Studia Geotechnica et Mechanica Feed

Determination of the vertical extent of transition zones based on the dispersion measures of CPTu tests and the impact of excluding these zones in estimating characteristic values of parameters

Sat, 17 Oct 2026 00:00:00 GMT

The natural spatial variability of soil properties is particularly evident near the boundaries between distinct soil layers. In such transition zones, there is usually a noticeable differentiation and increased dynamics of changes in the values of geotechnical parameters. The identified soil layers were assumed to have similar properties based on lithological and geotechnical criteria. Zones surrounding the interpreted contact surface of the layers with significant variability in geotechnical and physical parameters were considered as transition zones. This variability is reflected in the variability of the basic Cone Penetration Test with pore pressure measurement behind the tip called u 2 (CPTu) sounding parameters. The application of basic statistical functions such as the local expected value μ L (X) calculated in a given neighborhood of sounding depth H, the dispersion measures σ L (X) and V L (X) ( local population standard deviation and local coefficient of variation defined at each depth H for a given neighborhood of that depth H) to the analysis of CPTu soundings enabled the development of a method for determining the depth range of transition zones near the boundaries between distinct layers and an algorithm enabling the implementation of this method in computer programs. Using the determined vertical ranges of transition zones, it was proposed to estimate characteristic parameter values based on the central parts of the layers, excluding the measurements in the transition zones from the calculations. In the next step, using the same CPTu tests and focusing on the same layers, the characteristic values of selected geotechnical parameters were compared, calculated both with and without inclusion of the measurements from the estimated transition zones in the calculations. Finally, the calculation results were summarized and discussed.

Seismic risk evaluation of historic masonry structures in an Algiers district, Algeria, using fragility and vulnerability functions: A case study of Belouizdad district

Tue, 25 Aug 2026 00:00:00 GMT

The seismic vulnerability of Algeria’s historic urban fabric, particularly its unreinforced masonry (URM) buildings, underscores the urgent need for effective risk-mitigation strategies. These culturally significant yet structurally fragile buildings are highly susceptible to earthquake damage. This study integrates fragility functions with a vulnerability index (VI) approach to evaluate the seismic risk of URM buildings in Algiers, with a focus on the Belouizdad district. By analyzing seismic scenarios with intensities ranging from Modified Mercalli intensity VII–X, the research develops and calibrates vulnerability and fragility curves, offering a probabilistic assessment of structural damage. Quantitative results indicate that about 80% of the surveyed URM buildings fall into the moderate vulnerability class (VI = 0.20–0.60), nearly 10% are classified as highly vulnerable (VI > 0.60), and approximately 9% show low vulnerability (VI < 0.20). Under a scenario consistent with the 2003 Boumerdes earthquake (PGA = 0.27 g), 29% of the building stock is expected to exceed the mean damage ratio (MDR) of 0.20 and 11% to exceed an MDR of 0.50. The findings confirm that the majority of URM buildings in the study area are moderately to highly vulnerable, largely due to their age, lack of maintenance, and structural modifications. The proposed methodology – implemented within a Geographic Information System for spatial analysis – facilitates the identification of priority areas for intervention and supports targeted risk-reduction policies. Ultimately, this work provides data-driven evidence for safeguarding Algeria’s architectural heritage and enhancing urban resilience against seismic hazards.

Stochastic numerical approach to the bearing capacity of adjacent footings on spatially variable soils

Mon, 18 May 2026 00:00:00 GMT

The interaction of adjacent footings in spatially variable soils presents significant challenges in geotechnical engineering, particularly when soil heterogeneity introduces uncertainty into foundation performance. Traditional deterministic methods provide valuable insights into bearing capacity (BC) and settlement behaviour; however, they capture the complex interactions arising from spatial variability. This study employs the random finite element method to investigate how anisotropic random fields affect the BC of adjacent footings. The problem is considered in three distinct soil types: perfectly cohesive, purely frictional, and cohesive-frictional. A series of numerical simulations is conducted to examine the effects of foundation spacing and the spatial variability of soil properties. Deterministic results indicate that BC increases at the critical spacing but gradually diminishes as the spacing increases further. Probabilistic analyses reveal that soil heterogeneity significantly impacts foundation behaviour, particularly in non-cohesive soils, where the coefficient of variation of BC is highly sensitive to spatial fluctuations. Reliability-based assessments reveal that failure probabilities vary significantly depending on soil type and correlation structure, underscoring the importance of stochastic modelling in geotechnical design. These findings contribute to the development of risk-informed design methodologies, highlighting the importance of modelling spatial variability using stationary random fields. As shown, such approaches enhance foundation reliability assessments and informed engineering decision-making.

