessment of the simulation models is performed by evaluating independently accuracy, precision, and consistency through four statistical indicators, including a novel indicator to evaluate the consistency of the results. The final results indicate that the model is capable of reproducing the selected experimental database and overall average accuracy, precision, and consistency below the 10% threshold and can be used for application of IUQ methods.

Advancing SWAT Model Calibration: A U-NSGA-III-Based Framework for Multi-Objective Optimization

In recent years, remote sensing data have revealed considerable potential in unraveling crucial information regarding water balance dynamics due to their unique spatiotemporal distribution characteristics, thereby advancing multi-objective optimization algorithms in hydrological model parameter calibration. However, existing optimization frameworks based on the Soil and Water Assessment Tool (SWAT) primarily focus on single-objective or multiple-objective (i.e., two or three objective functions), lacking an open, efficient, and flexible framework to integrate many-objective (i.e., four or more objective functions) optimization algorithms to satisfy the growing demands of complex hydrological systems. This study addresses this gap by designing and implementing a multi-objective optimization framework, Py-SWAT-U-NSGA-III, which integrates the Unified Non-dominated Sorting Genetic Algorithm III (U-NSGA-III). Built on the SWAT model, this framework supports a broad range of optimization problems, from single- to many-objective. Developed within a Python environment, the SWAT model modules are integrated with the Pymoo library to construct a U-NSGA-III algorithm-based optimization framework. This framework accommodates various calibration schemes, including multi-site, multi-variable, and multi-objective functions. Additionally, it incorporates sensitivity analysis and post-processing modules to shed insights into model behavior and evaluate optimization results. The framework supports multi-core parallel processing to enhance efficiency. The framework was tested in the Meijiang River Basin in southern China, using daily streamflow data and Penman–Monteith–Leuning Version 2 (PML-V2(China)) remote sensing evapotranspiration (ET) data for sensitivity analysis and parallel efficiency evaluation. Three case studies demonstrated its effectiveness in optimizing complex hydrological models, with multi-core processing achieving a speedup of up to 8.95 despite I/O bottlenecks. Py-SWAT-U-NSGA-III provides an open, efficient, and flexible tool for the hydrological community that strives to facilitate the application and advancement of multi-objective optimization in hydrological modeling.

MiPrime: A model for the microbially mediated impacts of organic amendments on measurable soil organic carbon fractions and associated priming effects

Priming effects can influence the efficiency with which organic amendments sequester carbon in the soil. Yet, few soil models currently include priming effects. Those models that do are often based on operationally defined soil pools and implicitly allow only for positive priming effects. This limits the verification of model processes with experimental data and hinders the optimization of our carbon sequestration strategies. To address these shortcomings, we developed MiPrime, which offers a framework for the mechanistic modelling of organic amendment impacts on microbially mediated transformation of carbon fractions that are quantifiable through parsimonious soil extraction methods. MiPrime allows for assessment of organic amendment impacts on soil carbon dynamics, including priming effects, by simulating changes in mineralized, microbial biomass, dissolvable, hot water extractable and insoluble carbon fractions in soil exogenous (i.e. organic amendment-derived) and endogenous (i.e. soil) pools. After calibration of model parameters using Markov Chain Monte Carlo methods to incubation data of three types of isotopically labelled roadside grasses (a fresh grass product, a compost thereof, and a Bokashi-fermented product thereof), MiPrime was able to simulate changes in carbon fractions of the soil with a good degree of accuracy for five compositionally complex organic amendments, namely the three types of roadside grasses, as well as non-isotopically labelled wood chips and water weeds and reeds. Validation of the model results with experimental data demonstrates that changes in total carbon were very well predicted but that there is room for improvement in predicting mineralization rates and changes in dissolvable, hot water extractable and insoluble carbon fractions in the soil endogenous pool. MiPrime thus offers an initial step towards the mechanistic modelling of organic amendment impacts on measurable soil carbon fractions and can operate as a new tool for designing effective carbon sequestration strategies and understanding organic amendment impacts.

