Structural Engineering Challenges Research Articles

Bayesian updating of relationships between crack width and corrosion level in reinforced concrete based on a large set of experimental data

AbstractThe evaluation of rebar corrosion in reinforced concrete (RC) structures presents a significant challenge for structural engineers, with on‐site visual inspections and crack width measurements playing a key role in the preliminary assessment. A general approach is to use corrosion models to predict the corrosion level of existing structures, and subsequently update these predictions by means of on‐site data. In this process, empirical models are often applied that relate the observed damage, such as corrosion‐induced cracks, to the corrosion level. However, these models have large uncertainties and are often not applicable to conditions that deviate from the test setups used to derive the empirical relations. This research aims to expand the applicability of these practical, existing empirical models for on‐site corrosion assessment through Bayesian updating techniques. To this aim, a Bayesian framework is developed to update crack width–corrosion models. The Bayesian updating methodology is illustrated for a simple regression model, and for a more complex relation that accounts for additional variables. A novel online database (KUL‐edCCRC) is used that is published accompanying this paper. The obtained results illustrate that the updated models have better agreement with the experimental results, and it is found that the confidence intervals of the regression parameters decrease for an increasing number of observations, even for a small number of additional datapoints. The results hence prove the efficiency of the approach to integrate information from new observations with prior information to adjust the crack width–corrosion model for specific conditions or cases, resulting in a more relevant model as more information becomes available.

Boosting tree with bootstrap technique for pre-stress design in cable dome structures

Tensegrity structures, known for their rigidity derived from feasible pre-stresses, present unique challenges in structural engineering. Traditional force-finding methods, though comprehensive, rely heavily on intricate matrix computations, making them computationally intensive and often uncomfortable for considering external loads in practical engineering scenarios. This paper introduces a novel approach to compute pre-stresses in cable dome structures by integrating machine learning and probability theory, collectively termed the boosting tree with bootstrap technique (BTWBT). This method reduces the sample size to as few as 100 per iteration, while improving computational efficiency by randomly generating internal forces. By reframing the force determination as an inverse problem, it ensures that structural displacement converges to zero under feasible pre-stresses. The effectiveness of BTWBT is demonstrated across three distinct cable dome structures: the Geiger dome, Kiewitt dome, and rotating hyperboloid cable dome. Results show that BTWBT achieves the preset displacement requirement (maximum nodal displacement below 0.01 mm) with fewer iterations and reduced computational cost compared to traditional machine learning methods. BTWBT's capability to manage complex structural configurations with minimal data, while incorporating random internal force generation ranges, highlights its potential as a superior alternative for force determination in tensegrity structures.

Acoustic emission monitoring of a large-scale 50-year-old prestressed concrete bridge girder during an eccentric three-point bending test

Deterioration of reinforced and prestressed concrete structures is one of the main challenges in structural engineering. As the majority of our infrastructure is built around 1960-1980, most structures have reached or will soon reach their design lifetime, giving rise to more structural problems and costs in the coming decades. It is therefore important to develop efficient assessment schemes allowing to assure the safety and reliability of these existing structures and to estimate their residual lifetime. Within the framework of the Bridge|50 research project, a 50-year-old prestressed concrete bridge showing signs of corrosion damage was decommissioned. The bridge girders were recovered and have been subjected to large-scale load tests with varying loading patterns. This paper presents the results acquired during acoustic emission (AE) monitoring of one of the I-shaped girders during a monotonic three-point bending test with an eccentric point load. The results show that the failure mode and location could be detected based on AE activity and zonal AE localization. The onset of concrete cracking was observed by a decrease in peak frequency of the AE signals. Average frequency (AF) and rise angle (RA) value analysis was used to characterize the crack mode, which shifted from tensile to shear mode during bending.

Application of the Rosenblatt transformation in First-Order System Reliability approximations

The reliability assessment of structural systems presents a significant challenge in structural engineering. A commonly employed approximation is the First-Order System Reliability Method (FOSRM), which estimates system reliability using the FORM component reliabilities and sensitivity factors. An essential step in FORM involves transforming the random vector X into the standard vector U, often using the Rosenblatt transformation (RT). Several studies demonstrated that different conditioning orders in the RT yield different FORM component results. This study investigates how these differences on component level propagate into the FOSRM system level. We conducted several typical engineering case studies with various failure probabilities, system sizes, and dependency structures (Gaussian and Frank Copula). For the Frank Copula, different Rosenblatt conditioning orders systematically yielded different FOSRM results, with most cases showing differences between 10% and 30% in estimated failure probability. For some systems, these differences increased with system size, suggesting that greater variations might be observed for larger systems. Notably, systems with Gaussian Copula functions also proved vulnerable to the Rosenblatt conditioning order when different components were assessed with different conditioning orders. The observed differences were larger than previously reported and should be carefully considered in uniform safety assessments.