Geofoam-enhanced soft embankments with a load distribution slab for improved pavement performance: A 3D numerical analysis

Thu, 07 May 2026 00:00:00 GMT

Constructing pavement on soft embankments poses significant challenges due to unpredictable lateral movement, excessive settlement, and poor shear resistance. Engineers often employ geotextile‐reinforced columns (GRCs) to mitigate these issues for pavement support. However, granular columns in soft soils may suffer from inadequate lateral confining pressure in their upper sections. To overcome this, high‐strength geofoam is deployed to confine the columns, and when paired with a load distribution slab (LDS), overall stability improves markedly. This method effectively curbs settlement, lateral displacement, and deflection by harnessing tensile stress. This study developed a hypothetical embankment model supported by GRCs with an underlying geofoam layer and LDS, subjected to 12, 33, and 66 kPa loading levels following the cyclic stress protocol defined in AASHTO T 307-17 (“Standard Method of Test for Determining the Resilient Modulus of Soils and Aggregate-Base Course Materials”). Using Continuum Fast Lagrangian Analysis in 3D for numerical analysis, we found that embankments without an LDS settled by 55 mm at 12 kPa within 10 months, increasing to 92 mm after 35 months. Under 33 and 66 kPa loads, immediate settlements reached 121 and 168 mm, respectively. Conversely, the system incorporating geofoam and an LDS maintained an average settlement of only 11 mm across all stress conditions. These results demonstrate that integrating an LDS yields a more uniform stress distribution, significantly reducing settlement and deflection while enhancing pavement stiffness on soft embankments. In summary, using geofoam and LDS offers a promising solution for constructing durable pavements on soft embankments. These findings provide a robust framework for enhancing pavement performance by systematically reinforcing soft embankments.

Surface and acoustic waves natural frequencies estimation by boundary element method

Mon, 27 Apr 2026 00:00:00 GMT

The article deals with the estimation of natural frequencies of surface and acoustic waves in fluids using the boundary element method. The phenomena appear in an incompressible or compressible fluid, respectively, and are described by the Laplace or Helmholtz differential equations. The Helmholtz equation fundamental solution contains the wavenumber, which remains unknown under integral operators in the equivalent inverse formulation. The multiple reciprocity method, in which wavenumber-independent higher order fundamental solutions of the Laplace equation occur, overcomes this difficulty. Moreover, this method gives a consistent description in which the incompressible fluid appears as a particular case of the compressible one. This article is divided into two parts: fluid in a rigid and flexible tank. An algorithm allows to take into account couplings between surface and acoustic waves and also tank and included fluid vibrations. The problems related to the interpretation of numerical results are widely discussed in the examples enclosed. The experience gained as a result of the analyses made it possible to compile a number of valuable advices for future research of the discussed problem.

Estimation of the stability of tailings dams based on genetic algorithm-supported calibration results and monitoring data

Tue, 21 Apr 2026 00:00:00 GMT

In consideration of the potential consequences, ensuring the safety of tailings dams is of paramount importance. A probable failure mechanism is the loss of global stability, which, in certain cases, may involve shearing within the subsoil. A significant issue is the inability to directly verify stability on site, in contrast to the routine collection of other monitoring data, such as displacement or groundwater level measurements. This study investigates, using numerically generated (synthetic) data, the feasibility of accurately estimating dam stability. To this end, a genetic algorithm was used to calibrate material parameters, aiming to achieve results that closely match the numerically generated monitoring data. The primary focus of this study is to assess whether successfully reconstructing the history of displacements and piezometric heads is sufficient for accurate estimation of the factor of safety (FOS), a principal indicator of stability. The findings indicate that an accurate estimation of the FOS strongly depends on the proper reconstruction of piezometric heads and the correct determination of the angle of internal friction. Consequently, this research has led to the development of a novel method for FOS estimation using genetic algorithm calibration applied to synthetic data, which holds considerable promise for improving the accuracy of tailings dam safety assessments.

