A methodology for damage evaluation of underground tunnels subjected to static loading using numerical modeling

We have proposed a methodology to assess the robustness of underground tunnels against potential failure.This involves developing vulnerability functions for various qualities of rock mass and static loading intensities.To account for these variations,we utilized a Monte Carlo Simulation(MCS)technique coupled with the finite difference code FLAC^(3D),to conduct two thousand seven hundred numerical simulations of a horseshoe tunnel located within a rock mass with different geological strength index system(GSIs)and subjected to different states of static loading.To quantify the severity of damage within the rock mass,we selected one stress-based(brittle shear ratio(BSR))and one strain-based failure criterion(plastic damage index(PDI)).Based on these criteria,we then developed fragility curves.Additionally,we used mathematical approximation techniques to produce vulnerability functions that relate the probabilities of various damage states to loading intensities for different quality classes of blocky rock mass.The results indicated that the fragility curves we obtained could accurately depict the evolution of the inner and outer shell damage around the tunnel.Therefore,we have provided engineers with a tool that can predict levels of damages associated with different failure mechanisms based on variations in rock mass quality and in situ stress state.Our method is a numerically developed,multi-variate approach that can aid engineers in making informed decisions about the robustness of underground tunnels.

Progressive fragmentation of granular assemblies within rockslides: Insights from discrete-continuous numerical modeling

Rock fragmentation plays a critical role in rock avalanches,yet conventional approaches such as classical granular flow models or the bonded particle model have limitations in accurately characterizing the progressive disintegration and kinematics of multi-deformable rock blocks during rockslides.The present study proposes a discrete-continuous numerical model,based on a cohesive zone model,to explicitly incorporate the progressive fragmentation and intricate interparticle interactions inherent in rockslides.Breakable rock granular assemblies are released along an inclined plane and flow onto a horizontal plane.The numerical scenarios are established to incorporate variations in slope angle,initial height,friction coefficient,and particle number.The evolutions of fragmentation,kinematic,runout and depositional characteristics are quantitatively analyzed and compared with experimental and field data.A positive linear relationship between the equivalent friction coefficient and the apparent friction coefficient is identified.In general,the granular mass predominantly exhibits characteristics of a dense granular flow,with the Savage number exhibiting a decreasing trend as the volume of mass increases.The process of particle breakage gradually occurs in a bottom-up manner,leading to a significant increase in the angular velocities of the rock blocks with increasing depth.The simulation results reproduce the field observations of inverse grading and source stratigraphy preservation in the deposit.We propose a disintegration index that incorporates factors such as drop height,rock mass volume,and rock strength.Our findings demonstrate a consistent linear relationship between this index and the fragmentation degree in all tested scenarios.

A Hybrid Dung Beetle Optimization Algorithm with Simulated Annealing for the Numerical Modeling of Asymmetric Wave Equations

In the generalized continuum mechanics(GCM)theory framework,asymmetric wave equations encompass the characteristic scale parameters of the medium,accounting for microstructure interactions.This study integrates two theoretical branches of the GCM,the modified couple stress theory(M-CST)and the one-parameter second-strain-gradient theory,to form a novel asymmetric wave equation in a unified framework.Numerical modeling of the asymmetric wave equation in a unified framework accurately describes subsurface structures with vital implications for subsequent seismic wave inversion and imaging endeavors.However,employing finite-difference(FD)methods for numerical modeling may introduce numerical dispersion,adversely affecting the accuracy of numerical modeling.The design of an optimal FD operator is crucial for enhancing the accuracy of numerical modeling and emphasizing the scale effects.Therefore,this study devises a hybrid scheme called the dung beetle optimization(DBO)algorithm with a simulated annealing(SA)algorithm,denoted as the SA-based hybrid DBO(SDBO)algorithm.An FD operator optimization method under the SDBO algorithm was developed and applied to the numerical modeling of asymmetric wave equations in a unified framework.Integrating the DBO and SA algorithms mitigates the risk of convergence to a local extreme.The numerical dispersion outcomes underscore that the proposed SDBO algorithm yields FD operators with precision errors constrained to 0.5‱while encompassing a broader spectrum coverage.This result confirms the efficacy of the SDBO algorithm.Ultimately,the numerical modeling results demonstrate that the new FD method based on the SDBO algorithm effectively suppresses numerical dispersion and enhances the accuracy of elastic wave numerical modeling,thereby accentuating scale effects.This result is significant for extracting wavefield perturbations induced by complex microstructures in the medium and the analysis of scale effects.