Integration of Geological Model and Numerical Simulation Technique to Characterize the Remaining Oil of Fractured Biogenic Limestone Reservoirs

AbstractFine geological modeling leads to accurate reservoirs numerical simulations. Fractured biogenic limestone has abundant storage spaces and flow paths to accumulate oil and gas. The complexity and diversity of fractured biogenic limestone also lead to challenges in accurately characterizing its pore volume and remaining oil. This investigation aimed to enhance the understanding of fractured biotite reservoir properties via geological modeling. Numerical simulations were used to characterize the remaining oil during the late stage of field development. Considering the differences in porosity and permeability between fractures and matrix, a facies-controlled stochastic modeling technique was used to establish a dual-porosity and dual-permeability (DPDP) model for numerical simulation. Core information, logging data, and multiple seismic attributes were combined to guide low-level sequence fault interpretation for tectonic refinement. Based on classified seismic inversion, sedimentary phases were reconstructed. A discrete fracture network (DFN) model was obtained based on fracture occurrences and density models. The optimized discrete adjoint (ODA) algorithm was utilized to calibrate model parameters. The findings revealed that dense tectonic fractures develop in thick biogenic limestone areas. Combined with advanced reservoir simulation technology, these findings suggest that areas of thicker biogenic limestone were consistent with areas of higher fracture matrix conductivity multipliers. The remaining oil distribution patterns were investigated, and to deploy new wells was guided. Therefore, it is essential to better understand the tectonic characteristics of fractured biogenic limestone reservoirs and their remaining oil distribution patterns by integrating multiple sources of information and mastering advanced reservoir simulation technology for oilfield development.

A sustainable semiconductor supply chain under regulation

Modern life would not exist without semiconductors as all electronic components used in computers, telecommunications, health care, transportation, and energy systems are equipped with chips. To examine both backward and forward activities in semiconductor industry, this paper formulates the industry as a closed-loop supply chain. It articulates how old semiconductors are processed and recycled to manufacture new silicon and chips, and examines the impact of a commonly applied subsidy scheme on the performance of semiconductor firms which operate in upstream and downstream layers of the industry. Specifically, the proposed semiconductor supply chain involves (i) a return function sensitive to monetary incentives; (ii) a subsidy legislation rewarding end-users for recycling; (iii) upstream industry where silicon is produced using virgin and scrap materials; (iv) downstream industry in which semiconductor manufacturers (such as TSMC, Samsung, Intel) buy silicon and other materials, hire workers, and then produce and sell chips. We characterize Stackelberg equilibrium silicon and semiconductor prices and outputs and calibrate model parameters using actual data to quantify the effects of subsidy and collection channels on silicon and semiconductor firms’ performance. We find that the subsidy scheme neither distorts firms’ strategies nor causes any inefficiency for the semiconductor industry. It stimulates circular economy activities and provides economic and environmental benefits.

Vision-guided robot calibration using photogrammetric methods

We propose novel photogrammetry-based robot calibration methods for industrial robots that are guided by cameras or 3D sensors. Compared to state-of-the-art methods, our methods are capable of calibrating the robot kinematics, the hand–eye transformations, and, for camera-guided robots, the interior orientation of the camera simultaneously. Our approach uses a minimal parameterization of the robot kinematics and hand–eye transformations. Furthermore, it uses a camera model that is capable of handling a large range of complex lens distortions that can occur in cameras that are typically used in machine vision applications. To determine the model parameters, geometrically meaningful photogrammetric error measures are used. They are independent of the parameterization of the model and typically result in a higher accuracy. We apply a stochastic model for all parameters (observations and unknowns), which allows us to assess the precision and significance of the calibrated model parameters. To evaluate our methods, we propose novel procedures that are relevant in real-world applications and do not require ground truth values. Experiments on synthetic and real data show that our approach improves the absolute positioning accuracy of industrial robots significantly. By applying our approach to two different uncalibrated UR3e robots, one guided by a camera and one by a 3D sensor, we were able to reduce the RMS evaluation error by approximately 85% for each robot.

Calibrating tumor growth and invasion parameters with spectral spatial analysis of cancer biopsy tissues

The reaction-diffusion equation is widely used in mathematical models of cancer. The calibration of model parameters based on limited clinical data is critical to using reaction-diffusion equation simulations for reliable predictions on a per-patient basis. Here, we focus on cell-level data as routinely available from tissue biopsies used for clinical cancer diagnosis. We analyze the spatial architecture in biopsy tissues stained with multiplex immunofluorescence. We derive a two-point correlation function and the corresponding spatial power spectral distribution. We show that this data-deduced power spectral distribution can fit the power spectrum of the solution of reaction-diffusion equations that can then identify patient-specific tumor growth and invasion rates. This approach allows the measurement of patient-specific critical tumor dynamical properties from routinely available biopsy material at a single snapshot in time.