Integrated analysis of pore size, shape, and position on mesoscale compressive strength of cementitious materials: Numerical modelling and statistical regression

Tue, 21 Apr 2026 00:00:00 GMT

Cement-based materials often suffer reduced compressive strength due to internal porosity, yet the specific roles of pore size, shape, and spatial distribution remain inadequately quantified. This study investigates the effect of pore geometry and position on the mesoscale compressive strength of a cement-clay mixture. High-resolution X-ray computed tomography (CT) captured three-dimensional pore structure and total porosity in cured specimens. The reconstructed microstructure was used in numerical models in FLAC3D, where a damage-plasticity concrete constitutive model was calibrated against in situ CT-monitored compression tests and validated with a second specimen. A series of parametric simulations were then conducted, systematically varying pore radius (1–2 mm), sphericity (0.79–1.00), and vertical location. The results show that increasing total porosity leads to a pronounced decrease in peak compressive strength (a strong inverse correlation, with exponential trends outperforming linear fits). However, strength in mesoscale should not be predicted by porosity alone: variations in pore size, shape, and position caused significant deviations from the single-parameter trend. To quantify the combined influence of pore-related features, a multiple linear regression model was developed using porosity, pore sphericity and pore position as predictors. The multi-parameter model achieved a high coefficient of determination (R 2 = 0.80) and a low prediction error (MSE = 0.34 MPa2), representing more than a threefold improvement in accuracy compared to porosity-only correlations. Standardised regression coefficients indicate that porosity is the dominant factor controlling compressive strength, followed by pore position and pore sphericity, all of which are statistically significant. The results demonstrate that pore geometry and spatial distribution critically influence the load-bearing capacity of cementitious mixtures. The proposed integration of CT imaging, physically calibrated numerical modelling, and statistical regression provides a robust framework for quantitative assessment of microstructure–performance relationships at the mesoscale.

First results of the lateral static load test on model piles

Wed, 24 Dec 2025 00:00:00 GMT

Laterally loaded pile foundations are more commonly employed in geotechnical engineering due to their widespread utilisation in contemporary construction projects, with examples including wind turbines. The most effective method for estimating pile lateral capacity is a static load test conducted in a natural scale. However, there are some challenges associated with field performance tests, which can be avoided by conducting them on model piles in a laboratory scale. This article presents the initial results from a series of lateral static load tests conducted on steel pipe piles in a laboratory scale. Based on the retrieved results, an analysis of the loaddisplacement pile lateral behaviour was performed, and the pile lateral bearing capacities were estimated with approximation methods. In addition, an approximation error analysis was performed.

Application of machine learning tools in road bridge weigh-in-motion systems

Wed, 19 Nov 2025 00:00:00 GMT

This study explores the application of machine learning (ML) techniques in road and bridge weigh-in-motion (B-WIM) systems, focusing on their potential to improve the accuracy and efficiency of load identification processes. The study begins with an introduction to the fundamentals of ML and artificial intelligence, providing an overview of key algorithm families and their applicability in bridge civil engineering. Subsequently, the concept of B-WIM systems is discussed, emphasizing the role of ML in vehicle classification, detection, and load estimation. A novel system architecture is proposed, integrating the You Only Look Once algorithm for real-time vehicle detection and tracking, and autoencoders for analysing the structural response signal to estimate axle loads. Proof-of-concept case studies, implemented within a numerical simulation environment (finite element software SOFiSTiK), are presented to illustrate the feasibility of such approaches. These examples demonstrate key concepts in a simplified form, supporting the proposed methodology without requiring full-scale experimental validation. Results demonstrate the advantages of ML tools in handling dynamic loads and diverse traffic conditions, significantly outperforming traditional methods regarding accuracy and scalability. The study concludes by highlighting the broader implications of using ML in structural monitoring and its potential to revolutionize load identification in bridge engineering.