Numerical study on settlement of high-fill airports in collapsible loess geomaterials:A case study of Lüliang Airport in Shanxi Province,China

Foundation settlement is of great significance for high-fill engineering in collapsible loess areas.To predict the construction settlement of Lüliang Airport located in Shanxi Province,China,a plane strain finite element method considering the linear variation in the modulus,was carried out in this paper based on the results of geotechnical tests.The stress and deformation of four typical sections caused by layered fill are simulated,and then the settlement of the high-fill airport is calculated and analyzed by inputting three sets of parameters.The relative soft parameters of loess geomaterials produce more settlement than the relatively hard parameters.The thicker the filling body is,the greater the settlement is.The filling body constrained by mountains on both sides produces less settlement than the filling body constrained by a mountain on only one side even the filling thickness is almost the same.The settlement caused by the original subbase accounts for 56%−77%of the total settlement,while the fill soils themselves accounts for 23%−44%of the total settlement,which is approximately consistent with the field monitoring results.It provides a good reference for predicting the settlement of similar high-fill engineering.

Seismic behavior of breakwaters on complex ground by numerical tests:Liquefaction and post liquefaction ground settlements

A large number of breakwaters have been constructed along coasts to protect humans and infrastructures from tsunamis.There is a risk that foundation soils of these structures may liquefy,or partially liquefy during the earthquake preceding a tsunami,which would greatly reduce the structures’capacity to resist the tsunami.It is necessary to consider not only the soil’s liquefaction behavior due to earthquake motions but also its post-liquefaction behavior because this behavior will affect the breakwater’s capacity to resist an incoming tsunami.In this study,numerical tests based on a sophisticated constitutive model and a soil-water coupled finite element method are used to predict the mechanical behavior of breakwaters and the surrounding soils.Two real breakwaters subjected to two different seismic excitations are examined through numerical simulation.The simulation results show that,earthquakes affect not only the immediate behavior of breakwaters and the surrounding soils but also their long-term settlements due to post-earthquake consolidation.A soil profile with thick clayey layers beneath liquefied soil is more vulnerable to tsunami than a soil profile with only sandy layers.Therefore,quantitatively evaluating the seismic behavior of breakwaters and surrounding soils is important for the design of breakwater structures to resist tsunamis.

Evaluation of behaviors of earth and rockfill dams during construction and initial impounding using instrumentation data and numerical modeling

In this study,the behavior of Gavoshan dam was evaluated during construction and the first impounding.A two-dimensional（2D） numerical analysis was conducted based on a finite difference method on the largest cross-section of the dam using the results of instrument measurements and back analysis.These evaluations will be completed in the case that back analysis is carried out in order to control the degree of the accuracy and the level of confidence of the measured behavior since each of the measurements could be controlled by comparing it to the result obtained from the numerical model.Following that,by comparing the results of the numerical analysis with the measured values,it is indicated that there is a proper consistency between these two values.Moreover,it was observed that the dam performance was suitable regarding the induced pore water pressure,the pore water pressure ratio r;,settlement,induced stresses,arching degree,and hydraulic fracturing probability during the construction and initial impounding periods.The results demonstrated that the maximum settlement of the core was 238 cm at the end of construction.In the following 6 years after construction（initial impounding and exploitation period）,the accumulative settlement of the dam was 270 cm.It is clear that 88% of the total settlement of the dam took place during dam construction.The reason is that the clay core was smashed in the wet side,i.e.the optimum moisture content.Whereas the average curving ratio was 0.64 during dam construction; at the end of the initial impounding,the maximum amount of curving ratio in the upstream was 0.81,and the minimum（critical） amount in the downstream was 0.52.It was also concluded that this dam is safe in comparison with the behaviors of other similar dams in the world.

