Robust Geotechnical Design Research Articles

Probability distributions of geotechnical properties for heterogeneous lignite mine spoils

ABSTRACT During surface coal mining, large amounts of overburden waste materials, known as spoils, are excavated and dumped, creating massive heaps. The sustainable management of these areas is a global priority, but a comprehensive geotechnical characterization has not yet been achieved due to limited research on the spoils’ geotechnical properties. This study conducts an advanced statistical analysis of lignite mine spoil materials from a large heap in Greece to determine suitable probability distributions. Five distributions - normal, lognormal, Weibull (2 and 3 parameters), and Gamma - were evaluated, considering the high variability of spoil material properties. The lognormal and Weibull distributions were found to best fit most geotechnical parameters, except for cohesion, which showed an uncommon distribution. In some cases, the normal distribution can be used for a simplified analysis. The findings can guide the analysis of spoil materials, as advanced numerical and stochastic methods are essential for robust geotechnical design.

Reliability-based robust geotechnical design of braced excavations considering multiple failure modes

Reliability design of braced excavation is still a challenge for geotechnical community. Optimization design is a normal method to control the safety and cost of braced excavations. This study presents an advanced reliability-based robust geotechnical design method, which can consider multiple failures and uncertainty of statistical information. A universal design sample was conducted to verify the necessity of considering the uncertainty of statistical information. Ultimate limit state and serviceability limit state of braced excavations were defined, and point estimating method was used to evaluate the standard deviation of failure probabilities. Two-objective and three-objective optimization models were developed to illustrate the application of proposed methods in detail. In addition, the performance of optimization algorithms and further application of multiple-objective models were discussed. The results from this study indicate that the proposed method has a good performance in determining the optimal design with reasonable robustness and cost. New algorithms have higher efficiency in solving nonlinear and multiple-objective optimization problems than the 2nd Non-dominated sorting genetic algorithm. This study can guide the design of retaining systems of braced excavations in clay.

Modified, Reliability-Based Robust Geotechnical Design Method, in Accordance with Eurocode 7

In this paper a modification of the reliability-based robust geotechnical design (RGD) method is proposed. The intention of the proposed modifications is to simplify the method, make it less computationally expensive, and harmonise of the results with Eurocode 7. The complexity of the RGD method mainly stems from the calculation of the design’s robustness measure, which is the feasibility robustness index (ββ). Due to this fact, the replacing of the existing robustness measure with a generalised reliability index (β) is considered. It was demonstrated that β fits into the robustness concept, and is traditionally used as a construction reliability measure, making it intuitive and “user friendly”. It is proposed to conduct a sensitivity analysis using Soboli indices, with the aim of freezing the variables whose contribution to the system response variance is negligible, which will further simplify the method. By changing the robustness measure, the number of the required reliability analyses is significantly decreased. Further reduction is achieved by conducting analyses only for the designs chosen in the scope of the genetic algorithm. The original RGD method is used as an extension of traditional reliability-based design. By applying the proposed modifications, the RGD method can be used as an alternative to the classic and reliability-based design method.

A Robust and Efficient Method of Designing Piles for Landslide Stabilization

ABSTRACT Stabilizing pile is a widely used method to reduce the development of large-scale landslides. Optimizing the pile geometry is a great challenge in the design of stabilizing piles with the purpose of cost-effectiveness, especially for soil strength parameters with large uncertainty. The objective of this study is to propose a robust and efficient method of designing piles for landslide stabilization with the consideration of the safety of slope, uncertainty of soil parameters, and cost of stabilizing piles. A new response surface, which incorporates soil parameters and stabilizing force into a quadratic polynomial function, is first proposed. Unknown coefficients of the quadratic polynomial function are solved with a numerical method at typical sampling points. Based on the solved quadratic polynomial function, the mean and standard deviation of factor of safety (FOS) of the pile-stabilized slope as well as the signal-to-noise factor are then calculated in order to evaluate the design robustness. A framework based on the concept of robust geotechnical design is presented, and its feasibility is illustrated by two cases of soil slopes. The results indicate that the proposed robust geotechnical design method could be used to optimize the design of landslide-stabilizing piles.

Improved robust design of rock wedge slopes with a new robustness measure

This paper presents a new, computationally efficient robustness measure for robust geotechnical design (RGD) faced with a lack of statistics of statistical parameters of variables, based on reliability analysis of the system response. Considering the computational coupling between the new robustness measure and the reliability of the system, the existing framework of the reliability-based RGD approach is simplified. To illustrate the simplified and improved RGD approach, the design of rock wedge slopes is considered herein as an example. For the robust design of rock wedge slopes with combined failure modes, an N-dimensional equivalent method is adopted to ensure the feasibility and accuracy. Taking design robustness and cost efficiency as two objectives, robust design optimization is conducted while the design constraint (safety requirement) is enforced. The robust design optimization yields a set of design solutions rather than a single best solution because of the conflicting relationship between the two objectives. Based on the developed Pareto front, the most preferred designs can be specified. This design approach is illustrated through the design example of a rock wedge slope, and compared with the most preferred designs of reliability-based design (RBD), some suggestions of this robust design approach in geological engineering are presented.

