Limit equilibrium method based on an approximate lower bound method with a variable factor of safety that can consider residual strength

In this paper, the factor of safety for a prescribed slip surface will be determined from an equivalent lower bound method (extremum principle), which can satisfy all equilibrium conditions without an interslice force function. This approach will give an overall factor of safety close to that from the classical methods for normal problems, while the thrust line, the local factor of safety for individual slice/block and the progressive yielding phenomenon can be estimated, which will be useful for some special cases. The force and moment equilibrium of every slice will be satisfied, while the location of the thrust line will always be acceptable in the present formulation. To solve the difficult optimisation problem, an innovative coupled particle swarm/harmony search algorithm is proposed in this paper, and a practical engineering problem for which the factor of safety is close to 1.0 is used to illustrate the consideration of the residual strength in the limit equilibrium slope stability analysis.     

Optimisation of pile groups

The optimisation of pile groups is studied using an optimisation technique in conjunction with a discrete element method for pile group settlement analysis. It is demonstrated that it is possible to optimise the performance of pile groups by minimising the load differentials between piles and/or differential settlements. This could be achieved by apportioning the lengths of the group piles to meet the requirement of their positions in the group. Numerical examples are presented to illustrate this principle.     

Upper bound limit analysis of cohesive soils using mesh-free method

A mesh-free based limit analysis approach is proposed, to determine the upper bound solutions for the collapse loads associated with cohesive soils, under plane strain conditions. In the presented technique, the geometry of problem is just simulated by nodes and there is no need of mesh in the traditional sense. The process of finding an upper bound solution consists of combining limit analysis theory and a mesh-free numerical technique as a discretisation tool. To satisfy the required conditions for the admissibility of the discretised velocity field at the entire problem domain, a strain rate smoothing technique has been adopted. The outcome of proposed combination is a nonlinear optimisation problem which is solved by a direct iterative technique. The solution found by an iterative algorithm is an upper bound for limit load of the stability problem. The efficiency of the proposed method is demonstrated by solving different example problems in the soil mechanics engineering field, at the end of the paper.     

Robust optimisation of CO2 sequestration strategies under geological uncertainty using adaptive sparse grid surrogates

Geologic CO₂ sequestration in deep saline aquifers is a promising technique to mitigate the effect of greenhouse gas emissions. Designing optimal CO₂ injection strategy becomes a challenging problem in the presence of geological uncertainty. We propose a surrogate assisted optimisation technique for robust optimisation of CO₂ injection strategies. The surrogate is built using Adaptive Sparse Grid Interpolation (ASGI) to accelerate the optimisation of CO₂ injection rates. The surrogate model is adaptively built with different numbers of evaluation points (simulation runs) in different dimensions to allow automatic refinement in the dimension where added resolution is needed. This technique is referred to as dimensional adaptivity and provides a good balance between the accuracy of the surrogate model and the number of simulation runs to save computational costs. For a robust design, we propose a utility function which comprises the statistical moment of the objective function. Numerical testing of the proposed approach applied to benchmark functions and reservoir models shows the efficiency of the method for the robust optimisation of CO₂ injection strategies under geological uncertainty.     

The optimisation of flotation networks

The generalised optimisation of a flotation network is studied by means of using variable connections (structural parameters) and variable enhancement factors which are used instead of a flotation model to describe the separation process. The enhancement factors are functions of variables affecting the flotation process. These functional relationship may be derived by means of using a flotation model. Bounds are placed on the enhancement factors by means of either using a flotation model or by inspection of existing pilot or commercial plant data. These bounds, together with external, system and mass balance constraints and an appropriate objective function, define the general optimisation problem for a flotation network.The optimisation problem above may be solved by non-linear programming methods, however, it is easily transformable into a Linear Programme which is easy to solve. The procedure has been applied to a flotation circuit comprising three banks of cells for which an optimal set of connections and enhancement factors has been computed for varying constraints.A simulation procedure based on a gamma flotation model has been applied to one of the optimal circuits so as to compute the flotation variables.     