Human Settlement Evaluation in Mountain Areas Based on Remote Sensing,GIS and Ecological Niche Modeling

The Qinghai-Tibet Plateau is the word＇s highest and largest plateau. Due to increasing demands for environment exploration and tourism, a large transitional area is required for altitude adaptation. Hehuang valley, which locates in the transition zone between the Loess Plateau and the Qinghai-Tibet Plateau, has convenient transportation and relatively low elevation. Our question is whether the geographic conditions here are appropriate for adapted stay before going into the Qinghai-Tibet Plateau. Therefore, in this study, we examined the potential use of ecological niche modeling （ENM） for mapping current and potential distribution patterns of human settlements. We chose the Maximum Entropy Method （Maxent）, an ENM which integrates climate, remote sensing and geographical data, to model distributions and assess land suitability for transition areas. After preprocessing and selection, the correlation between variables and spatial auto- correlation input data were removed and 106 occurrence points and 9 environmental layers were determined as the model inputs. The threshold- independent model performance was reasonable according to lO times model running, with the area under the curve （AUC） values being 0.917± 0.01, and 0.923±0.002 for test data. Cohen＇s kappa coefficient of model performance was 0.848. Results showed that 82.22% of the study extent was not suitable for human settlement. Of the remaining areas, highly suitable areas aceounted for 1.19%, moderately for 5.3% and marginally for 11.28%. These suitable areas totaled 418.79 km2, and 86.25% of the sample data was identified in the different gradient of suitable area.The decisive environmental factors were slope and two climate variables： mean diurnal temperature range and temperature seasonality. Our model showed a good performance in mapping and assessing human settlements. This study provides the first predicted potential habitat distribution map for human settlement in Ledu County, which could also help in land use management.

Model-Based Systems Engineering Approach to Design a Human Settlement to Better Serve Displaced People

The challenge of transitioning from temporary humanitarian settlements to more sustainable human settlements is due to a significant increase in the number of forcibly displaced people over recent decades, difficulties in providing social services that meet the required standards, and the prolongation of emergencies. Despite this challenging context, short-term considerations continue to guide their planning and management rather than more integrated, longer-term perspectives, thus preventing viable, sustainable development. Over the years, the design of humanitarian settlements has not been adapted to local contexts and perspectives, nor to the dynamics of urbanization and population growth and data. In addition, the current approach to temporary settlement harms the environment and can strain limited resources. Inefficient land use and ad hoc development models have compounded difficulties and generated new challenges. As a result, living conditions in settlements have deteriorated over the last few decades and continue to pose new challenges. The stakes are such that major shortcomings have emerged along the way, leading to disruption, budget overruns in a context marked by a steady decline in funding. However, some attempts have been made to shift towards more sustainable approaches, but these have mainly focused on vague, sector-oriented themes, failing to consider systematic and integration views. This study is a contribution in addressing these shortcomings by designing a model-driving solution, emphasizing an integrated system conceptualized as a system of systems. This paper proposes a new methodology for designing an integrated and sustainable human settlement model, based on Model-Based Systems Engineering and a Systems Modeling Language to provide valuable insights toward sustainable solutions for displaced populations aligning with the United Nations 2030 agenda for sustainable development.

Finite-difference numerical modeling with even-order accuracy in two-phase anisotropic media

To improve the accuracy of the conventional finite-difference method, finitedifference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of any-order derivatives derived from Taylor series expansion. Then, a finite-difference numerical modeling method with any evenorder accuracy is utilized to simulate seismic wave propagation in two-phase anisotropic media. Results indicate that modeling accuracy improves with the increase of difference accuracy order number. It is essential to find the optimal order number, grid size, and time step to balance modeling precision and computational complexity. Four kinds of waves, static mode in the source point, SV wave cusps, reflection and transmission waves are observed in two-phase anisotropic media through modeling.

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

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

Numerical simulation for settlement urban tunnel construction

The excavation for the municipal tunnel will disturb the soil around the tunnel,and the deformation and subsidence of the earth surface always take place,which may lead to instability and even collapse for the building above the tunnel. At the same time the deformation and subsidence of the earth surface affect the normal use of underground municipal pipelines,and may cause the road sudden collapse,leading to significantly traffic accidents. The authors did a research by simulating for the excavation of municipal tunnel and designed the related supporting plan,and put forward some suggestions and measures for the design and construction of urban tunnel.