Robust Geotechnical Design for Soil Slopes considering Uncertain Parameters

Designing the geometry of soil slope is an effective treatment for preventing slope failure. How to deal with the uncertainties involved in soil parameters in geotechnical design is a main concern of geotechnical engineers. In this study, a robust geotechnical design for soil slopes (RGDS) approach was proposed, in which the Uncertainty Theory was introduced to describe explicitly the uncertainties involved in soil parameters. The uncertain reliability is often used to describe the risk of slope failure. The design robustness describing the insensitivity between the variation in the system response and the variation of input uncertain soil parameters was evaluated by the signal-to-noise ratio. The objectives of this design are to maximize the design robustness, minimize the excavation cost, and guarantee the safety (maximize the uncertain reliability). Therefore, the RGDS was formulated as a multiobjective optimization, and the optimal design can be determined based on the concepts of Pareto front and knee point. The proposed RGDS approach was illustrated through a numerical case of a two-layer slope design. The numerical results indicate that the RGDS approach is not only more intuitive and easier to follow but also more computationally efficient.

Modified robust geotechnical design approach based on the sensitivity of reliability index

The robust geotechnical design (RGD), which aims to ensure a design that is robust against variations in the input variables, is receiving wider attention and acceptance in the past few years. In this paper, the authors proposed the sensitivity of reliability index (SRI) to evaluate the feasibility robustness of the design, resulting in a modified RGD approach. The performance of the proposed approach was examined by a geotechnical design example, and its advantages are evidenced.

Optimal design of stone columns reinforced soft clay foundation considering design robustness

Stone columns are widely used to treat soft clay ground. Optimizing the design of stone columns based on cost-effectiveness is always an attractive subject in the practice of ground treatment. In this paper, the design of stone columns is optimized using the concept of robust geotechnical design. Standard deviation of failure probability, which is a system response of concern of the stone column-reinforced foundation, is used as a measure of the design robustness due to the uncertainty in the coefficient of variation (COV) of the noise factors in practice. The failure probability of a stone column-reinforced foundation can be readily determined using Monte Carlo simulation (MCS) based on the settlements of the stone column-reinforced foundation, which are evaluated by a deterministic method. A framework based on the concept of robust geotechnical design is proposed for determining the most preferred design of stone columns considering multiple objectives including safety, cost and design robustness. This framework is illustrated with an example, a stone column-reinforced foundation under embankment loading. Based on the outcome of this study, the most preferred design of stone columns is obtained.

Reliability-based robust geotechnical design of spread foundations considering multiple failure modes

This paper presents an update for the reliability-based robust geotechnical design (RGD) method in the design of a soil-foundation system by systematically considering four different potential failure modes including: bearing resistance failure of subsoil, excessive foundation settlement, punching and bending failure of the spread foundation. Given the uncertainties in the critical geotechnical and structural parameters, a comprehensive investigation of the reliability and robustness of the soil-foundation system considering both single failure mode and multiple failure modes were conducted in this study. Moreover, the optimal designs of the soil-foundation system with respect to robustness and cost efficiency are found on the premise of satisfying the safety requirements. The results from this study indicate that both the uncertainties of the geotechnical and structural parameters should be taken into account in the RGD of soil-foundation system considering multiple failure modes. Without properly accounting for the width-to-height ratio of the foundation, increase of the footing geometries and the construction cost will not always lead to a safer and robust design. Besides, bearing resistance failure of subsoil has most significant influence on the reliability and robustness of the soil-foundation system and is identified as the control failure mode.

Response surface-based robust geotechnical design of supported excavation – spreadsheet-based solution

ABSTRACTThe robust geotechnical design (RGD) approach which involves optimization to obtain a design that is safe, cost-efficient, and robust in the face of uncertainties, can be computationally challenging for complex geotechnical structures. In this study, the RGD approach has become practical by introducing a response surface as a surrogate to finite element- or finite difference-based computer code that is used for analyzing the system, and developing a fast algorithm for the optimization process. For demonstration purposes, a real-world supported excavation project is designed using this modified RGD approach and it is compared with the one designed by a local expert.

