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.

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.

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.

Application of Back Analysis on Laterally Loaded Single Pile

In views of the limitations of the existing methods for calculating the pile foundation capacity, a back analysis approach of the m-value is introduced. In order to consider the sensitivity of pile behavior to the m-value,the relationships between the applied horizontal loads at pile head and the corresponding m-value along with the pile stiffness changes are studied. Based on statistics data from the extensive in-situ tests, the back analysis results suggest an exponential expression for the m-value in various soil conditions and horizontal displacements at pile head. This method is capable of providing an accurate m-value in calculating the pile responses under lateral loads.

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.

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.

Stage Predictions of Landslide and Subsidence from an Once-Through Cycle

In this paper both processes of landslide and subsidence are considered to be limited systems. Each of these systems in nature might be regarded as an organism. Generally their lifespan must develop with common ecological characteristics, including several evolutional stages, such as initiation, growth, maturation, decline and death. Among these stages, maturation is emphasized so as to find the occurring or thriving date of both systems. An once-through cycle of both landslide and subsidence is established and is accurately predicted by a developed, mathematic model of the Poisson cycle. The Weibull distribution is cited for a landslide example. Both fundamentals are discussed. Stage predictions of landslide and subsidence are performed for several examples. Back analysis of landslides that have already happened are studied with the same model. And when compared with results from the biological mathematic model and with practical results, it is found that they correspond. Stage prediction of subsidences is also researched by the principle of the Poisson cycle.

Numerical study of the mechanical process of long-distance replacement of the definitive lining in severely damaged highway tunnels

Mountain road tunnels are prone to water leakage and lining corrosion under the complex geological conditions and corrosive envi-ronments,which will reduce the strength of the lining structure until it loses its load-bearing capacity;eventually,the definitive lining will need to be replaced.In this paper,a highway tunnel in a mountainous area in Southwest China is taken as an example.Field investi-gation found that the tunnel was seriously corroded by sulfate,the strength of the definitive lining decreased,and large-scale cracks and spalling appeared on the surface,so the operator decided to replace the definitive lining by the method of interval replacement.Based on the data obtained from drilling and coring,a numerical model of long-distance replacement of the definitive lining of the damaged tunnel is established.First,the back analysis of the calculation parameters is carried out,and the modified calculation results are com-pared with the field monitoring results for verification.Then,the deformation trend of the tunnel and the development of the plastic zone during the process of long-distance replacement of the definitive lining are studied.Finally,the construction scheme is optimized.Numer-ical analysis results show that the replacement of the definitive lining of the tunnel mainly leads to the settlement of the arch crown and the uplift of the inverted arch.The deformation of the tunnel shows two rapid growth stages and two stable stages during the replace-ment process;after replacement,the deformation of the arch crown and the inverted arch is divided into two buffer zones and one stable zone.In the progress of the replacement of the definitive lining,the plastic zone does not change.Regarding the reinforcement measures,with the increase in the grouting range,the grouting efficiency decreases,and the effect of the temporary steel arch on controlling the overall deformation is not obvious.The length of the replacement of the single section should be determined according to the geological conditions of the replacement section and the monitoring data during construction.The research results can provide a reference for sim-ilar projects for the replacement of the definitive lining.

Breaches of the Baige Barrier Lake: Emergency response and dam breach flood

This paper documents the emergency response to the breaches of the Baige Barrier Lake. The lake was successively formed by landslides that occurred on October 10 and November 3, 2018 at the provincial border between Sichuan and Tibet in China. The barrier lake created by the "10.10" landslide breached on October 12 and triggered a flood with a peak discharge around 10000 m^3/s. The residual landslide barrier was enhanced by a second landslide on November 3, resulting in a higher barrier with larger flood potential. An overflow channel was excavated in the crest of the barrier to prompt the breach to be triggered at a lower water level. The second breach happened on November 12 with a measured peak discharge of 31000 m^3/s. Nearly 75000 people were evacuated before the two breaches. In order to prevent the downstream dams from possible over-topping, nearly 3.27×10~8 m^3 of the stored volume was released from the Liyuan reservoir 688 km downstream of Baige Barrier Lake. This paper presents the measured hydrographs and the back-analysis results for the "11.03" barrier lake. It is shown that the modern models of dam breach hydraulics can reasonably reproduce the barrier breach hydrographs;however, further studies are needed to define the key parameters which highly influence the calculated results. Knowledge acquired during the emergency response to the case can be shared with experts working on breaches of embankment dams and can be referenced to promote both the theory study and the engineering practice to mitigate the potential risks caused by this type of catastrophic events.

A REVISED SOLUTION OF EQUIVALENT PERMEABILITY TENSOR FOR DISCONTINUOUS FRACTURES

The equivalent permeability tensor is essential to the application of the equivalent porous media model in the numerical seepage simulation for fractured rock masses. In this paper, a revised solution of the equivalent permeability tensor is proposed to represent the influence of the fracture connectivity in discontinuous fractures. A correction coefficient is involved to reflect the com- plex seepage flow type through the rock bridge. This correction coefficient is back analyzed from single-hole packer tests, based on the Artificial Neural Network （ANN） back analysis and the Finite Element Method （FEM） seepage simulation. The limitation of this back analysis algorithm is that the number of single-hole packer tests should be equal or greater than the number of fracture sets, and three is the maximum number of the fracture sets. The proposed solution and the back analysis algorithm are applied in the permea- bility measurement and the seepage simulation for the Xiaowan arch dam foundation.

Optimal measurement design for parameter identification in mechanized tunneling

When performing shallow tunnel construction,settlements on the ground surface often cannot be prevented.Anticipating these sur-face displacements is only possible with profound knowledge of the constitutive parameters of the surrounding soil.Performing inverse analysis on the basis of in situ settlement data is an effcient method for obtaining such information.However,during this process,con-sidering which measurement arrangement can provide the most reliable results is generally neglected.This aspect is addressed in this study by applying the so-called“optimal experimental design”to the mechanized tunnelingfield.A global sensitivity analysis(GSA)isfirstly performed to determine the most relevant model parameters to be identified via back analysis,by employing the considered numerical model and experimental data.Furthermore,the GSA results are utilized to determine where and when measurements should be performed to minimize uncertainty in the identified constitutive parameters.The optimal experimental design(OED)concept is fur-ther applied to evaluate the observation set-up effciency for damage mitigation measures within a representative synthetic example of a tunneling project passing beneath an existing building.Parameter identification based on synthetic noisy experiments is performed to validate the presented method for optimal experimental design.Thus,the soil stiffness and strength parameters are identified according to both an intuitive and the elaborated method,employing the proposed OED strategy and experimental designs,making it possible to assess the feasibility of the OED results.