Development of a high-fidelity digital twin using the discrete element method for a continuous direct compression process. Part 1. Calibration workflow

In this work, a high-fidelity digital twin was developed to support the design and testing of control strategies for drug product manufacturing via direct compression. The high-fidelity digital twin platform was based on typical pharmaceutical equipment, materials, and direct compression continuous processes. The paper describes in detail the material characterization, the Discrete Element Method (DEM) model and the DEM model parameter calibration approach and provides a comparison of the system’s response to the experimental results for stepwise changes in the API concentration at the mixer inlet. A calibration method for a cohesive DEM contact model parameter estimation was introduced. To assure a correct prediction for a wide range of processes, the calibration approach contained four characterization experiments using different stress states and different measurement principles, namely the bulk density test, compression with elastic recovery, the shear cell, and the rotating drum. To demonstrate the sensitivity of the DEM contact parameters to the process response, two powder characterization data sets with different powder flowability were applied. The results showed that the calibration method could differentiate between the different material batches of the same blend and that small-scale material characterization tests could be used to predict the residence time distribution in a continuous manufacturing process.

Energy allocation theory for bacterial growth control in and out of steady state

Efficient allocation of energy resources to key physiological functions allows living organisms to grow and thrive in diverse environments and adapt to a wide range of perturbations. To quantitatively understand how unicellular organisms utilize their energy resources in response to changes in growth environment, we introduce a theory of dynamic energy allocation that describes cellular growth dynamics by partitioning metabolizable energy into key physiological functions: growth, division, cell shape regulation, energy storage and loss through dissipation. By optimizing the energy flux for growth, we develop the equations governing the time evolution of cell morphology and growth rate in diverse environments. The resulting model accurately captures experimentally observed dependencies of bacterial cell size on growth rate, superlinear scaling of metabolic rate with cell size and predicts nutrient-dependent trade-offs between energy expended for growth, division and shape maintenance. By calibrating model parameters with experimental data for the model organism Escherichia coli , our model describes bacterial growth control in dynamic conditions, particularly during nutrient shifts and osmotic shocks. Integrating both the mechanical properties of the cell and underlying biochemical regulation, our model predicts the driving factors behind a wide range of observed morphological and growth phenomena with minimal added complexity.

Maximizing similarity: using correlation coefficients to calibrate kinetic parameters in population balance models

Crystallization plays a crucial role as a separation and purification technique, particularly in the chemical and pharmaceutical industries. By adjusting process parameters, the productivity, product quality, and efficiency of downstream processes can be improved. In complex processes, model-based design becomes invaluable. Population Balance Models (PBMs) have successfully aided the chemical industry in achieving more effective production processes for decades. These models can utilize various input data sources to identify the dominant mechanisms and calibrate model parameters. While inline particle monitoring tools serve as excellent qualitative descriptors, challenges arise from experimentation and data interpretation, hindering their direct application in the kinetic parameter estimation of PBMs. In this study, we present a novel approach that utilizes information from inline particle monitoring tools for the kinetic parameter estimation of PBMs, bypassing the associated obstacles. Our pioneering approach relies on offline product size data and the correlation-based utilization of inline particle monitoring information. The paper compares this novel strategy with two parameter estimation techniques: the classical method using solute concentration and product size data and a somewhat naïve approach, which assumes that the inline particle monitoring data can directly be compared with the simulations. The prediction capabilities are evaluated through two in-silico case studies. The results indicate that the precision and predictive capability of the correlation-based technique are comparable to the classical approach, both for noisy data and for a system undergoing significant agglomeration and deagglomeration. The use of Pearson’s correlation coefficient yields the best results in the novel cases. These findings in in-silico datasets provide a foundation and motivation for the practical application of this idea, unleashing the so-far hidden model development potential of such measurements.

Seismic response of deep soft soil sites with varying shear wave velocities

The variations in seismic response between deep soft soil sites with different shear wave velocities were not fully understood. This study focuses on the seismic response of deep soft soil sites in the lower reaches of the Yangtze River, China. A nonlinear dynamic finite element model was developed for two representative deep soft soil sites with borehole profiles and the shear wave velocity tested by the single borehole method. Two nonlinear cyclic constitutive models are used and thus compared through the site seismic response. To accurately calibrate the nonlinear cyclic model parameters, resonant column tests were conducted on 21 soil samples collected from the two boreholes. The results show that the peak ground acceleration (PGA) under low-frequency (Liuan) input motion was higher for soft soil sites compared to that under medium- and high-frequency (Kobe and Nahanni) input motions. The PGA amplification factor for deep soft soil sites under different input motions can be approximated by an exponential function. The peak ground acceleration tends to be lower as the equivalent shear wave velocity (Vse) decreases. The shapes of the spectral acceleration were similar for the two sites, despite a substantial difference in the Vse between them. Additionally, a crossover point was observed in the spectral acceleration for the two sites. The period corresponding to this crossover point increased with increasing intensity of input motions, indicating that the sites became softer with higher intensity and thus generally exhibited a longer characteristic period of the spectral acceleration. This paper also highlights the significance of selecting nonlinear constitutive models and the precise calibration of model parameters in the seismic response analysis of deep soft soil sites, providing a scientific basis for future similar site analyses.