Improved group decision-making evaluation method of offshore pipeline routing optimisation in submarine landslide-prone area

Submarine landslides are a great hazard to offshore pipelines. The comparison and optimisation of pipeline routing schemes to reduce the potential submarine landslide risk is a key issue in offshore oil and gas development engineering. This paper presents an improved group decision-making evaluation method for offshore pipeline routing optimisation in areas prone to submarine landslides. An information integrity variable is proposed to adjust the relative weight of each factor considering the incompleteness of the engineering geological survey information and data. The credibility level of each expert involved in the evaluation, which is calculated based on the similarity and difference of the experts’ judgment matrices, is introduced to correct the information integrity variable, relative weights, and memberships. The group decision-making for offshore pipeline routing selection is then obtained based on the principle of the majority rule. Finally, a case of pipeline routing optimisation in the submarine canyon area of the Baiyun depression, northern South China Sea, is assessed by using the proposed method. The result shows that the proposed group decision-making method can enhance the objectivity of the assessment for the offshore pipeline routing optimisation under a subjective environment.

     

Strategy for consistent model parameter calibration for soft soils using multi-objective optimisation

Constitutive models for soft soils require a large number of parameters to model the complex material response. One set of parameters should capture the soil response for various laboratory & in situ stress paths. This requires a new method to calibrate a consistent set of model parameters using test data from different load paths of classic geomechanical tests. The feasibility of the proposed method is demonstrated with the recently developed CREEP-SCLAY1S model. After a sensitivity analysis that highlights the model parameters for optimisation, an optimisation process for two different configurations is designed. The latter is successfully verified against artificially generated laboratory data.     

Simplified procedure for reliability-based robust geotechnical design of drilled shafts in clay using spreadsheet

This paper provides a simplified procedure for reliability-based robust geotechnical design (RGD) using spreadsheet. In the RGD methodology, design robustness is achieved by adjusting “design parameters” without reducing the uncertainties in noise factors. This design approach generally involves a multi-objective optimisation, which is computationally challenging. To improve the efficiency of the RGD methodology, the design robustness is evaluated in terms of sensitivity index and the safety requirement is evaluated using mean value first order second moment (MFOSM). To ease the concern that the reliability index obtained with MFOSM may not be sufficiently accurate, a mapping function that relates MFOSM to a more accurate method such as first order reliability method is introduced. To further improve the efficiency of the proposed simplified RGD method, a new simplified procedure along with a more accurate robustness measure is developed that eliminates the need for multi-objective optimisation. With these modifications, the proposed simplified RGD method can efficiently be implemented in a single Excel spreadsheet. The proposed simplified method, which goes beyond any existing reliability-based RGD methods in terms of ease of use and computational efficiency, is illustrated in this paper with an example of robust design of drilled shaft in clay.     

Calibration of an elasto-plastic constitutive model by a constrained optimisation procedure

The presented paper deals with a constrained optimisation technique for the calibration of elasto-plastic model parameters in a rational and objective manner. The procedure consists in finding a set of model parameters which minimise the difference between the experimental data and the numerical simulations defined by an objective function. For this purpose, an optimisation routine, termed ParaID, has been developed which combines the quasi-Newton and stochastic methods. The optimisation technique was employed to calibrate a multi-mechanism elasto-plastic constitutive model. Using the results of three isotropically consolidated drained triaxial compression tests, a comparison between numerical and experimental results clearly shows the capability of the optimisation procedure to determine the model parameters correctly.     

Shape optimisation of the support section of a tunnel at great depths

The shape optimisation of a cavity is typically performed without considering the previous support, which may significantly reduce the practical significance of such analyses. Even when an excavation section is optimised, failure of the surrounding rock in a tunnel cannot be prevented in the presence of excessive in situ stress. Thus, a support should be established to protect the stability of a tunnel from the failure of the surrounding rock. This study examines the optimal shape of the support that satisfies the optimisation criterion, which minimises the largest tangential stress along the inner edge of the support, for a specific net tunnel size and support strength. The optimisation process is to solve a series of forward problems using the conformal mapping method for a plane elasticity complex function. The tangential stress along the inner edge of the support is selected as the objective function, and the coefficients of the mapping function are considered as the design variables. The minimum value of the objective function is calculated based on the mixed penalty function method and the optimal support shape that satisfies the given constraints can be obtained. The stress state of an optimally shaped tunnel support is significantly improved compared to non-optimal configurations, and the stress concentration along the inner edge of the support is minimised.     