Optimization of the dimensions of a tapered thin-walled cantilever, aimed at reaching a maximum critical buckling load

Mon, 17 Nov 2025 00:00:00 GMT

The aim of this research was to determine the optimal dimensions of a tapered, bisymmetric, thin-walled, I-shaped cantilever for which, at a constant mass, the critical load causing the buckling of the beam reaches the maximum value. Optimal solutions were sought in a discrete set of admissible values of the taper coefficients of the I-bar’s web and/or flanges. A model of a thin-walled bar with an open cross-section, whose mathematical description was derived on the basis of the momentless theory of shells, was used to analyse the considered problem described by a system of four coupled differential equations with variable coefficients. The equations were solved using Chebyshev series of the first kind to approximate the generalized displacement functions, and the recurrence algorithm presented in earlier publications by the author(s). A tapered cantilever with a bisymmetric cross-section, subjected to the action of a uniformly distributed load, was analysed. The load can be applied to the I-bar’s upper flange or to its lower flange, or it can act in the centre of the web. The obtained critical load values were compared with those obtained using the finite element method and the commercial Sofistik software. In the set of linearly tapered cantilevers with a bisymmetric double-tee cross section, the cantilevers with the highest taper coefficients of the web and the flanges (the free end having the smallest possible dimensions) were found to be optimal (in their case, at a constant mass, the critical buckling load reaches its maximum value).

Application of second-order sensitivity analysis to stabilisation of unstable continuous multi-degree-of-freedom parametric periodic systems

Fri, 19 Sep 2025 00:00:00 GMT

The work presents a method of automatic stabilisation of unstable multi-degree-of-freedom linear parametric systems. The publication is a continuation and extension of the subject matter described in Wójcicki’s earlier work ‘Application of first-order sensitivity analysis to stabilization of unstable continuous MDOF parametric periodic systems’ (Studia Geotechnica et Mechanica). While in that paper first-order sensitivity analysis was used, in this paper it was extended to the second-order sensitivity analysis. The algorithm of the presented method of stabilisation of an unstable continuous in time parametric system has become significantly more complicated, but the new formulas allow for better (nonlinear) prediction of extrapolated changes in the values of design parameters, which should accelerate the system stabilisation procedure. The obtained formulas were verified and validated using the same examples that were used in the study cited earlier. The method’s innovation is the idea to achieve the non-homogeneous parametric sensitivity equation by evaluating analytically the first and second derivatives of the parametric homogeneous equation of motion with respect to design parameter. Then, by solving the obtained sensitivity equation, the first and second derivatives of monodromy matrix and finally the first and second derivatives of multipliers are evaluated. Ultimately, this method is based on sensitivity analysis of absolute values of multipliers. Furthermore, the sensitivity analysis method was improved and generalised to allow to correctly determine the eigenderivatives also with respect to those system parameters on which the parametric excitation period depends. In particular, it becomes possible to use the parametric excitation period as a design parameter.

Application of first-order sensitivity analysis to stabilisation of unstable continuous multi-degree-of-freedom parametric periodic systems

Fri, 19 Sep 2025 00:00:00 GMT

From a practical point of view, the most important feature of a parametric periodic system is the instability phenomenon. Unlike in systems with constant coefficients, in which only points of instability exist, in parametric systems, whole areas of instability occur. This study presents a method of automatic stabilisation of unstable multi-degree-of-freedom linear continuous-in-time parametric systems. In this method, a parametric excitation can only be a continuous function of time. This paper concerns the sensitivity analysis of multipliers – complex eigenvalues of the monodromy matrix. The method is an alternative approach to that proposed in all other previous works on this subject. A procedure based on sensitivity analysis and directional derivative was used. The method's innovation is achieving the non-homogeneous parametric sensitivity equation by evaluating analytically the derivative of the homogeneous parametric equation of motion with respect to the design parameter. Then, by solving this sensitivity equation, evaluating the first derivative of the monodromy matrix, and finally, the first derivatives of multipliers. Ultimately, this method is based on a sensitivity analysis of the absolute values of multipliers. Furthermore, the sensitivity analysis method was improved and generalised to allow to correctly determine the eigenderivatives also with respect to those system parameters, on which the parametric excitation period depends. In particular, it becomes possible to use the parametric excitation period as a design parameter, which was not possible in the works of other authors. Examples of this method's implementation are also presented. This work continues the topics developed by the author in his earlier works.