Reliability-based robust geotechnical design using Monte Carlo simulation

The reliability-based robust geotechnical design (RGD) approach provides an effective tool to deal with the uncertainty in the estimated statistics of geotechnical parameters in a reliability-based design. However, the existing reliability-based RGD approach is not straightforward to apply as it involves multiple concepts. In this paper, the applicability of the existing reliability-based RGD approach is improved by utilizing Monte Carlo simulation (MCS). Here, an MCS-based weighted technique is used to evaluate the failure probability of a geotechnical system. With the aid of this weighted technique, the variation in the failure probability, caused by the uncertainty in the estimated statistics of geotechnical parameters, is computed using MCS. To further improve the efficiency of the RGD method, a series of single-objective optimizations are used in lieu of a multi-objective optimization in the robust design optimization process. The proposed MCS-based RGD approach is illustrated through an example of rock slope design. Compared with the existing reliability-based RGD approach, the MCS-based RGD approach is not only more intuitive and easier to follow, but also more computationally efficient.

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

ABSTRACTThis 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.

R-LRFD: Load and resistance factor design considering robustness

LRFD (Load and Resistance Factor Design) is becoming a design method of choice in geotechnical practice, in lieu of the factor of safety (FS)-based design approach. However, even with LRFD, the need to reduce the variation in the predicted performance of a geotechnical system (or a geotechnical structure), referred to herein as the system response under applied loads, is still apparent. This paper presents a novel approach for applying existing LRFD codes, with explicit consideration of design robustness, safety, and cost efficiency. The recently developed reliability-based robust geotechnical design (RGD) approach is modified such that it can be integrated with the standard LRFD approach. This modified RGD approach is termed R-LRFD, which stands for Robust Load and Resistance Factor Design. In R-LRFD, the robustness of the system response against the variation in uncertain parameters is explicitly considered. Unlike the reliability-based design (RBD), the user is not required to conduct a full statistical characterization of uncertain parameters. With R-LRFD, the gain in the robustness, as reflected by the reduction in the sensitivity of the system response to the recognized but unquantified uncertainty of input parameters, is accompanied by an increase in cost. Thus, the concepts of Pareto front and knee point are introduced to aid in making an informed design decision. Further, a simplified procedure is developed to identify the most preferred design (knee point) in the design space, which is generally solved with multi-objective optimization algorithms. The effectiveness and significance of the proposed R-LRFD approach are demonstrated with two examples: one is the design of drilled shaft in sand (illustrated with a discrete design space) and the other is the design of drilled shaft in clay (illustrated with a continuous design space).

Simplified-robust geotechnical design of soldier pile–anchor tieback shoring system for deep excavation

ABSTRACTThe shoring system that consists of soldier piles and anchor tiebacks is often used in deep excavations in sandy deposits. However, uncertainties often exist in the design of such shoring systems. In this article, a simplified-robust geotechnical design method is proposed to account for these uncertainties in the shoring system design. Specifically, for a given deep excavation, uncertain soil parameters and surcharges are treated as noise factors, and the parameters of soldier piles and tieback anchors are treated as design parameters. Robust design is then implemented as a multiobjective optimization problem, in which the design robustness is sought along with cost efficiency and safety requirements. A trade-off between design robustness and cost efficiency exists and the optimization usually leads to a Pareto front. By applying the knee point concept, the most preferred design that meets the safety requirements and yields the best compromise between design robustness and cost efficiency can be identified on the Pareto front. Improvements made to the existing robust geotechnical design method include an efficient formulation of the design robustness and a new procedure for finding the most preferred design in the design pool. The new simplified-robust geotechnical design method is illustrated with a real-world excavation case study.

Gradient-based design robustness measure for robust geotechnical design

This paper presents a gradient-based robustness measure for robust geotechnical design (RGD) that considers safety, design robustness, and cost efficiency simultaneously. In the context of robust design, a design is deemed robust if the system response of concern is insensitive, to a certain degree, to the variation of noise factors (i.e., uncertain geotechnical parameters, loading parameters, construction variation, and model biases or errors). The key to a robust design is a quantifiable robustness measure with which the robust design optimization can be effectively and efficiently implemented. Based on the developed gradient-based robustness measure, a robust design optimization framework is proposed. In this framework, the design (safety) constraint is analyzed using advanced first-order second-moment (AFOSM) method, considering the variation in the noise factors. The design robustness, in terms of sensitivity index (SI), is evaluated using the normalized gradient of the system response to the noise factors, which can be efficiently computed from the by-product of AFOSM analysis. Within the proposed framework, robust design optimization is performed with two objectives, design robustness and cost efficiency, while the design (safety) constraint is satisfied by meeting a target reliability index. Generally, cost efficiency and design robustness are conflicting objectives and the robust design optimization yields a Pareto front, which reveals a tradeoff between the two objectives. Through an illustrative example of a shallow foundation design, the effectiveness and significance of this new robust design approach is demonstrated.