Machine learning and interactive GUI for concrete compressive strength prediction

Concrete compressive strength (CS) is a crucial performance parameter in concrete structure design. Reliable strength prediction reduces costs and time in design and prevents material waste from extensive mixture trials. Machine learning techniques solve structural engineering challenges such as CS prediction. This study used Machine Learning (ML) models to enhance the prediction of CS, analyzing 1030 experimental CS data ranging from 2.33 to 82.60 MPa from previous research databases. The ML models included both non-ensemble and ensemble types. The non-ensemble models were regression-based, evolutionary, neural network, and fuzzy-inference-system. Meanwhile, the ensemble models consisted of adaptive boosting, random forest, and gradient boosting. There were eight input parameters: cement, blast-furnace-slag, aggregates (coarse and fine), fly ash, water, superplasticizer, and curing days, with the CS as the output. Comprehensive performance evaluations include visual and quantitative methods and k-fold cross-validation to assess the study’s reliability and accuracy. A sensitivity analysis using Shapley-Additive-exPlanations (SHAP) was conducted to understand better how each input variable affects CS. The findings showed that the Categorical-Gradient-Boosting (CatBoost) model was the most accurate prediction during the testing stage. It had the highest determination-coefficient (R2) of 0.966 and the lowest Root-Mean-Square-Error (RMSE) of 3.06 MPa. The SHAP analysis showed that the age of the concrete was the most critical factor in the predictive accuracy. Finally, a Graphical User Interface (GUI) was offered for designers to predict concrete CS quickly and economically instead of costly computational or experimental tests.

Panoramic Perfection: Unveiling Technical Insights from “The Henderson” in Hong Kong

The organic design and seamlessly reflective surface of “The Henderson” establish it as a landmark in Hong Kong. With its all-glass façade and a height of 210 m, the skyscraper designed by Zaha Hadid Architects offers spectacular panoramic views. Particularly noteworthy is the “Banquet Hall” on the top floor, distinguished by its fully glazed roof and engineered by Eckersley O’Callaghan. Large-format, coated and curved glass panes with the best possible technical specification in terms of thickness and minimal dimensional tolerances counterbalance architectural aesthetics and structural resilience. Engineered, manufactured and installed by seele, they serve as effective shields against solar radiation and glare, seamlessly complementing the organic architecture. Collaborative efforts focused on maximizing the transparency of the building envelope as interdisciplinary teams navigated challenges in structural engineering, design aesthetics and compliance with strict regulatory standards of the building authorities in Hong Kong. Thanks to targeted investigations, advancements in glass construction technology and engineering innovation, a procedure was developed that ensured optimum bearing of the panoramic glass panes. This project contributes to the safety and durability of high-rise glass structures to withstand extreme conditions and showcases the transformative potential of bold design concepts, rigorous testing, and international collaboration. The result is a visually stunning and structurally outstanding masterpiece.

Coprecipitation Strategy for Halide-Based Solid-State Electrolytes and Atmospheric-Dependent In Situ Analysis.

In the continuous pursuit of an energy-efficient alternative to the energy-intensive mechanochemical process, we developed a coprecipitation strategy for synthesizing halide-based solid-state electrolytes that warrant both structural control and commercial scalability. In this study, we propose a new coprecipitation approach to synthesized Li3InCl6, exhibiting both structural and electrochemical performance stability, with a high ionic conductivity of 1.42 × 10-3 S cm-1, comparable to that of traditionally prepared counterparts. Through the in situ synchrotron X-ray diffraction technique, we unveil the stability mechanisms and rapid chemical reactions of Li3InCl6 under dry Ar, dry O2, and high-humidity atmosphere, which were not previously reported. Furthermore, the fast reversibility capability of moisture-exposed Li3InCl6 was tracked under vacuum, revealing the optimal recovery conditions at low temperatures (150-200 °C). This work addresses the critical challenges in structural engineering and sustainable mass production and provides insights into chemical reactions under real-world conditions.

