A modified back analysis method for deep excavation with multi-objective optimization procedure

Real-time prediction of excavation-induced displacement of retaining pile during the deep excavation process is crucial for construction safety.This paper proposes a modified back analysis method with multi-objective optimization procedure,which enables a real-time prediction of horizontal displacement of retaining pile during construction.As opposed to the traditional stage-by-stage back analysis,time series monitoring data till the current excavation stage are utilized to form a multi-objective function.Then,the multi-objective particle swarm optimization (MOPSO) algorithm is applied for parameter identification.The optimized model parameters are immediately adopted to predict the excavation-induced pile deformation in the continuous construction stages.To achieve efficient parameter optimization and real-time prediction of system behavior,the back propagation neural network (BPNN) is established to substitute the finite element model,which is further implemented together with MOPSO for automatic operation.The proposed approach is applied in the Taihu tunnel excavation project,where the effectiveness of the method is demonstrated via the comparisons with the site monitoring data.The method is reliable with a prediction accuracy of more than 90%.Moreover,different optimization algorithms,including non-dominated sorting genetic algorithm (NSGA-II),Pareto Envelope-based Selection Algorithm II (PESA-II) and MOPSO,are compared,and their influences on the prediction accuracy at different excavation stages are studied.The results show that MOPSO has the best performance for high dimensional optimization task.

Displacement-based back analysis of mitigating the effects of displacement loss in underground engineering

Displacement-monitoring-based back analysis is a popular method for geomechanical parameter estimation.However,due to the delayed installation of multi-point extensometers,the monitoring curve is only a part of the overall one,leading to displacement loss.Besides,the monitoring and construction time on the monitoring curve is difficult to determine.In the literature,the final displacement was selected for the back analysis,which could induce unreliable results.In this paper,a displacement-based back analysis method to mitigate the influence of displacement loss is developed.A robust hybrid optimization algorithm is proposed as a substitute for time-consuming numerical simulation.It integrates the strengths of the nonlinear mapping and prediction capability of the support vector machine(SVM)algorithm,the global searching and optimization characteristics of the optimized particle swarm optimization(OPSO)algorithm,and the nonlinear numerical simulation capability of ABAQUS.To avoid being trapped in the local optimum and to improve the efficiency of optimization,the standard PSO algorithm is improved and is compared with other three algorithms(genetic algorithm(GA),simulated annealing(SA),and standard PSO).The results indicate the superiority of OPSO algorithm.Finally,the hybrid optimization algorithm is applied to an engineering project.The back-analyzed parameters are submitted to numerical analysis,and comparison between the calculated and monitoring displacement curve shows that this hybrid algorithm can offer a reasonable reference for geomechanical parameters estimation.

Rigorous back analysis of shear strength parameters of landslide slip

A rigorous back analysis of shear strength parameters of landslide slip was presented. Kinematical element method was adopted to determine factor of safety and critical failure surface, which overcomes the disadvantage of limit equilibrium method. The theoretical relationship between the combination of shear strength parameters and stability state was studied. The results show that the location of critical slip surface, F/tan f and F/c depend only on the value of c/tan f. The failure surface moves towards the inside of slope as c/tan f increases. According to the information involving factor of safety and critical failure surface in a specific cross-section, strength parameters can be back calculated based on the above findings. Three examples were given for demonstrating the validity of the present method. The shear strength parameters obtained by back analysis are almost consistent with their correct solutions or test results.

Back analysis of general slope under earthquake forces using upper bound theorem

Long time monitoring is acquired to obtain the displacement data for displacement-based geotechnical material back analysis, and these data are hard to be measured under some special condition, such as earthquake. For a simple homogeneous slope, the position of a critical failure surface is determined by value of c/tan ~b. Utilizing upper bound theorem of limit analysis, the external work rate and internal energy for normal slope under earthquake forces are given, and the formula for minimum safety factor is derived. On this basis, the equation of slip surface and the surface depth of a given position are solved. In this way, the strength parameter can be analyzed by known slip surface depth. For practical use, the surface depth for a given slope under varying strength parameter is presented. Finally, two examples are given to show its simplicity and effectiveness.

