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Improvement of the Approximate Method for Determining the Average Vertical Stress Increase Below the rectangular foundation Using Differential Evolution Algorithm

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ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2025年 1-20页

作者： Dagdeviren, Ugur Kutahya Dumlupinar Univ Fac Engn Dept Civil Engn Kutahya Turkiye

External loads transferred from the structure's foundations to the soil induce stress increases in the soil stratum. Since stress increases within the soil mass vary with depth and across the plane at a given depth, approaches that estimate the average stress increase under foundations can be advantageous for effective foundation design. This study aims to develop optimization-based approximate methods for calculating average vertical stress increases with higher accuracy than the conventional 2V:1H method for rectangular foundations with different L/B ratios. For this purpose, vertical stress increases within the foundation projection at 120 different depths for 12 different L/B ratios were numerically calculated using Boussinesq's stress expressions. The model parameters of the proposed approximate models, such as expansion slopes (k or k1, k2) and normalized critical depth (zcr/B), for each L/B ratio were optimized using the differential evolution algorithm. The proposed three-parameter approximate method achieved the highest accuracy, reducing the RMSE values by an average of 53% compared to the conventional method, while the one-parameter model reduced the RMSE by 9%. The maximum absolute errors in the three-parameter model remained between 0.0217 and 0.0283, with R2 values greater than 0.9972. Building upon and improving the conventional method, this study presents a practical and novel three-parameter method that provides a more reliable and accurate estimation of the average vertical stress increase under flexible rectangular foundations, significantly reducing errors. This study contributes to geotechnical engineering by improving the accuracy of stress increase prediction models, potentially leading to more economical and safer foundation designs.

关键词： Vertical stress increase Influence factor rectangular foundation Approximate method Differential evolution algorithm

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Settlement and tilting of a rigid rectangular foundation on a compressible foundation bed of finite thickness

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Soil Mechanics and foundation Engineering 1976年第4期13卷 270-275页

作者： Urisman, V.S.

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Algorithm and program for design of rectangular foundation slabs under a group of columns

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Soil Mechanics and foundation Engineering 1971年第5期8卷 347-351页

作者： Gorlov, A.M. Rogov, Yu.A.

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Ultimate bearing capacity of rectangular foundation on geogrid-reinforced sand under eccentric load

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INTERNATIONAL JOURNAL OF GEOTECHNICAL ENGINEERING 2016年第1期10卷 52-56页

作者： Sahu, R. Patra, C. R. Das, B. M. Sivakugan, N. Natl Inst Technol Rourkela Rourkela India James Cook Univ Townsville Qld 4811 Australia Calif State Univ Sacramento Sacramento CA 95819 USA

Laboratory model test results for the ultimate bearing capacity of rectangular surface foundations supported by multi-layered geogrid reinforcement and subjected to eccentric loading have been presented. Based on the model test results a reduction factor has been developed, which is a function of width-to-length ratio (B/L), eccentricity ratio (e/B), and reinforcement depth ratio (d/B) of the foundation. The reduction factor can be used to estimate the ultimate bearing capacity of an eccentrically loaded foundation from the ultimate bearing capacity of a vertically loaded foundation.

关键词： Bearing capacity Eccentric loading Geogrid-reinforcement Model test rectangular foundation Sand

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Forced vertical and horizontal movements of a rectangular rigid foundation on a transversely isotropic half-space

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INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS 2013年第14期37卷 2301-2320页

作者： Eskandari-Ghadi, Morteza Ardeshir-Behrestaghi, Azizollah Pak, Ronald Y. S. Karimi, Mostafa Momeni-Badeleh, Masoud Univ Tehran Dept Engn Sci Coll Engn Tehran Iran Mazandaran Univ Sci & Technol Dept Civil Engn Babol Sar Iran Univ Colorado Dept Civil Environm & Architectural Engn Boulder CO 80309 USA

An analytical investigation of a half-space containing transversely isotropic material under forced vertical and horizontal displacements applied on a rectangular rigid foundation is presented in this paper. With the goal of a rigorous solution to the shape- and rigidity- induced singular mixed boundary value problem, the formulation employs scalar potential representation, the Fourier expansion and the Hankel integral transforms method to obtain the surface arbitrary point-load solution in cylindrical coordinate system. The obtained Green's functions are rewritten in rectangular coordinate system, allowing the response of the half-space because of an arbitrary distributed load on a rectangular surface area be given in terms of a double integral. The numerical evaluations of stresses are done with the use of an element, which is singular at the edge and the corner of the rectangle. Upon the imposition of the rigidity displacement boundary condition for a rigid foundation and the use of a set of two-dimensional adaptive-gradient elements, which can capture the singular behavior in the contact stress effectively, a set of new numerical results are presented to illustrate the effect of transverse isotropy on the foundation response. Copyright (c) 2012 John Wiley & Sons, Ltd.