Estimating nonlinear wind-induced response of roof cable nets by aeroelastic experiments and ML modeling

The paper examines the structural engineering challenges related to the assessment of the wind-induced vertical displacements of lightweight, hyperbolic-paraboloid cable-supported membrane roofs. Analysis and comparisons are conducted using three distinct methods for calculating the roof vertical, out-of-plane displacements. Finite element method (FEM) analysis is employed using: (i) estimated static nodal forces obtained from wind pressure coefficients determined by aerodynamic wind tunnel tests on a rigid building model, and (ii) loads found from wind pressure coefficients, estimated through machine learning (ML) methods, and (iii) measured roof response found from aeroelastic wind tunnel tests on a flexible model. The study examines three different roof geometries (square, rectangular and circular) and two distinct membrane curvatures for each geometry. Furthermore, wind directionality (three mean-wind incidence angles) and Reynolds number effects (seven mean wind velocities) are studied. Comparisons show that the non-linear FEM analysis, based on estimated static wind loads, underestimates the roof displacements at the roof center, compared to the direct measurements on the aeroelastic model. The main contribution of the study consists of a novel application of ML models, and Artificial Neural Networks (ANNs) in particular, which are employed to correct roof displacement estimations, found by simplified aerodynamic test pressure measurements on rigid roof models. The goal is to better describe the complex fluid-structure interaction of the roof membranes, which can only be achieved by direct aeroelastic tests that are difficult to design and execute. Finally, the study demonstrates that ANNs can be used not only for the preliminary design of the full-scale structure but also for construction of wind tunnel scale models.

Application and Assessment of an Experiential Deformation Approach as a Didactive Tool of Truss Structures in Architectural Engineering

Experiential learning methods are advantageous for students as they motivate them to comprehend structural concepts without complex calculations, enhancing their inherent understanding of static principles. This research introduces a novel, cost-effective haptic didactic tool to enhance the approach to teaching trusses to students in a School of Architecture. The primary goal is to address challenges associated with the complexities of teaching structural systems within the context of architectural education. The proposed approach is related to the most critical issue, which is the state in which the individual elements are under applied load, compression, or tension. The approach explores the deformation of the truss elements and establishes a connection between their visible deformation and the stress they develop under various loads. As a didactic tool, this approach offers an alternative perspective to help students understand truss function under various loads. Also, an assessment procedure of learning outcomes and satisfaction indices has been structured to validate the impact on students on the proposed educational procedure. The findings underscore the significant educational efficiency of the proposed procedure as a sustainable way to connect the structural engineering challenges arising during design courses and creative skills in architecture engineering.

Unboxing machine learning models for concrete strength prediction using XAI

Concrete is a cost-effective construction material widely used in various building infrastructure projects. High-performance concrete, characterized by strength and durability, is crucial for structures that must withstand heavy loads and extreme weather conditions. Accurate prediction of concrete strength under different mixtures and loading conditions is essential for optimizing performance, reducing costs, and enhancing safety. Recent advancements in machine learning offer solutions to challenges in structural engineering, including concrete strength prediction. This paper evaluated the performance of eight popular machine learning models, encompassing regression methods such as Linear, Ridge, and LASSO, as well as tree-based models like Decision Trees, Random Forests, XGBoost, SVM, and ANN. The assessment was conducted using a standard dataset comprising 1030 concrete samples. Our experimental results demonstrated that ensemble learning techniques, notably XGBoost, outperformed other algorithms with an R-Square (R2) of 0.91 and a Root Mean Squared Error (RMSE) of 4.37. Additionally, we employed the SHAP (SHapley Additive exPlanations) technique to analyze the XGBoost model, providing civil engineers with insights to make informed decisions regarding concrete mix design and construction practices.

Comparison of risk-based robustness indices in progressive collapse analysis of building structures

A current challenge in Structural Engineering is the identification of a robustness index for the design of structures subject to low-probability high-consequence load events. Robustness indices proposed in the literature have not been subject to comprehensive scrutiny. Few comparisons presented so far have been limited to simple academic examples involving idealized systems, which cannot suggest robustness values for practical design. In this paper a comprehensive evaluation of two risk-based robustness indices is presented, addressing progressive collapse of regular frame structures subject to damage by abnormal loads. Herein frames of different aspect ratios are considered, subject to local damage of different size, in hazard-independent and hazard-dependent (blast loading) scenarios. System damage states include plastic bending failure of beams, as well as local and global column crushing. Moreover, robustness indices are compared for structures conventionally designed, for structures strengthened following the codified Alternate Path Method (APM), and for structures resulting from risk-based optimization, for different hazard probability levels. Results suggest that the robustness index of Baker, Schubert and Faber performs better when comparing conventional to APM-strengthened codified designs. The Praxedes, Yuan and He robustness index is less sensitive but appears to be more appropriate to describe structures resulting from risk-based optimization.