Back analysis for soil slope based on measuring inclination data

Based on the analysis of several objective functions,a new method was proposed.Firstly,the feature of the inclination curve was analyzed.On this basis,the soil could be divided into several blocks with different displacements and deformations.Then,the method of the soil division was presented,and the characteristic of single soil block was studied.The displacement of the block had two components:sliding and deformation.Moreover,a new objective function was constructed according to the deformation of the soil block.Finally,the sensitivities of the objective functions by traditional method and the new method were calculated,respectively.The result shows that the new objective function is more sensitive to mechanical parameters and the inversion result is close to that obtained by the large direct shear apparatus.So,this method can be used in slope back analysis and its effectiveness is proved.

Probabilistic back analysis for geotechnical engineering based on Bayesian and support vector machine

Geomechanical parameters are complex and uncertain.In order to take this complexity and uncertainty into account,a probabilistic back-analysis method combining the Bayesian probability with the least squares support vector machine(LS-SVM) technique was proposed.The Bayesian probability was used to deal with the uncertainties in the geomechanical parameters,and an LS-SVM was utilized to establish the relationship between the displacement and the geomechanical parameters.The proposed approach was applied to the geomechanical parameter identification in a slope stability case study which was related to the permanent ship lock within the Three Gorges project in China.The results indicate that the proposed method presents the uncertainties in the geomechanical parameters reasonably well,and also improves the understanding that the monitored information is important in real projects.

Intelligent back analysis of geotechnical parameters for time-dependent rock mass surrounding mine openings using grey Verhulst model

In this paper,we present a new method of intelligent back analysis(IBA)using grey Verhulst model(GVM)to identify geotechnical parameters of rock mass surrounding tunnel,and validate it via a test for a main openings of−600 m level in Coal Mine“6.13”,Democratic People's Republic of Korea.The displacement components used for back analysis are the crown settlement and sidewalls convergence monitored at the end of the openings excavation,and the final closures predicted by GVM.The non-linear relation between displacements and back analysis parameters was obtained by artificial neural network(ANN)and Burger-creep viscoplastic(CVISC)model of FLAC3D.Then,the optimal parameters were determined for rock mass surrounding tunnel by genetic algorithm(GA)with both groups of measured displacements at the end of the final excavation and closures predicted by GVM.The maximum absolute error(MAE)and standard deviation(Std)between calculated displacements by numerical simulation with back analysis parameters and in situ ones were less than 6 and 2 mm,respectively.Therefore,it was found that the proposed method could be successfully applied to determining design parameters and stability for tunnels and underground cavities,as well as mine openings and stopes.

A back-propagation neural-network-based displacement back analysis for the identification of the geomechanical parameters of the Yonglang landslide in China

Xigeda formation is a type of hundredmeter-thick lacustrine sediments of being prone to triggering landslides along the trunk channel and tributaries of the upper Yangtze River in China. The Yonglang landslide located near Yonglang Town of Dechang County in Sichuan Province of China, which was a typical Xigeda formation landslide, was stabilized by anti-slide piles. Loading tests on a loading-test pile were conducted to measure the displacements and moments. The uncertainty of the tested geomechanical parameters of the Yonglang landslide over certain ranges would be problematic during the evaluation of the landslide. Thus, uniform design was introduced in the experimental design,and by which, numerical analyses of the loading-test pile were performed using Fast Lagrangian Analysis of Continua(FLAC3D) to acquire a database of the geomechanical parameters of the Yonglang landslide and the corresponding displacements of the loadingtest pile. A three-layer back-propagation neural network was established and trained with the database, and then tested and verified for its accuracy and reliability in numerical simulations. Displacement back analysis was conducted by substituting the displacements of the loading-test pile to the well-trained three-layer back-propagation neural network so as to identify the geomechanical parameters of the Yonglang landslide. The neuralnetwork-based displacement back analysis method with the proposed methodology is verified to be accurate and reliable for the identification of the uncertain geomechanical parameters of landslides.

