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In the present paper, the problem of finding the location of the so-called “characteristic point” of flexible footings is revisited. As known, the settlement at the characteristic point is equal to the uniform settlement of the respective rigid footing. The cases of infinitely long strips and circular footings are studied fully analytically. For the case of rectangular footings, analytical results for flexible footings are compared against the respective 3D numerical results for rigid footings; 210 different cases were examined. As shown, the location of the characteristic point may greatly deviate from what it has been proposed in the literature in mid '50s, while it strongly depends on footing shape, as well as on the thickness and the Poisson’s ratio of the compressible medium. Apart from the elastic settlement, the characteristic point is also useful in problems involving the knowledge of the vertical stress increase in the compressible medium due to footing loading, such as the consolidation settlement. In this respect, stress influence factor curves are given for rectangular and circular footings. Finally, the applicability and limitations of the “characteristic point” concept are also discussed.

In the present paper, the strain influence area method is introduced, which, technically, is classified between the classical elastic theory and Schmertmann’s semi-empirical method for immediate settlement analysis, exploiting the advantages of both. Strain influence area values are given in chart form for the calculation of elastic settlement at various locations on the plan view of flexible circular and rectangular footings, embankment loadings as well as for circular rigid footings on sands and clays. Among the major advantages of the proposed method is the direct and convenient calculation of the water table correction factor through the same charts; as known when the water table rises into the influence zone, the soil stiffness reduces, thus, additional settlement is induced. Finally, a new correction factor related to the effect of footing load on the modulus of elasticity of sands is proposed, whilst the Terzaghi’s empirical formula giving the effect of footing shape on the modulus of elasticity of soils has been revisited. It is very interesting that this empirical correction seems to cancel out the adverse effect of the second dimension of footing on elastic settlement analysis.

Root pile is a new type of pile that improves the load carrying capacity by roots penetrating into soils. To carry out the nonlinear settlement analysis of such a root pile in multilayered soils, the hyperbolicity-based load transfer model is in this paper reformulated to account for the discontinuities between the segments with and without roots. The procedure to determine the model parameters for root piles is presented accordingly. The feasibility and reliability of such a proposed modified hyperbolic model for nonlinear settlement analysis of root piles in multilayered soils are verified by a numerical case and two real experimental cases. The numerical case study shows that the root pile does increase the pile load carrying capacity to some extent. In a parametric study based on this numerical case, it can be found that the bearing capacity of root piles increases along with the increase in the root number, size, depth and the elastic modulus of the surrounding soil. The loading test results on two real root piles sited in Chizhou Yangtze River Bridge, China, are used to further verify the proposed method. Comparing with other analytical methods, it is demonstrated that the proposed method incorporated with the proposed modified hyperbolic model can achieve a better agreement with the measured ones especially in a large loading stage.

This paper offers an in-depth review of Schmertmann’s strain influence factor method for immediate settlement analysis. The method in question is among the most popular worldwide, whilst, it is included in various important design codes worldwide (e.g. Eurocode 7, FHWA NHI-06-089). As shown, Schmertmann’s method has been proposed without proper and adequate documentation, whilst it presents serious weaknesses related to its calibration and the values adopted for various factors used. In addition, comparison between measured and calculated settlement values of structures or full-size test footings (data taken from independent studies) indicates that Schmertmann’s method is a poor prediction tool. In this respect, an integrated index is suggested for the quantification of the “effectiveness” of the various settlement analysis methods (including the Schmertmann’s one). This consists of the mean and the coefficient of variation of the calculated over the measured settlement ratio values and the percentage of the cases for which the calculated settlement results greater than or equal to the measured settlement. The very low “effectiveness” index values obtained gave rise to investigating the possible sources of error. A parametric finite element analysis was, finally, carried out for supporting the main findings.

The present research introduces an optimum performance soft computing model by comparing deep (multi-layer perceptron neural network, support vector machine, least square support vector machine, support vector regression, Takagi Sugeno fuzzy model, radial basis function neural network, and feed-forward neural network) and hybrid (relevance vector machine) learning models for estimating the pile group settlement. Six kernel functions have been used to develop the RVM model. For the first time, the single (mentioned by SRVM) and dual (mentioned by DRVM) kernel function-based RVM models have been employed for the reliability analysis of settlement of pile group in clay, optimized by genetic and particle swarm optimization algorithms. For that purpose, a database has been collected from the published article. Sixteen performance metrics have been implemented to record the model's performance. Based on the performance comparison and score analysis, models MS3, MS9, MS17, MS23, and MS25 have been recognized as the better-performing models. Furthermore, the regression error characteristics curve, Uncertainty analysis, cross-validation (k-fold = 10), and Anderson–Darling test reveal that model MS23 is the best architectural model in reliability analysis of pile group settlement. The comparison of model MS23 with published models shows that model MS23 has outperformed with a performance index of 1.9997, a20-index of 100, an agreement index of 0.9971, and a scatter index of 0.0013. The compression index, void ratio, and density influence the pile group settlement prediction. Also, the problematic multicollinearity level (variance inflation for > 10) significantly affects the performance and accuracy of the deep learning model.