Seismic control of vertically and horizontally irregular steel high-rise buildings by tuned mass dampers including SSI

The architectural requirements imposed on the structural design of buildings sometimes necessitate vertical and horizontal irregularities with their possibly dangerous effects when these structures are subjected to earthquakes. One of the greatest challenges in structural engineering is the design of a steel high-rise building (HRB) with vertical and horizontal irregularities. In this research, two irregular steel high-rise buildings (HRBs) were seismically analyzed as 3D models considering soil–structure interaction (SSI) and tuned mass damper (TMD) systems were used to mitigate their seismic response under different earthquakes. The two studied HRBs were a vertically irregular (step-pyramid-shaped) steel HRB, and a both vertically and horizontally irregular (L-shaped in-plan, stadium-shaped) steel HRB. The SSI provides the actual response of the tall buildings subjected to earthquake, and mitigation schemes using TMDs were suggested with arrangements of the TMDs on the top plan and along the elevation of the steel high-rise buildings to achieve seismic control of these structures. The present study has shown that the best efficiency in the mitigation of the effect of earthquakes on vertically and horizontally irregular steel high-rise buildings is obtained by implementing TMDs at the corners of the HRB plan on the top of the HRB and also at different floor levels along the upper half-height of the HRB.

Retrofitting Reinforced Concrete One–Way Damaged Slabs Exposed to High Temperature

Exposure of reinforced concrete buildings to an accidental fire may result in cracking and loss in the bearing capacity of their major components, columns, beams, and slabs. It is a challenge for structural engineers to develop efficient retrofitting techniques that enable RC slabs to restore their structural integrity, after being exposed to intense fires for a long period of time. Experimentalinvestigation was carried out on twenty one slab specimens made of self compacting concrete, eighteen of them are retrofitted with CFRP sheets after burning and loading till failure while three of them (which represent control specimens) are retrofitted with CFRP sheet after loading till failure without burning. All slabs had been tested in a simply supported span and subjected to two-point loading. The main variables were the effect of different temperature levels (300ºC, 500ºC and 700ºC),different concrete compressive strength (20MPa, 30MPa and 40MPa) and cooling rate (gradually and sudden cooling conditions) on the behavior of retrofitted one way slabs .The structural response of each slab specimen was investigated in terms of load-deflection behavior, ultimate load carryingcapacity and mode of failure. The experimental results, generally, indicate that slabs retrofitted using CFRP sheets restored flexural strength values nearly equal to or lower than those of the reference slabs, the retrofitted slabs exhibited larger deflection than the control slabs at ultimate loads. Retrofitted control slabs after loading regained about 93.95% to 97.92% of their original load capacity(before retrofitting) while the other slabs regained from 42.% to 84% of the load capacity of the original control specimens. Most of the tested slabs failed by concrete crushing at mid span and partial debonding of certain retrofitting systems was also observed for a few cases

Case Study: Roof Truss Structure With Large Cut Out and Elliptic Glazing Surface

The article presents the technical solutions implemented during the design of the roof trusses and the elliptic skylight structure (Figure. 1) for the extension of the "Shopping City Sibiu" commercial centre in Romania. The area of the roof structure was approximately 1600 sqm (29x56 m). In the central region of the roof, a 27 m long and 10 m wide elliptic skylight was placed. The challenges of the project arouse from the relatively large span of the structure, being supported only on 13 non-symmetrically placed perimeter concrete columns. Thus, the structure had to be designed in such a way, that it would support the extra 20 tones coming from the skylight structure, while also bring inside the natural light unobstructed by any main structural elements. The relatively large deformations between the supporting points of the skylight under variable loads (especially snow loads) can also have adverse effects on the glazing surface during operational phase. Due to this, also the serviceability limit state checks had an important role in the engineering calculations. The structural configuration steps with performed analyses on the partial structural models and on the complex 3D model were especially useful for the identification of the sensitive zones, helping to create the surface shape and develop adequate structural details. The paper summarizes the structural engineering challenges during the design and execution process.

Modal testing and finite element model updating of full-scale hybrid timber-concrete building

Serviceability of tall timber and hybrid timber buildings under wind-induced vibrations has become their leading design criterion. Accurate finite element models for predicting their modal properties are crucial for designing buildings that satisfy the current serviceability criteria. It is a challenge for structural engineers to decide what to include in the structural modelling. This is because elements that are typically considered non-structural (partition walls, plasterboards, screed, façade, etc.) have been shown to act structurally and can significantly influence the modal properties of timber buildings.This paper discusses the importance of including certain entities in finite element models of timber and hybrid timber buildings. A case study of a 5-storey hybrid timber-concrete building with masonry cladding is presented. Full-scale in-situ dynamic tests were performed on the building, using forced vibration testing with a shaker. Frequency-response-function-based modal identification resulted in 3 modes of vibration, identifying natural frequencies, mode shapes and damping ratios. A detailed finite element model was developed that estimated the measured natural frequencies with an error of slightly more than 11%.With an extensive sensitivity analysis was found that modelling of the foundation, the effect of the adjacent abutting building in contact, and the masonry cladding was needed. After model updating, it was found that the shear stiffness of CLT walls was initially underestimated, concluding that non-structural elements such as plasterboards and partition walls might influence the dynamic properties of this hybrid timber-concrete building.