Numerical and back analysis-based methodology for support design of cut slopes at the Turkish – Georgian Border(NE Turkey)

In this study, geophysical and geotechnical studies were carried out in NE Turkey to evaluate the stability and support design of cut slopes that will be excavated during the construction of a new border control complex. 13 vertical and 3 inclined boreholes were drilled, and 2D electrical resistivity tomography surveys were conducted along 8 profiles to investigate the horizontal and vertical continuity of the geological units. Strength characteristics of all units were determined by laboratory tests. Limit equilibrium(LE) slope stability analyses were conducted on the geological model for static and pseudo-static conditions and factor of safety values as low as 0.227 were determined for post-excavation. Back analysis was conducted for the determination of required support forces on the slopes to achieve a factor of safety of 1.3. A feasible support system consisting of bored piles and rock anchors was designed based on back analysis results for each cut slope. LE analyses were repeated after the implementation of the designed support systems and the lowest factor of safety value increased to 1.35. The utility and safety of the designed support systems were investigated using finite element slope stability analyses and strength reduction factor values higher than 1.3 were determined which means support systems will function as intended and no support failure will occur. Lastly, quick reference charts were created for alluvium and residual soil materials to easily determine the safe slope angle in the future in case no support measures will be applied.

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.

Stochastic back analysis of permeability coefficient using generalized Bayesian method

Owing to the fact that the conventional deterministic back analysis of the permeability coefficient cannot reflect the uncertainties of parameters, including the hydraulic head at the boundary, the permeability coefficient and measured hydraulic head, a stochastic back analysis taking consideration of uncertainties of parameters was performed using the generalized Bayesian method. Based on the stochastic finite element method （SFEM） for a seepage field, the variable metric algorithm and the generalized Bayesian method, formulas for stochastic back analysis of the permeability coefficient were derived. A case study of seepage analysis of a sluice foundation was performed to illustrate the proposed method. The results indicate that, with the generalized Bayesian method that considers the uncertainties of measured hydraulic head, the permeability coefficient and the hydraulic head at the boundary, both the mean and standard deviation of the permeability coefficient can be obtained and the standard deviation is less than that obtained by the conventional Bayesian method. Therefore, the present method is valid and applicable.

ELASTO-PLASTIC BACK ANALYSIS OF FROZEN SOIL WALL

The paper briefly describes the range and methods of the research on the stability of frozen wall. Using the Back Analysis Method combining with the model test of frozen wall, the comprebensive study on the stability of frozen wail is firstly carried out by the authors. Finally, a new viewpoint of adopting limited strain as the major eriteria of stability in frozen soil engineering is proposed.

Failure mechanism and stability analysis of the Zhenggang landslide in Yunnan Province of China using 3D particle flow code simulation

Based on the principle of 3D particle flow code,a numerical landslide run-out model is presented to simulate the failure process of the Zhenggang landslide(in southwestern China) under the effect of water after a rainfall.The relationship between the micro-mechanical parameters and the macro-shear strength of the grain material is determined through numerical calibrations.Then the rainfall effect is considered in numerical simulations and rain-induced sliding processes are performed,which help us to discuss the mechanism of deformation and failure of this landslide together with field observations.It shows the Zhenggang landslide would most likely be activated in Zone I and would gain momentum in Zone II.In order to prevent the potential disaster,a tailing dam is advised to be designed about 175 m downstream from the current landslide boundary of Zone II.Verified by field observations,the presented landslide model can reflect the failure mechanism after rainfall.It can also provide a method to predict the potential disaster and draft disaster prevention measures.