The theory of elasticity is used in geotechnical engineering for the calculation of foundation settlement. The equation used in the evaluation of consolidation settlement uses the soil compressibility parameters which usually are determined on cylindrical soil specimens with ϕ 71.4 mm. Laboratory tests performed on soil specimens showed that the parameters that are used in foundation settlement analysis are influenced by the dimensions of the tested soil specimens and the shape of that specimen. The paper presents the influence of specimen size, shape and method used for the coefficient of consolidation evaluation on the final value of the foundation settlement. The analysis was performed using the Settle3 software from Rocsience, considering the case of an elastic foundation flexible square foundation (1.5 m × 1.5 m) which transmits to the ground a pressure of 100 kPa.

Deep foundation pit settlement prediction based on machine learning is widely used for ensuring the safety of construction, but previous studies are limited to not fully considering the spatial correlation between monitoring points. This paper proposes a transformer-based deep learning method that considers both the spatial and temporal correlations among excavation monitoring points. The proposed method creates a dataset that collects all excavation monitoring points into a vector to consider all spatial correlations among monitoring points. The deep learning method is based on the transformer, which can handle the temporal correlations and spatial correlations. To verify the model’s accuracy, it was compared with an LSTM network and an RNN-LSTM hybrid model that only considers temporal correlations without considering spatial correlations, and quantitatively compared with previous research results. Experimental results show that the proposed method can predict excavation deformations more accurately. The main conclusions are that the spatial correlation and the transformer-based method are significant factors in excavation deformation prediction, leading to more accurate prediction results.

Based on a high fill subgrade in Indonesia, in order to make reasonable arrangements for the safety of the construction period and the reserved earth and stone work, this paper simulated and analyzed the high fill subgrade at different heights and predicted the settlement of the subgrade after construction. The calculation results show that most of the settlement of high fill subgrade with different heights has been completed during the construction period, and the settlement after construction meets the requirements, but it is suggested to increase the load during the construction period for some sections with large settlement after construction.

The traditional settlement monitoring has the problems of small monitoring range and low adaptability of settlement prediction model; Based on SBAS-InSAR technology and PSO-BP neural network algorithm, this paper constructs a PSO-BP settlement prediction model based on Sentinel-1A data. Take Jinan(E116°8’, N36°8’)the regional monitoring data is a data sample set. The algorithm proposed in this paper is compared with typical algorithms such as SVM. The results show that the MAE of 30 points predicted by this algorithm is 0.17, which is better than six typical algorithms such as SVM. This algorithm can be used as an effective means to provide early warning of surface subsidence.

In contemporary geotechnical projects, various approaches are employed for forecasting the settlement of shallow foundations (Sm). However, achieving precise modeling of foundation behavior using certain techniques (such as analytical, numerical, and regression) is challenging and sometimes unattainable. This is primarily due to the inherent nonlinearity of the model, the intricate nature of geotechnical materials, the complex interaction between soil and foundation, and the inherent uncertainty in soil parameters. Therefore, these methods often introduce assumptions and simplifications, resulting in relationships that deviate from the actual problem’s reality. In addition, many of these methods demand significant investments of time and resources but neglect to account for the uncertainty inherent in soil/rock parameters. This study explores the application of innovative intelligent techniques to predict Sm to address these shortcomings. Specifically, two optimization algorithms, namely teaching-learning-based optimization (TLBO) and harmony search (HS), are harnessed for this purpose. The modeling process involves utilizing input parameters, such as the width of the footing (B), the pressure exerted on the footing (q), the count of SPT (Standard Penetration Test) blows (N), the ratio of footing embedment (Df/B), and the footing’s geometry (L/B), during the training phase with a dataset comprising 151 data points. Then, the models’ accuracy is assessed during the testing phase using statistical metrics, including the coefficient of determination (R2), mean square error (MSE), and root mean square error (RMSE), based on a dataset of 38 data points. The findings of this investigation underscore the substantial efficacy of intelligent optimization algorithms as valuable tools for geotechnical engineers when estimating Sm. In addition, a sensitivity analysis of the input parameters in Sm estimation is conducted using @RISK software, revealing that among the various input parameters, the N exerts the most pronounced influence on Sm.