Efficient Robust Geotechnical Design of Drilled Shafts in Clay Using a Spreadsheet

Abstract This paper presents an efficient robust geotechnical design (RGD) approach that considers performance requirements, design robustness, and cost efficiency simultaneously. In this paper, design robustness is measured via the variation in the performance function of concern that can be evaluated using reliability analysis. Furthermore, the performance requirements of the system are also evaluated using reliability analysis. Thus, the evaluation of design robustness and the evaluation of performance requirements share common computational steps, referred to herein as computational coupling. This coupling for computational efficiency is a significant feature of the proposed RGD approach. Within the framework of the proposed RGD approach, design robustness, cost efficiency, and performance requirements can be considered simultaneously by means of multiobjective optimization. Furthermore, a practical and efficient procedure is developed for such optimization using a feature resident in a popular spread...

Robust design in geotechnical engineering – an update

This paper presents an update for the robust geotechnical design (RGD) methodology, which seeks an optimal design with respect to design robustness and cost efficiency, while satisfying the safety requirements. In general, the design robustness is achieved if the system response is insensitive to the variation in the uncertain input parameters (called “noise factors”). In other words, a design is considered robust if the system response exhibits little variation, even though there is high variation in the input parameters. Robust design achieves this desirable outcome by carefully adjusting ‘design parameters’ (i.e., the parameters that can be controlled by the designer, such as the geometry and dimensions) without reducing the uncertainty in the noise factors. In this paper, the existing RGD methodology is updated with a gradient-based robustness measure and a simplified procedure for seeking the knee point. The RGD methodology and its simplified version (with new updates) are illustrated with three design examples. The results presented in this paper show that the RGD methodology and its simplified version are effective design tools that considers safety, cost and design robustness simultaneously. The advantages of the simplified RGD approach are discussed.

Robust Geotechnical Design of Earth Slopes Using Fuzzy Sets

This paper presents a fuzzy set–based robust geotechnical design (RGD) approach for the design of earth slopes in which uncertain soil parameters are represented as fuzzy sets. For a slope with fuzzy sets as inputs, the stability (factor of safety) of the slope is also a fuzzy set. The failure probability of the slope can readily be determined based on the obtained fuzzy factor of safety; further, the design robustness in terms of the signal-to-noise ratio (SNR) can also be evaluated. The purpose of the RGD is to derive a design that is robust against the uncertainty in the input parameters, with an explicit consideration on safety and cost. Therefore, a multiobjective optimization is performed and a three-dimensional or two-dimensional Pareto front showing a trade-off between objectives can be obtained, which allows for an informed design decision. The effectiveness of the proposed fuzzy set–based RGD approach is demonstrated through an illustrative example.

Robust design of rock slopes with multiple failure modes: modeling uncertainty of estimated parameter statistics with fuzzy number

The variability of shear characteristics of rock discontinuities is often difficult to ascertain. Thus, even with the reliability-based design (RBD) approach, which allows for consideration of the uncertainty of input parameters, the design of a rock slope system may be either cost-inefficient (overdesign) or unsafe (under-design), depending on whether the variation of input parameters is overestimated or underestimated. The uncertainty about the variation of input parameters is a critical issue in a RBD. This paper presents a feasible approach to addressing this problem using robust design concept. First, the uncertainty of the estimated statistics of input parameters (such as rock properties) is represented by fuzzy sets, which requires only the knowledge of lower and upper bounds of the estimated statistics. Then, the robust design concept is implemented to ensure that the final design is insensitive to, or robust against, the uncertainty of the estimated statistics of input parameters. The design methodology is demonstrated with an application to the design of a rock slope system with multiple failure modes. This design methodology, termed robust geotechnical design (RGD), aims to achieve a certain level of design robustness, in addition to meeting safety and cost requirements. In this paper, the RGD framework is realized through a multi-objective optimization, as it involves three requirements, safety, cost, and robustness. The significance of the design methodology is demonstrated with an example of rock slope design.

Robust geotechnical design of braced excavations in clays

In this paper, the authors present a methodology for the robust geotechnical design (RGD) of braced excavations in clayey soils. The maximum wall deflection induced by the excavation was chosen as the response of concern in the design and was computed using a finite element analysis model based upon the beam-on-elastic-foundation theory. The variation of the maximum wall deflection of a given design of a braced excavation due to uncertainty in the soil parameters and the surcharges was used as a measure of the design robustness. The robust design of the braced excavation system (including soil, wall, and support) was then formulated as a multi-objective optimization problem, in which the variation of the maximum wall deflection (a signal of the design robustness) and the cost were optimized with the strict safety constraints. Using a multi-objective genetic algorithm, the optimal designs were then determined, the results of which were presented as a Pareto Front that exhibited a trade-off relationship useful for design decision-making. Furthermore, the “knee point” concept, based upon the “gain-sacrifice” trade-off is used in the selection of the most-preferred design from the Pareto Front. Finally, a design example of a braced excavation system was used to illustrate the significance of this proposed methodology.