Analysis of sp Pillar Stability Experiment: Continuous thermo-mechanical model development and calibration

The paper describes an analysis of thermo-mechanical （TM） processes appearing during the Aspo Pillar Stability Experiment （APSE）. This analysis is based on finite elements with elasticity, plasticity and dam- age mechanics models of rock behaviour and some least squares calibration techniques. The main aim is to examine the capability of continuous mechanics models to predict brittle damage behaviour of gran- ite rocks. The performed simulations use an in-house finite element software GEM and self-developed experimental continuum damage MATLAB code. The main contributions are twofold. First, it is an inverse analysis, which is used for （1） verification of an initial stress measurement by back analysis of conver- gence measurement during construction of the access tunnel and （2） identification of heat transfer rock mass properties by an inverse method based on the known heat sources and temperature measurements. Second, three different hierarchically built models are used to estimate the pillar damage zones, i.e. elas- tic model with Drucker-Prager strength criterion, elasto-plastic model with the same yield limit and a combination of elasto-plasticity with continuum damage mechanics. The damage mechanics model is also used to simulate uniaxial and triaxial compressive strength tests on the ,Aspo granite.

Analysis of a Failed Port Slope and Stabilization

A nonmetal transportation port with soft soil foundation of Tianjin New Harbor failed during construction in 1997. The soil properties and geological changes before and after landslide were in- vestigated by in situ test means. The stability of the slope was estimated with several calculation methods, such as the simplified Bishop method and the non-circle analysis method. According to the investigation and analysis results, the factors that may cause the slope failure can be deter- mined as follows: excessive excavating, violating the normal construction procedure, excessive pore water pressure during earlier piling and sudden water-level fluctuation in front of the slope. Measures to improve the soil foundation for reconstructing the port include strengthening the failed slope with vibro sand piles, filling up the crushed stone layer, dividing the excavation into four steps and driving piles by larger intervals. The port now has been successfully reconstructed and begun operation.

Numerical scheme for elastoplastic parameter identification and finite element analysis of wall-slope of the Fushun West Open Pit Mine

The elasto brittle plastic finite element analysis has been taken on the prediction for the deformation of the northwall of an open pit of Fushun, China. Numerical simulation has been made on the reinforcement measures of the slope structure. Using parameter identification techniques and connecting with elasto brittle plastic finite element program, the displacement back analysis has been made on the material parameters of the rockslope. The equivalent parameter values of the real slope structure have been obtained. The process of the rapid increment of the slope′s deformation caused by open mining during 1987～1990 has been reappeared through the numerical simulation.

Numerical Simulation of Vacuum Preloading for Chemically Conditioned Municipal Sludge

Municipal sludge is a sedimentation waste produced during the wastewater process in sewage treatment plants.Among recent studies,pilot and field tests showed that chemical conditioning combined with vacuum preloading can effectively treat municipal sludge.To further understand the drainage and consolidation characteristics of the conditioning sludge during vacuum preloading,a large deformation nonlinear numerical simulation model based on the equal strain condition was developed to simulate and analyze the pilot and field tests,whereas the simulation results were not satisfactory.The results of the numerical analysis of the pilot test showed that the predicted consolidation degree was greater than that measured by the field tests,which is attributed to the relatively low permeability layer formed during the preloading process of the prefabricated vertical drain.To better reflect the consolidation process of the conditioned sludge,a simplified analysis method considering the low permeability layer around the prefabricated vertical drain was proposed.The initial permeability coefficient of the low permeability layer is determined via numerical simulations using finite difference method.The predicted settlement curve was in good agreement with the measured results,which indicated that the numerical simulation based on the equal strain condition considering the relatively low permeability layer can better analyze the consolidation process of ferric chloride-conditioning sludge with vacuum preloading.