3-D discontinuum numerical modeling of subsidence incorporating ore extraction and backfilling operations in an underground iron mine in China

An underground iron mine in China has been used as a case-study to research the subsidence due to ore extraction and backfilling during open stoping operations. A 3-D discontinuum numerical model was built incorporating geologic complexities including faults and interfaces between different lithologies,and the stoping and backfilling sequence adopted from the mine plans. The stoping was carried out in two vertically stacked horizontal layers, with a total of 16 stopes. Large displacements of up to 50 cm were observed along the roof of the stopes, and a maximum surface subsidence of 22.5 cm was observed.Backfilling was found to eliminate subsequent displacements and subsidence. The extraction of the upper orebody was found to influence displacements in the lower orebody. Finally, a subsidence profile was constructed to show the subsidence at all locations along the length of the surface and region of influence on the surface.

Meshing effects of the 3-D FEM numerical modeling in seismo-electromagnetics:An application in selectivity of seismic electric signal (SES)

We investigated how density and quality of mesh around interest domain affect electromagnetic （EM） responses of 3D Earth layered media using finite element method （FEM）. Effect of different mesh shapes was also investigated using a method of mixing structured and unstructured mesh. As a case study, we estimated the effects of meshing on selectivity phenomenon of seismic electric signal （SES）. Our results suggest that the relative errors resulting from mesh effects may not be negligible, which may lead to some unconvincing explanation of the SES selectivity based on the numerical modeling results.

Theory of numerical modeling of constitutive relation for geotechnical materials

Under the direction of the principle of interaction between plastic volumetric and shear strains, the general expression of constitutive relation for geotechnical materials has been derived within the framework of irreversible thermo- dynamics. The constitutive modeling, in fact, is an inverse problem that belongs to the medium inverse problems of model identification, which is expressed as a reversion of coefficient of differential equation. Thus the constitutive modeling of geotechnical materials will become the reversion of coefficient functions of the general expression of constitutive relation, which is carried out in the stress field （p,q） by means Of numerical techniques, so that is called numerical modeling. Applying the numerical modeling, a number of plasticity-based models for clay and sand have been obtained, which are able to characterize the fundamental features of deformation for geotechnieal materials. In addition, the approach of numerical modeling also can be applied to the situation of unsaturated soils by means of the Bishop＇s effective stress formula and Khalili＇s expression of effective stress parameter.

Ground settlement and tunnel response due to twin-curved shield tunnelling in soft ground with small clear distance

Twin curved tunnels are often encountered in shield tunnelling,where significant complexities in densely exploited underground space are observed.In this study,the ground settlement and tunnel deformation due to twin-curved shield tunnelling in soft ground were investigated using numerical simulation and field monitoring.Different curvature radii of twin curved tunnels and subsequent effects of tunnel construction were considered to reveal the tunnelling effect on ground surface settlement and tunnel deformation.The results show that the settlement trough yields one offset towards inside of curved shield tunnelling.The location of settlement trough and maximum settlement were affected by curvature radius but except for the shape and width of settlement trough.Adjacent parallel twin-curved shield tunnelling could increase the offset of existing settlement trough and maximum settlement.Then,an empirical prediction of surface settlement trough due to twin-curved shield tunnelling with same tunnel diameters in soft clay was proposed,which was applicable to curvature radius less than 800 m.Finally,a minimum radius of 600 m of curvature tunnel was proposed in terms of allowable convergence deformation of tunnel.The result could provide guidance on safety evaluation for twin curved shield tunnelling construction.

An efficient physics-guided Bayesian framework for predicting ground settlement profile during excavations in clay

Recently,the application of Bayesian updating to predict excavation-induced deformation has proven successful and improved prediction accuracy significantly.However,updating the ground settlement profile,which is crucial for determining potential damage to nearby infrastructures,has received limited attention.To address this,this paper proposes a physics-guided simplified model combined with a Bayesian updating framework to accurately predict the ground settlement profile.The advantage of this model is that it eliminates the need for complex finite element modeling and makes the updating framework user-friendly.Furthermore,the model is physically interpretable,which can provide valuable references for construction adjustments.The effectiveness of the proposed method is demonstrated through two field case studies,showing that it can yield satisfactory predictions for the settlement profile.