A novel physics-based computational framework to model spacecraft solar array power under degradation: application to European Space Agency (ESA) Cluster mission

Accurate modeling and simulation (M&S) of spacecraft solar array power under degradation is essential for mission planning, remaining useful life assessment, and lifetime extension. A relevant example is ESA’s Cluster spacecraft fleet, launched in 2000 and operated at the European Space Operation Centre (ESOC), whose solar arrays have suffered severe degradation due to space radiation that has caused challenges to routine operations and mission planning. However, currently available physics-based and machine learning models have been proven ineffective in modeling the drastic reduction in power generation over the long operational life of the spacecraft.In response to these limitations, this work introduces a framework to model solar array degradation and predict power generation. It embeds a novel simplified physics-based model and a meta-heuristic optimization algorithm which exploits domain-specific knowledge and monitoring data for robust model parameter calibration and accurate power generation predictions. The results show the effectiveness of the proposed approach in avoiding overfitting and providing an accurate estimate of Cluster solar array power evolution.

Analysis of Low-Carbon, Energy-Saving, and Emission Reduction Models Based on Rail Transit

It is difficult to define scientific applicability conditions when dealing with different evaluation objects and scope. This article is based on multi-source big data such as the Automatic Fare Collection System (AFC) of urban rail transit, comprehensively considering the multidimensional impact of urban rail transit on the urban transportation system, and conducting a quantitative analysis of the energy-saving and emission reduction effects of urban rail transit. This study adopts a traffic emission model based on specific driving forces and a traffic demand prediction model, coupling the model and data to establish an urban rail transit energy conservation and emission reduction evaluation model suitable for different urban rail transit setting scenarios. Finally, this study selected six districts in Beijing as model application cases and used a combination of RP (display preference) survey and SP (state preference) survey to complete model parameter calibration for application cases.

Nonparametric and Continuous Variable-Based Stratigraphic Modelling from Sparse Boreholes using Signed Distance Function and Bayesian Compressive Sensing

An accurate stochastic interpretation of subsurface stratigraphy with quantified uncertainty can benefit the subsequent risk management of geotechnical infrastructure. Traditional approaches to developing geological cross-sections from sparse boreholes typically require the calibration or definition of empirical model parameters and functions, which may introduce subjectivity and bias. In this study, a non-parametric and continuous variable-based spatial predictor that leverages the signed distance function and Bayesian compressive sensing (BCS) is proposed for subsurface stratigraphic modelling. The proposed method transforms sparse categorical borehole data from a low-dimensional space into continuous variables in a high-dimensional space, enabling a comprehensive representation of more implicit characteristics of intricate geological patterns. This transformation facilitates the use of the continuous-variable-based BCS for non-parametric spatial prediction. The most probable geological cross-section and uncertainty qualification plot are derived after transforming spatially interpreted fields of continuous variables back into soil types. The performance of the proposed method is demonstrated using synthetic and real-world cases. Results indicate that the proposed approach can handle intricate stratigraphic scenarios characterized by complex geological structures, such as crossed-inclined, folded, inclined-folded, and interbedded strata, in a data-driven and non-parametric manner. The advantages of the proposed method over existing spatial predictors for developing geological cross-sections are also demonstrated.

Linking basin-scale hydrology with climatic parameters in western Himalaya: Application of satellite data, temperature index modelling and in-situ observations