Towards an integrated arid zone water management using simulation-based optimisation

For ensuring both optimal sustainable water resources management and long-term planning in a changing arid environment, we propose an integrated Assessment-, Prognoses-, Planning- and Management tool (APPM). The new APPM integrates the complex interactions of the strongly nonlinear meteorological, hydrological and agricultural phenomena, considering the socio-economic aspects. It aims at achieving best possible solutions for water allocation, groundwater storage and withdrawals including saline water management together with a substantial increase of the water use efficiency employing novel optimisation strategies for irrigation control and scheduling. To obtain a robust and fast operation of the water management system, it unites process modeling with artificial intelligence tools and evolutionary optimisation techniques for managing both water quality and quantity. We demonstrate some key components of our methodology by an exemplary application to the south Al-Batinah region in the Sultanate of Oman which is affected by saltwater intrusion into a coastal aquifer due to excessive groundwater withdrawal for irrigated agriculture. We show the effectiveness and functionality of a new simulation-based water management system for the optimisation and evaluation of different irrigation practices, crop pattern and resulting abstraction scenarios. The results of several optimisation runs indicate that due to contradicting objectives, such as profit-oriented agriculture versus aquifer sustainability only a multi-objective optimisation can provide sustainable solutions for the management of the water resources in respect of the environment as well as the socio-economic development.     

Permissible range of model parameters for natural fine-grained materials

This paper presents a three-dimensional constitutive model for natural clay that includes creep, anisotropy and structure, as well as a theoretical means to estimate the range for anisotropy- and structure-related parameters, as needed for parameter optimisation. Creep-SCLAY1S is an extension of the Creep-SCLAY1 model proposed by Sivasithamparam et al. (Comput Geotech 69:46–57, 2015) which includes the effects of bonding and destructuration. The model needs 14 model parameters, of which five are similar to those used in the modified Cam–Clay model. A method is developed to quantify the range for the three parameters related to structure and anisotropy that cannot be derived directly from experimental data. The theoretically derived range compares favourably with the values found in the literature. As a result, the model now can be used with more confidence, enabling sensitivity analysis and systematic parameter derivation with optimisation techniques.     

考虑孔隙水压力及非线性Mohr-Coulomb破坏准则下浅埋土质隧道三维塌落机制的上限分析

浅埋土质隧道的稳定性研究一直是隧道工程的关键问题,而孔隙水压力的存在影响着浅埋土质隧道的安全。构建了隧道顶部为圆弧形的浅埋土质隧道的三维塌落机制,基于非线性Mohr-Coulomb破坏准则和极限分析上限法,并考虑孔隙水压力的作用,推导出浅埋土质隧道的塌落范围及支护力的最优上限解计算公式。通过与既有研究进行对比,验证了所提方法的合理性。分析了不同参数对塌落范围、塌落土体的重力及支护力的影响,结果表明：孔隙水压力对浅埋土质隧道的塌落范围、塌落土体的重力及支护力有着显著的影响;孔隙水压力对塌落范围、塌落土体重力的影响比较复杂,而支护力都随着孔隙水压力系数的增大而增大;不同参数对浅埋土质隧道的塌落范围、塌落土体的重力及支护力的影响规律不同。新方法可为浅埋土质隧道的设计优化提供理论支撑。     

Multimodal reliability analysis of 3D slopes with a genetic algorithm

Acta Geotechnica - This paper presents a genetic algorithm (GA) to solve the multimodal optimisation problem resulting from 3D slopes prone to multiple regions of failure. A probabilistic approach...     

