The liquid limit (LL) is considered the most fundamental parameter in soil mechanics for the design and analysis of geotechnical systems. According to the literature, the LL is governed by different particle sizes such as sand content (S), clay content (C), and silt content (M). However, conventional methods do not incorporate the effect of all the influencing factors because traditional methods utilize material passing through a # 40 sieve for LL determination (LL₄₀), which may contain a substantial number of coarse particles. Therefore, recent advancements suggest that the LL must be determined using material passing from a # 200 sieve. However, determining the liquid limit using # 200 sieve material, referred to as LL₂₀₀ in the laboratory, is a time-consuming and difficult task. In this regard, artificial-intelligence-based techniques are considered the most reliable and robust solutions to such issues. Previous studies have adopted experimental routes to determine LL₂₀₀ and no such attempt has been made to propose empirical correlation for LL₂₀₀ determination based on influencing factors such as S, C, M, and LL₄₀. Therefore, this study presents a novel prediction model for the liquid limit based on soil particle sizes smaller than 0.075 mm (# 200 sieve) using gene expression programming (GEP). Laboratory experimental data were utilized to develop a prediction model. The results indicate that the proposed model satisfies all the acceptance requirements of artificial-intelligence-based prediction models in terms of statistical checks such as the correlation coefficient (R²), root-mean-square error (RMSE), mean absolute error (MAE), and relatively squared error (RSE) with minimal error. Sensitivity and parametric studies were also conducted to assess the importance of the individual parameters involved in developing the model. It was observed that LL₄₀ is the most significant parameter, followed by C, M, and S, with sensitivity values of 0.99, 0.93, 0.88, and 0.78, respectively. The model can be utilized in the field with more robustness and has practical applications due to its simple and deterministic nature.

This study presents a cost-based optimization model for the design of isolated foundations in cohesive soils. The optimization algorithm not only incorporates safety requirements in the form of ultimate limit state (ULS) and serviceability limit state (SLS) criteria but also deals with the economics simultaneously. In that regard, the generalized reduced gradient (GRG) method is used for the optimization purpose to achieve the least construction cost of an isolated foundation along with the integration of design parameters as optimization variables. The optimization technique is elaborated using a design example in silty clayey soil and the results of the optimized design are compared with those of the conventional design. The optimization model shows that the optimized design can reduce the construction cost by up to 44% as compared to the conventional design cost for the particular example. Moreover, a sensitivity analysis is also performed to evaluate the quantitative impact of cohesive soil properties, design load, and groundwater table on the construction cost. The results indicate that the construction cost majorly depends on the combined effect of four key parameters: Young’s modulus, recompression index, design load, and groundwater table.

We prove that given a hyperbolic manifold endowed with an auxiliary Riemannian metric whose sectional curvature is negative and whose volume is sufficiently small in comparison to the hyperbolic one, we can always find for any radius at least $1$ a ball in its universal cover whose volume is bigger than the hyperbolic one. This result is deduced from a nonsharp macroscopic version of a conjecture by R. Schoen about scalar curvature, whose proof is a variation of an argument due to M. Gromov and is based on a smoothing technique. We take the opportunity of this work to present a full account of this technique, which involves simplicial volume and deserves to be better known.

In this paper, we prove uniform lower bounds on the volume growth of balls in the universal covers of Riemannian surfaces and graphs. More precisely, there exists a constant 0$"> such that if is a closed hyperbolic surface and another metric on with <!-- MATH $\mathrm {Area}(M,h)\leq \delta \mathrm {Area}(M,hyp)$ --> , then for every radius the universal cover of contains an -ball with area at least the area of an -ball in the hyperbolic plane. This positively answers a question of L. Guth for surfaces. We also prove an analog theorem for graphs.