Due to limited spatial and temporal in-situ runoff data availability, Himalaya-Karakoram (HK) glaciohydrology has a significant knowledge gap between large-scale and small-scale runoff modelling studies. This study reconstructs longest basin-wide runoff series in Chandra-Bhaga Basin by applying a high-resolution glaciohydrological model SPHY (Spatial Processes in Hydrology) over 1950–2022. Two-tier model calibration is done using in-situ basin-wide runoff (1973–2006) and MODIS snow cover (2003–2018). Model validation is done against in-situ Chhota Shigri Glacier catchment-wide runoff (2010–2015). The modelled mean annual basin-wide runoff is 60.21 ± 6.17 m3/s over 1950–2022, with maximum runoff in summer-monsoon months, peaking in July (182.69 m3/s). Glacier runoff (ice melt + snowmelt over glacier) contributes maximum (39%) followed by equal contributions from snowmelt runoff from non-glacierized basin area and baseflow (25%), while rainfall-runoff contributes minimum (11 %) to total runoff. There is a significant volumetric increase by ∼7% from pre- (59.17 m3/s) to post-2000 (63.47 m3/s) mainly because of early onset of snowmelt post-2000 that resulted in a hydrograph shift by ∼25 days earlier in spring. The glacier runoff is overestimated by 3% from RGI 7.0 inventory compared to different manually delineated inventories over 1950–2022, because of higher glacierized area from RGI 7.0. The precipitation shows a negative trend, but total runoff shows a positive trend due to positive trend of temperature that resulted in more glacier runoff and rainfall-runoff for basin over last 72 years. Basin-wide runoff is mainly governed by summer temperature which directly controls the amount of glacier and snowmelt runoffs and is supported by summer rainfall. This study highlights importance of basin-scale model calibration with in-situ data in large scale studies and stresses the need for in-situ observations in high-altitude Himalayan region. Basin-scale calibrated model parameters are transferable to glacier catchment scale within Chandra-Bhaga Basin, showing the model robustness at a small catchment scale.

Analysis of Granite Deformation and Rupture Law and Evolution of Grain-Based Model Force Chain Network under Anchor Reinforcement

In actual underground rock engineering, to prevent the deformation and damage of the rock mass, rock bolt reinforcement technology is commonly employed to maintain the stability of the surrounding rock. Therefore, studying the anchoring and crack-stopping effect of rock bolts on fractured granite rock mass is essential. It can provide significant reference and support for the design of underground engineering, engineering safety assessment, the theory of rock mechanics, and resource development. In this study, indoor experiments are combined with numerical simulations to explore the impact of fracture dip angles on the mechanical behavior of unanchored and anchored granite samples from both macroscopic and microscopic perspectives. It also investigates the evolution of the anchoring and crack-stopping effect of rock bolts on granite containing fractures with different dip angles. The results show that the load-displacement trends, displacement fields, and debris fields from indoor experiments and numerical simulations are highly similar. Additionally, it was discovered that, in comparison to the unanchored samples, the anchored samples with fractures at various angles all exhibited a higher degree of tensile failure rather than shear failure that propagates diagonally across the samples from the regions around the fracture tips. This finding verifies the effectiveness of the numerical model parameter calibration. At the same time, it was observed that the internal force chain value level in the anchored samples is higher than in the unanchored samples, indicating that the anchored samples possess greater load-bearing capacity. Furthermore, as the angle αs increases, the reinforcing and crack-stopping effects of the rock bolts become increasingly less pronounced.

Failure analysis of Nehbandan granite under various stress states and strain rates using a calibrated Riedel–Hiermaier–Thoma constitutive model

This study presents a comprehensive procedure for determining, calibrating, and validating the Riedel–Hiermaier–Thoma (RHT) material model parameters for granite. The process involves collecting a comprehensive dataset of conventional mechanical tests conducted on various types of granite worldwide. Based on this dataset, one set of RHT material model parameters is determined. Additionally, a specific granite sample from Iran, known as Nehbandan granite, is characterized through physical and mechanical testing to obtain another set of parameters. The challenging task of determining the third set of parameters, which are difficult to obtain analytically and experimentally, is accomplished through a calibration process that iteratively adjusts the parameters based on comparisons between numerical simulation results and experimental data. To validate the determined parameters, a series of tests, including uniaxial compressive strength (UCS), triaxial compressive strength (TCS), Brazilian tensile strength, and dynamic Brazilian using split Hopkinson pressure bar (SHPB) tests, are conducted on the Nehbandan granite. These tests are also simulated using LS-Dyna software, and the numerical simulation results are compared with the corresponding experimental test results. The comparison between the numerical and experimental data serves as a means of validating and verifying the accuracy and reliability of the determined RHT material model parameters for granite. The results demonstrate the successful determination and calibration of the RHT material model parameters for granite. The model exhibits effectiveness in predicting the behavior of granite under various loading conditions. The validation process confirms the accuracy and reliability of the determined parameters through a close agreement between numerical simulations and experimental data. The findings contribute to a better understanding of granite's mechanical response and provide a reliable tool for simulating and predicting its behavior in engineering applications. The validated RHT material model parameters offer a robust framework for accurate numerical simulations, enabling engineers to make informed decisions in rock engineering projects.