Multiwavelet and multiwavelet packet analysis in qualitative assessment of the chaotic states

Thu, 14 Aug 2025 00:00:00 GMT

This article demonstrates the application of multiwavelet analysis and multiwavelet packet analysis in qualitatively assessing the chaotic nature of a system’s response. Ranges of model parameters that induce chaotic behavior are identified, and the system’s response under these conditions is then analyzed using multiwavelet analysis and multiwavelet packet analysis. By employing a one-degree-of-freedom nonlinear system as an illustrative example, the transition from a non-chaotic to a chaotic state is shown to affect both the magnitude and the temporal distribution of wavelet coefficients across multiple levels of the response analysis. The cumulative energy of the signal’s multiwavelet approximation is calculated to distinguish between chaotic and non-chaotic signals. The results obtained through multiwavelet analysis in identifying the system’s critical states are compared with those derived from traditional wavelet analysis and other established methods for assessing chaos. The presented approach is an alternative to other methods of qualitative identification of chaotic states, and also to provide a generalization to the method in analyzing complex systems.

Bearing capacity of tapered walls: Physical modeling and numerical analysis

Thu, 14 Aug 2025 00:00:00 GMT

This study investigates the load–displacement behavior and failure mechanisms of tapered walls using numerical methods validated against experimental data. A two-dimensional (2D) plane strain approach was adopted to effectively represent the behavior of tapered piles under vertical loading. Finite element method simulations (using both Mohr–Coulomb and hardening Mohr–Coulomb models) and limit analysis with LimitState GEO were employed to analyze three tapered wall configurations with taper angles of 0° (straight wall), 0.75° (moderately tapered), and 1.5° (sharply tapered) in dense sand. The results reveal the significant influence of taper geometry on load-bearing capacity and failure mechanisms, with the moderately tapered wall achieving the optimal balance of shaft friction and base resistance. Numerical predictions underestimated the experimental results by up to 30%, primarily due to installation effects, which were not incorporated into numerical models. This study underscores the necessity of incorporating installation-induced effects for realistic design and modeling of displacement piles.

Research on the failure behavior of cement- and fiber-reinforced sand under triaxial tensile loads

Thu, 14 Aug 2025 00:00:00 GMT

The primary objective of this research is to investigate the failure behavior of sand treated with cement and fibers under triaxial tensile loading conditions. To achieve this, a new loading system and triaxial cell were developed for conducting tensile tests. The specimens included sand samples with 3 and 5% cement content (dry weight) and two types of polypropylene fibers with a length of 24 mm and diameters of 23 and 300 μm, incorporated at dosages of 0.0 and 0.5% (dry weight) of the sand–cement mixture. After a curing period of 7 days, the specimens were tested under direct triaxial tension at confining pressures of 100, 200, and 300 kPa under drained conditions. The stress–strain behavior, volumetric changes, and energy absorbed by the cement- and fiber-reinforced sand were analyzed and compared with data from other studies. The results showed that the addition of fibers led to a reduction in the peak deviator stress and an increase in the residual deviator stress of the cement- and fiber-reinforced sand, indicating a transition from brittle to ductile behavior. Additionally, a decrease in initial stiffness and stiffness at 50% of the maximum tensile stress was observed with the incorporation of fibers, with the effect becoming more pronounced as the fiber diameter increased. The energy absorbed by fibers with a diameter of 23 μm was lower compared to those with a diameter of 300 μm. The addition of fibers also influenced the strength parameters, resulting in a decrease in the cohesion intercept and an increase in the internal friction angle.

Example of geotechnical monitoring of soil improvement using rigid inclusions under road embankment

Wed, 13 Aug 2025 00:00:00 GMT

The article describes an existing and pioneering measurement system, which can be called a geotechnical monitoring system. This system has string sensors measuring strains, stresses and forces and was installed in concrete columns strengthening weak soil subgrades. Concrete columns using full displacement technology strengthen the ground under the embankment of the expressway No. S7 between Gdańsk and Elbląg in Poland. In terms of geological structure, the area where the measuring columns were made is characterized by the presence of low-bearing, large-thickness organic soils, such as peats and soft plastic silts, and a high groundwater level. The described geotechnical monitoring system consists of a total of eight measurement columns in four test areas. This article is a presentation of the measurement system and the first results of measurements carried out during column load-bearing tests.