A Heavy Sea Fog Event over the Yellow Sea in March 2005: Analysis and Numerical Modeling

In this paper, a heavy sea fog episode that occurred over the Yellow Sea on 9 March 2005 is investigated. The sea fog patch, with a spatial scale of several hundred kilometers at its mature stage, reduced visibility along the Shandong Peninsula coast to 100 m or much less at some sites. Satellite images, surface observations and soundings at islands and coasts, and analyses from the Japan Meteorology Agency （JMA） axe used to describe and analyze this event. The analysis indicates that this sea fog can be categorized as advection cooling fog. The main features of this sea fog including fog area and its movement axe reasonably reproduced by the Fifth-generation Pennsylvania State University/National Center for Atmospheric Research Mesoscale Model （MM5）. Model results suggest that the formation and evolution of this event can be outlined as： （1） southerly warm/moist advection of low-level air resulted in a strong sea-surface-based inversion with a thickness of about 600 m; （2） when the inversion moved from the warmer East Sea to the colder Yellow Sea, a thermal internal boundary layer （TIBL） gradually formed at the base of the inversion while the sea fog grew in response to cooling and moistening by turbulence mixing; （3） the sea fog developed as the TIBL moved northward and （4） strong northerly cold and dry wind destroyed the TIBL and dissipated the sea fog. The principal findings of this study axe that sea fog forms in response to relatively persistent southerly waxm/moist wind and a cold sea surface, and that turbulence mixing by wind shear is the primary mechanism for the cooling and moistening the marine layer. In addition, the study of sensitivity experiments indicates that deterministic numerical modeling offers a promising approach to the prediction of sea fog over the Yellow Sea but it may be more efficient to consider ensemble numerical modeling because of the extreme sensitivity to model input.

State Key Lab of Numerical Modeling for Atmospheric Science and Geophysical Fluid Dynamics

The State Key Laboratory of Numerical Modeling for Atmospheric Science and Geophysical Fluid Dynamics (LASG) was set up as early as in 1985. It has been appraised as an Excellent State Key Lab in each of the three national assessments organized by State Economic Planning Commission, National Natural Science Foundation (NSFC) and the Ministry of Science and Technology (MOST) in 1991, 1996 and 2000, respectively.

Voyage of the Indian subcontinent since Pangea breakup and driving force of supercontinent cycles: Insights on dynamics from numerical modeling

Recent advances in three-dimensional numerical simulations of mantle convection have aided in approximately reproducing continental movement since the Pangea breakup at 200 Ma. These have also led to a better understanding of the thermal and mechanical coupling between mantle convection and surface plate motion and predictions of the configuration of the next supercontinent. The simulations of mantle convection from 200 Ma to the present reveals that the development of large-scale cold mantle downwellings in the North Tethys Ocean at the earlier stage of the Pangea breakup triggered the northward movement of the Indian subcontinent. The model of high temperature anomaly region beneath Pangea resulting from the thermal insulation effect support the breakup of Pangea in the real Earth time scale, as also suggested in previous geological and geodynamic models. However, considering the low radioactive heat generation rate of the depleted upper mantle, the high temperature anomaly region might have been generated by upwelling plumes with contribution of deep subducted TTG(tonalite-trondhjemite-granite) materials enriched in radiogenic elements. Integrating the numerical results of mantle convection from 200 Ma to the present, and from the present to the future, it is considered that the mantle drag force acting on the base of continents may be comparable to the slab pull force, which implies that convection in the shallower part of the mantle is strongly coupled with surface plate motion.

Evaluation of the effect of geometrical parameters on stope probability of failure in the open stoping method using numerical modeling

Stress-induced failure is among the most common causes of instability in Canadian deep underground mines.Open stoping is the most widely practiced underground excavation method in these mines,and creates large stopes which are subjected to stress-induced failure.The probability of failure(POF)depends on many factors,of which the geometry of an open stope is especially important.In this study,a methodology is proposed to assess the effect of stope geometrical parameters on the POF,using numerical modelling.Different ranges for each input parameter are defined according to previous surveys on open stope geometry in a number of Canadian underground mines.A Monte-Carlo simulation technique is combined with the finite difference code FLAC3D,to generate model realizations containing stopes with different geometrical features.The probability of failure(POF)for different categories of stope geometry,is calculated by considering two modes of failure;relaxation-related gravity driven(tensile)failure and rock mass brittle failure.The individual and interactive effects of stope geometrical parameters on the POF,are analyzed using a general multi-level factorial design.Finally,mathematical optimization techniques are employed to estimate the most stable stope conditions,by determining the optimal ranges for each stope’s geometrical parameter.