Automatic calibration of soil–water characteristic curves using genetic algorithms

An automatic technique for the determination of the coefficients of models for soil–water characteristic curves (SWCC) or water retention curves (WRC) is presented. The technique is based on optimisation using genetic algorithms, in which the error between predictions and experimental data is minimised by varying the model parameters. The method is powerful and reasonably efficient in finding the best parameters. Four models are analysed including one accounting for hysteresis behaviour. Details of a simple genetic algorithm (SGA) and its complete application are explained. To account for the hysteresis of the SWCC, the models are programmed in a rate form, in which numerical integration is employed to advance the state variables. One advantage of the optimisation presented is that the best curves averaging both the drying and wetting paths are obtained when hysteresis is present.     

Determination of Discontinuity Size Distributions from Scanline Data

Summary The paper outlines a new method for estimating the distribution form, and mean size, of discontinuities from scanline data. By assuming that the discontinuities are circular discs it has been possible to apply existing solutions for the distributions of censored semi-trace lengths sampled by a scanline at an exposed rock face. These solutions have been implemented by numerical quadrature in a standard Excel spreadsheet, with solution optimisation achieved with Solver. Problems caused by a singularity in the integration were overcome by applying an integration offset parameter. A trigonometrical substitution for removing this singularity is also outlined. The numerical quadrature strategy was validated by comparison with the analytical solution for the uniform distribution, and by comparison with the results of an extensive geometrical simulation of the stereological process. A new distribution, here named the Wicksell distribution, has been identified. This distribution is characterised by the fact that the distribution of disc diameters and the distribution of complete traces on a cutting plane are identical. Two examples, based on real scanline data, are presented to illustrate the practical application of the new methods.     

Using CRD method for quantification of groundwater recharge in the Gaza Strip, Palestine

Rainfall is the main source of groundwater recharge in the Gaza Strip area in Palestine. The area is located in the semi-arid zone and there is no source of recharge other than rainfall. Estimation of groundwater recharge from rainfall is not an easy task since it depends on many uncertain parameters. The cumulative rainfall departure (CRD) method, which depends on the water balance principle, was used in this study to estimate the net groundwater recharge from rainfall. This method does not require much data as is the case with other classical recharge estimation methods. The CRD method was carried out using optimisation approach to minimise the root mean square error (RMSE) between the measured and the simulated groundwater head. The results of this method were compared with the results of other recharge estimation methods from literature. It was found that the results of the CRD method are very close to the results of the other methods, but with less data requirements and greater ease of application. Based on the CRD method, the annual amount of groundwater recharge from rainfall in the Gaza Strip is about 43 million m³. An erratum to this article can be found at     

The use of the simple genetic algorithm in finding the critical factor of safety in slope stability analysis

A simple genetic algorithm (SGA) is applied to the search for the minimum factor of safety in slope stability analysis. The method is shown to be superior to simple optimisation routines, which can find false minima, and to ‘brute force’ approaches, which require the analysis of a very large number of possibilities. An approach to implementing SGA is defined and refined, indicating principles which may be used in applying the method to other engineering problems.     

Optimisation of deep mixing technique by artificial neural network based on laboratory and field experiments

ABSTRACT

Ground improvement techniques are inevitable for weak soils that cannot endure the design load imposed by superstructures. Deep mixing technique (DMT) as one of these methods is promising and effective when a deep soil layer with low bearing capacity is encountered. Such deposits are quite common in the South-west of Iran where the studied site is located. In order to validate the influence of DMT on the enhancement of strength, both in-situ and laboratory tests were conducted. Afterwards, a parametric study was carried out to investigate the influence of key factors including cement content, water–cement ratio, curing time and plasticity index (PI) on the performance of DMT. In summary, a total of 192 different conditions were examined in this study by using two methods of 3D plotting and artificial neural networks (ANNs) as the optimisation tool. Results proved the importance of water–cement ratio as a key parameter in DMT. Based on the trained networks, ANN was revealed to give satisfactory predictions on the strength of an improved soil with different admixture conditions. More important, the optimisation made by ANN could determine the specific values for selected key admixture factors to reach a desired strength level with the coefficient of determination higher than 0.85.