Effect of structure–ground interaction on shrinkage stresses in foundation reinforced concrete elements

Wed, 04 Jun 2025 00:00:00 GMT

This paper presents a numerical analysis of the shrinkage of reinforced concrete foundations on the ground, known as mat foundations. It presents Finite Element Method (FEM) calculations of a beam and its verification with analytical solutions. Two numerical models of mat foundations have been adopted for the purpose of this study. The first model is a foundation resting directly on the ground, that is, on an elastic Winkler base. The second numerical model consists of layers, that is, a mat foundation and a substructure (lean concrete), taking into account the frictional forces between these layers. The Mohr–Coulomb model was used in the analyses. Conclusions were drawn from the numerical analyses on the influence of the soil substrate on the magnitude of the shrinkage stresses. Modelling the interaction between the foundation and a concrete sole using elastic bonds is clearly suboptimal. Using friction to model this connection is a better approach as it avoids underestimating shrinkage stresses. The differences can be up to an order of magnitude.

Influence of Raft in the Analysis of Granular Piles

Wed, 04 Jun 2025 00:00:00 GMT

In an era marked by rapid growth and diminishing natural resources, including land, ground improvement has become imperative, particularly for civil engineers dealing with soft soils. This study explores the potential of granular piles (GPs) and granular piled rafts (GPRs) as cost-effective and sustainable solutions for overcoming resource-related challenges. The research focuses on a comparative analysis of the settlement interaction factor (SIF) within groups of GPRs and GPs as foundation systems. By evaluating and comparing the settlement magnification effects induced by adjacent foundation elements, the study aims to uncover insights into the influence of spacing and relative stiffness on the SIF. These findings offer valuable information for engineers, enabling them to optimize designs and address potential settlement-related issues in a resource-conscious manner

Optimizing DVA placement using evolutionary algorithms for dynamic beam loading

Thu, 29 May 2025 00:00:00 GMT

Danamic vibration absorbers (DVAs) are used to suppress the excessive structural response due to dynamic loading. To maximize their effectiveness, the placement and characteristics of DVAs need to be carefully chosen. To address this challenge, a methodology that enables this task to be accomplished by means of an evolutionary algorithm is presented in this paper. A beam subjected to a sequence of forces with random amplitudes, which move at random time instances with a constant velocity, is considered. The beam has either one or a set of two arbitrarily located DVAs. The loading is modeled using a filtered Poisson process, while the DVAs are modeled as single-degree-of-freedom (SDOF) systems. It is shown that the proposed algorithm can serve as a powerful tool when selecting an arrangement of DVAs, in turn effectively mitigating any undesired structural response. Moreover, the optimization of DVAs leads to the asymmetry of the absorber’s position along the length of a bridge’s beam. The obtained results can be used to evaluate the correctness of calculations conducted for the purpose of assessing structural damping requirements.

Assessment of spread foundation settlement using statistical determination of characteristic values of subsoil properties

Mon, 12 May 2025 00:00:00 GMT

According to Eurocode 7, limit state design codes generally draw more attention to ultimate limit states than to serviceability limit states. This paper presents the problem of settlement assessment of spread foundations on clays when the foundation design is governed by the serviceability limit state requirements. The paper presents the test results of geotechnical parameters for heavily preconsolidated boulder clays (sandy clay saCl and silty sandy clay sasiCl), which prevail on the Warsaw University of Life Sciences – SGGW campus. The test results were used for settlement calculations of spread foundations. Based on the results of field and laboratory tests, the problem of spatial variability assessment and determination of the characteristic value of soil parameters was addressed. Classical statistics and Bayesian analysis were used in the statistical analysis of the test results. Settlements of spread foundations were calculated based on the soil parameters obtained from cone penetration tests (CPTs) and dilatometer tests (DMTs). Special attention was drawn to the selection of the characteristic values of soil parameters. Determination of the characteristic value of the constrained modulus Mk was performed using two methods: according to the well-known and frequently used formula proposed by Schneider (1997; 1999) and according to the European draft standard prEN 1997-1:2022-09. Settlement calculations of spread foundations were carried out taking into account changes in the stresses and the constrained modulus in the subsoil. The calculated settlements were verified by field measurements performed during the construction of the object. Comparison of settlements obtained from the characteristic values of the constrained modulus Mk estimated according to prEN 1997-1:2022-09 with the measured settlements indicates that the calculated values were significantly higher than the measured values. Smaller differences between the measured and calculated settlements were obtained when the characteristic values of the constrained modulus Mk were determined from Schneider's formula, while smaller differences were obtained when the mean values of the constrained modulus Mmean were used.