关键词： transversely isotropic half-space rectangular foundation finite element method adaptive gradient element

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Seismic bearing capacity of rectangular foundations near slopes using the upper bound method

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COMPUTERS AND GEOTECHNICS 2025年 182卷

作者： Xu, Sheng Yang, Xiao-Li Yin, Zhen-Yu Hong Kong Polytech Univ Dept Civil & Environm Engn Kowloon Hong Kong Peoples R China Hong Kong Polytech Univ Res Ctr Nat based Urban Infrastructure Solut Hong Kong Peoples R China Cent South Univ Sch Civil Engn Hunan 410075 Peoples R China

When the upper load of a rectangular foundation exceeds its ultimate bearing capacity, its failure mechanism is typically an irregular three-dimensional (3D) geometry. By constructing this 3D failure mechanism, this article introduces a theoretical framework for evaluating the seismic bearing capacity of rectangular foundations adjacent to slopes. This 3D mechanism's profile is the classical multi-block mechanism, and the construction of the end faces follows strict associated flow rule. Additionally, the pseudo-static method is utilized to calculate the action of seismic loads. Finally, an energy balance equation is constructed, from which the upper bound solution for seismic bearing capacity is derived. To facilitate practical design, a simple superposition method is provided to calculate the seismic bearing capacity. The effects of aspect ratio, slope inclination, and distance to the slope edge on the seismic bearing capacity are extensively explored. A shape factor is introduced to investigate the differences in bearing capacity between rectangular and strip foundations, with results indicating that a smaller aspect ratio yields a larger shape factor. The investigation into critical 3D failure mechanisms indicates that an increase in seismic intensity reduces the overall size of the mechanism, while an increase in internal friction angle enlarges it.

关键词： Upper bound solution Seismic bearing capacity 3D failure mechanism rectangular foundation Shape factor

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Stability Evaluation Model of Large rectangular foundations on Soil under Combined Loading

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INTERNATIONAL JOURNAL OF GEOMECHANICS 2024年第6期24卷 04024096-04024096页

作者： Du, Yuxiang Fu, Xiaodong Sheng, Qian Zhang, Zhenping Du, Wenjie Chai, Shaobo Jianghan Univ State Key Lab Precis Blasting Wuhan 430056 Peoples R China Jianghan Univ Hubei Key Lab Blasting Engn Wuhan 430056 Peoples R China Jianghan Univ Hubei Wuhan Inst Explos Sci & Blasting Technol Wuhan 430056 Peoples R China Chinese Acad Sci Inst Rock & Soil Mech State Key Lab Geomech & Geotech Engn Wuhan 430071 Peoples R China Shenyang Univ Technol Sch Architecture & Civil Engn Shenyang 110870 Liaoning Peoples R China Changan Univ Sch Civil Engn Xian 710061 Peoples R China

The bearing capacity of large rectangular foundations on soil subjected to combined loading [simultaneously subjected to vertical load (V), overturning moment (M), and horizontal or lateral load (H)] is one of the central topics of interest to geotechnical engineers as it relates to the design of foundations such as ground anchorages of bridges, offshore structures, and gravity dams. To solve this problem, a combination of numerical simulation and theoretical research was used, and a stability evaluation model of large rectangular foundations on soil subjected to combined loading was established. First, an empirical equation for the failure envelope in the V-M-H loading space of rectangular foundations was developed. Second, the safety factor for load-path dependency (LPD) was established by considering the combined effects of V, M, and H, the stability evaluation model for large rectangular foundations on soil subjected to combined loading was constructed by proposing a method for calculating the LPD safety factor based on the V-M-H failure envelope. Last, the accuracy and effectiveness of the stability evaluation model proposed was verified. The proposed model provides a convenient means of calculating the stability of large rectangular foundations on soil under combined loading. The model was applied to the optimal design of a gravity anchorage project of a suspension bridge, which proves that the proposed model is rational and efficient.