Application of numerical modeling and genetic programming to estimate rock mass modulus of deformation

Estimation of the rock mass modulus of deformation(Em)is one of the most important design parameters in designing many structures in and on rock.This parameter can be obtained by in situ tests,empirical relations between deformation modulus and rock mass classifcation,and estimating from laboratory tests results.In this paper,a back analysis calculation is performed to present an equation for estimation of the rock mass modulus of deformation using genetic programming(GP)and numerical modeling.A database of 40,960 datasets,including vertical stress(rz),horizontal to vertical stresses ratio(k),Poisson’s ratio(m),radius of circular tunnel(r)and wall displacement of circular tunnel on the horizontal diameter(d)for input parameters and modulus of deformation for output,was established.The selected parameters are easy to determine and rock mass modulus of deformation can be obtained from instrumentation data of any size circular galleries.The resulting RMSE of 0.86 and correlation coeffcient of97%of the proposed equation demonstrated the capability of the computer program(CP)generated by GP.

Updating the models and uncertainty of mechanical parameters for rock tunnels using Bayesian inference

Rock mechanical parameters and their uncertainties are critical to rock stability analysis,engineering design,and safe construction in rock mechanics and engineering.The back analysis is widely adopted in rock engineering to determine the mechanical parameters of the surrounding rock mass,but this does not consider the uncertainty.This problem is addressed here by the proposed approach by developing a system of Bayesian inferences for updating mechanical parameters and their statistical properties using monitored field data,then integrating the monitored data,prior knowledge of geotechnical parameters,and a mechanical model of a rock tunnel using Markov chain Monte Carlo(MCMC)simulation.The proposed approach is illustrated by a circular tunnel with an analytical solution,which was then applied to an experimental tunnel in Goupitan Hydropower Station,China.The mechanical properties and strength parameters of the surrounding rock mass were modeled as random variables.The displacement was predicted with the aid of the parameters updated by Bayesian inferences and agreed closely with monitored displacements.It indicates that Bayesian inferences combined the monitored data into the tunnel model to update its parameters dynamically.Further study indicated that the performance of Bayesian inferences is improved greatly by regularly supplementing field monitoring data.Bayesian inference is a significant and new approach for determining the mechanical parameters of the surrounding rock mass in a tunnel model and contributes to safe construction in rock engineering.

Application and Validation of a Multi-block Constitutive Model at Landslides of the Wenchuan Earthquake

A multi-block model and a corresponding computer program have been developed which predict the kinematics of landslides.Furthermore,a unique event for studying different models simulating the triggering and movement of landslides is the 2008Wenchuan earthquake in the mountainous region in Sichuan Province of China,which caused a large number of rapid landslides.The purpose of the paper is two-fold:(a)to propose and incorporate into the multi-block model constitutive relations predicting soil response along slip surfaces,and(b)to apply the multi-block model with the constitutive relations at landslides triggered by the Wenchuan earthquake.The proposed constitutive equations predict the shape of the shear stress-displacement response measured in ring shear tests.In the application,four landslides caused by the Wenchuan earthquake were considered.Only in one of these landslides the shear resistance-displacement response along the slip surface has been measured in laboratory tests.At this landslide,the triggering and movement of the landslide was predicted.In the other landslides,back analyses were performed and it was observed that the multi-block model predicted reasonably well the final configuration of all slides.In addition,as the measured and back-estimated total friction angle of all landslides was less than 180,and the materials along the slip surface were sandy,it is inferred that some,or all of the slip surface during these slides was sheared in an undrained manner and excess pore pressures generated during sliding played a key role in the triggering and movement of these landslides.Concluding,the paper(A)proposed and validated a multi-block constitutive model which can be applied to predict the triggering and movement of earthquake-induced slides and(B)by analyzing four landslides of the 2008 Wenchuan earthquake,it concludes that some,or all of the slip surface during these slides,was sheared in an undrained manner and excess pore pressures generated during sliding played a key role in the triggering and movement of these landslides.