The paper investigates the possibility of applying the genetic algorithm NSGA-II to optimize a reinforced concrete retaining wall embedded in saturated silty sand. Multi-objective constrained optimization was performed to minimize the cost, while maximizing the overdesign factors (ODF) against sliding, overturning, and soil bearing resistance. For a given change in ground elevation of 5.0 m, the width of the foundation and the embedment depth were optimized. Comparing the algorithm's performance in the cases of two-objective and three objective optimizations showed that the number of objectives significantly affects its convergence rate. It was also found that the verification of the wall against the sliding yields a lower ODF value than verifications against overturning and soil bearing capacity. Because of that, it is possible to exclude them from the definition of optimization problem. The application of the NSGA-II algorithm has been demonstrated to be an effective tool for determining the set of optimal retaining wall designs.
A geotechnical structure’s reliability index calculated using identical input parameters and assumptions can significantly vary as a function of the used method. The different approaches to solving the reliability problem could result in an error which depends on many factors. The most important error sources are the complexity of the performance function, the number of random variables, their mutual correlations, and marginal statistical distributions. A review of relevant literature in the field of reliability in geotechnical engineering revealed a lack of information on the errors of individual reliability methods for geotechnical problems and general criteria for assessing their suitability concerning the error size. The paper defines the reliability method error and proposes criteria for assessing the suitability of reliability methods in geotechnical engineering. Based on the proposed criteria, the suitability of common reliability methods was evaluated in the example of a shallow foundation, analysed according to Eurocode 7, DA 3, such that Ed=Rd. It is shown that due to the mathematically complex expression of the reliability integral, methods that are easier to use result in a larger error and are not suitable for a reliability analysis of shallow foundations. Sophisticated methods are more accurate but require specific knowledge and resources that are not often used in daily engineering practice.
According to the design code Eurocode 7, analysis procedures require reaching a prescribed safety margin, based on the conditions of levelling design action and design resistance. Such semi-probabilistic procedures do not result in a consistent equivalent value of the Overall Factor of Safety (OFS), neither in individual analysis nor in different tasks in geotechnical engineering. Furthermore, the implementation of different calculation approaches in Eurocode 7 also does not guarantee an equal probability of the occurrence of a relevant limit state. A comparative analysis is conducted for an example of a centrically loaded spread foundation on homogenous, isotropic, and coarse-grained soil, according to procedures in Eurocode 7, Design Approach 3. An algorithm is developed to estimate failure probability, taking into consideration the relevant statistical characteristics of each calculation parameter. A significant influence of the statistical characteristics of the relevant sample is emphasized. The degree of required modification of the equivalent Overdesign Factor (ODF) and the Overall Factor of Safety (OFS), based on the criterion of the required reliability index β and failure probability pf , is quantified.
In a beam positioned on a soil bed, counteractive stresses, the determination of the distribution of which is a major concern for solution of the so-called contact problem of a beam on a continuous bed, develop under an external load and the weight of the beam itself. The stress distribution should satisfy equilibrium and compatibility conditions for the beam and the bed beneath it. At the present time, limitations associated with deformations of the system (plain strain, or axisymmetric problem) are assigned to the computational programs most frequently used, implying that the actual width of the beam is not used.Model tests were performed using a three-level concrete basin with various thicknesses of an "artificial soil" serving as the bed for the loaded rectangular beams (Fig. 1).We tested several compositions of a mixture with different contents of components from which the following optimal content with respect to strength was selected: 87% sand, 10% bentonite, 3% cement, and water in an amount of 400 wt. % of the bentonite. The mixture selected was retained in the liquid state in the testing basin for a period of 20 days after mixing (see Fig. 1, c).Immediately prior to testing, i.e., 20 days after the soil had been charged into the basin, specimens were removed for determination of their characteristics.Compressibility characteristics and the average compression modulus M s = 6,500 kN/m 2 were determined from oedometric tests using loaded circular plates 15 and 30 cm in diameter (see Fig. 1, d). The coefficient of cohesion c = 20 kN/m 2 , the angle of internal friction ϕ = 33 o , and the strength of the undrained soil as measured by a vane c u = 140 kN/m 2 . The artificial soil with the composition cited and the method employed for its preparation in the basin can be used for similar model experiments.A steel beam with a length L = 1.5 m, width b = 0.085 m, and height h = 0.050 m was used for the testing. The elastic modulus was determined in accordance with Fig. 2, a, and from the expression for the deflection of a beam on two supports, when a force acts halfway between them The paper describes model tests of a rectangular, transversely loaded flexible beam on an artificially prepared soil of different layers and variable thickness (mixture: sand, bentonite, cement, water). Settlements and bending moments (relative deformations of the beam) were determined along its length. Data relative to the model tests are compared.
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 (). Due to this fact, the replacing of the existing robustness measure with a generalised reliability index () is considered. It was demonstrated that 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.
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