关键词： Bearing capacity rectangular foundation V-M-H loading space Load-path dependency (LPD) safety factor

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3D seismic bearing capacity of rectangular foundations near rock slopes using upper bound method

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ALEXANDRIA ENGINEERING JOURNAL 2024年 109卷 778-791页

作者： Liao, Hong Xu, Sheng Wu, Chaoguang Cent South Univ Sch Civil Engn Changsha 410075 Hunan Peoples R China

The analysis of foundation's bearing capacity is generally conducted under the assumption of plane strain. However, the damage of rectangular foundation usually presents obvious three-dimensional (3D) effect. This article considers this 3D effect, which, for the first time, provides a theoretical framework for assessing the bearing capacity of rectangular foundations placed on rock slopes under seismic condition. In order to apply the kinematic method of limit analysis, a new 3D kinematically admissible collapse mechanism is first constructed. Owing to the point-to-point discretized technique, this 3D mechanism can avoid complex surface integration and effectively reduce spatial coordinate iterative calculations while maintaining high accuracy. The pseudo-static method is adopted to simulate the effects of earthquakes. Generalized multi-tangential technique is employed to derive the Mohr-Coulomb constants from Hoek-Brown criterion. The comparison between the present results and results of previous literatures proves the validity of the theoretical framework in this paper. Shape factor and reduction factor are introduced in the parametric study, showing that the 3D effect is more obvious when the rectangular foundation aspect ratio is reduced. As the rectangular foundation location moves away from the slope, its bearing capacity gradually converges towards that of the horizontal foundation. The critical collapse mechanism is also explored, demonstrating that the collapse extent expands with increasing internal friction angle of the rock.

关键词： Seismic bearing capacity Upper bound Nonlinear failure criterion Collapse mechanism rectangular foundation

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Prediction of Ultimate Bearing Capacity of Eccentrically Loaded rectangular foundations Using ANN 1st

Prediction of Ultimate Bearing Capacity of Eccentrically Loa...

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1st GeoMEast International Congress and Exhibition on Sustainable Civil Infrastructures

作者： Sethy, B. P. Patra, C. R. Sivakugan, N. Das, B. M. Natl Inst Technol Rourkela Rourkela India James Cook Univ Townsville Qld Australia Calif State Univ Sacramento Sacramento CA 95819 USA

ISBN: (纸本)9783319635705;9783319635699

Extensive laboratory model tests were conducted on a rectangular embedded foundations resting over homogeneous sand bed and subjected to eccentric load to determine the ultimate bearing capacity. The depth of embedment varies from 0 to B with an increment of 0.5B;where B is the width of foundation and the eccentricity ratio (e/B) was varied from 0 to 0.15 with increments of 0.05. Based on the laboratory model test results, a neural network model has been developed to estimate the reduction factor (RF). The reduction factor can be used to estimate the ultimate bearing capacity of an eccentrically loaded foundation from the ultimate bearing capacity of a centrally loaded foundation. A thorough sensitivity analysis has been carried out to determine the important parameters affecting the reduction factor. Importance was given on the construction of neural interpretation diagram, and based on this diagram, whether direct or inverse relationships exist between the input and output parameters was determined. The results from artificial neural network (ANN) were compared with the laboratory model test results and the agreement is good.

关键词： Eccentric load rectangular foundation Depth of embedment Sand Neural network Reduction factor

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Application of ANN and ANFIS for Predicting the Ultimate Bearing Capacity of Eccentrically Loaded rectangular foundations

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INTERNATIONAL JOURNAL OF GEOSYNTHETICS AND GROUND ENGINEERING 2017年第4期3卷 1-14页

作者： Sethy, B. P. Patra, C. R. Sivakugan, N. Das, B. M. Natl Inst Technol Rourkela India James Cook Univ Townsville Qld Australia Calif State Univ Sacramento Sacramento CA 95819 USA

Extensive laboratory model tests were conducted on a rectangular embedded foundation resting over homogeneous sand bed and subjected to an eccentric load to determine the ultimate bearing capacity. Tests were conducted for foundations with width-to-length ratios (B/L) of zero (strip case), 0.333, 0.5, and 1. The depth of embedment varies from 0 to 1B with an increment of 0.5B;where B is the width of foundation and the eccentricity ratio (e/B) varies from 0 to 0.15 with an increment of 0.05. Based on the laboratory model test results, two different approaches are proposed to determine the ultimate bearing capacity. Firstly, a neural network model is developed to estimate the reduction factor. The reduction factor can be used to estimate the ultimate bearing capacity of an eccentrically loaded foundation from the ultimate bearing capacity of a centrally loaded foundation. A thorough sensitivity analysis was carried out to determine the important parameters affecting the reduction factor. Importance was given to the construction of neural interpretation diagram. Based on this diagram, whether direct or inverse relationships exist between the input and output parameters were determined. Secondly, an adaptive neuro-fuzzy interface system (ANFIS) is used to predict the ultimate bearing capacity. The neuro-fuzzy models combine the transparent, linguistic representation of a fuzzy system with learning ability of artificial neural networks (ANNs). The results from the ANN and ANFIS were compared with the laboratory model test results. It is clearly seen that the performance of the ANFIS model in our study is better than that of the ANN model.

关键词： Reduction factor rectangular foundation Sand Eccentric load ANN ANFIS

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