Assessment of lime stabilization of black cotton soil for roads construction projects

The design foundation (i.e., pavements) on black cotton soil has always been a difficult task for the engineers as the structure resting on black cotton soil cracks without any warning. This research evaluates the effect of lime (anhydrous sodium sulphate) on engineering properties of black cotton soil which are considered highly problematic to civil engineering works. Black cotton soil brings about significant geotechnical and structural engineering challenges to property and infrastructure development around the world. The objective of the study is to investigate the use of lime-stabilized black cotton soil as subbase material in flexible pavements. Black cotton soil procured from the local area in Gaborone, Botswana, tested for suitability as subbase material, turned out to be unsuitable as it resulted in very less CBR value (4.8%). The black cotton soil-lime mix was checked for consistency limits, compaction, CBR for different proportions of lime (i.e., 0, 5, 10 and 15%). It was observed that the plasticity index of the soil shows a substantial decrease upon addition of the lime whereas CBR values show a marked increase with unsoaked CBR. The addition of 5%, 10% and 15% of lime produced some desirable soil properties. It can be concluded lime could be one of the best alternative stabilizer materials for highly expansive clayey.

Adaptive Chaotic Marine Predators Hill Climbing Algorithm for Large-Scale Design Optimizations

Meta-heuristic algorithms have been effectively employed to tackle a wide range of optimisation issues, including structural engineering challenges. The optimisation of the shape and size of large-scale truss structures is difficult due to the nonlinear interplay between the cross-sectional and nodal coordinate pressures of structures. Recently, it was demonstrated that the newly proposed Marine Predator Algorithm (MPA) performs very well on mathematical challenges. The MPA is a meta-heuristic that simulates the essential hunting habits of natural marine predators. However, this algorithm has some disadvantages, such as becoming locked in locally optimal solutions and not exhibiting a high level of exploratory behaviour. This paper proposes two hybrid marine predator algorithms, Nonlinear Marine Predator (HNMPA) and Nonlinear-Chaotic Marine Predator Algorithm (HNCMPA), as improved variations of the marine predator algorithm paired with a hill-climbing (HC) technique for truss optimisation on form and size. The major advantage of these techniques are that they seek to overcome the MPA’s disadvantages by using nonlinear values and prolonging the exploration phase with chaotic values; also, the HC algorithm has been used to avoid locally optimum solutions. In terms of truss optimisation performance, the proposed algorithm is compared to fourteen well-known meta-heuristics, including the Dragonfly Algorithm (DA), Henry Gas Solubility optimisation (HGSO), Arithmetic optimisation Algorithm (AOA), Generalized Normal Distribution Optimisation (GNDO), Salp Swarm Algorithm (SSA), Marine Predators Algorithm (MPA), Neural Network Algorithm (NNA), Water Cycle Algorithm (WCA), Artificial Gorilla Troops Optimiser (GTO), Gray Wolf Optimiser (GWO), Moth Flame Optimiser (MFO), Multi-Verse Optimiser (MVO), Equilibrium Optimiser (EO), and Cheetah Optimiser (CO). Furthermore, seven algorithms were chosen to test HNCMPA performance on benchmark optimisation sets, including MPA, MVO, PSO, MFO, SSA, GWO, and WOA. The results of the experiment demonstrate that the optimisation techniques put forth surpass previously established meta-heuristics in the field of optimisation, encompassing both traditional and CEC problems, by a margin of over 95% in terms of attaining a superior ultimate solution. Additionally, with regards to solving truss optimisation difficulties as a large-scale real-world engineering challenge, the outcomes indicate a performance boost of over 65% in obtaining significantly better solutions for problems involving 260-bar and 314-bar; conversely, in the case of 340-bar issues, the improvement rate is slightly lower at almost 25%.

On the DInSAR technique for the structural monitoring of modern existing bridges

The setting up of efficient strategies for safety assessments and maintenance of modern existing bridges is a crucial research challenge in structural engineering. In Italy, this topic has recently been addressed in guidelines issued by the Ministry of Infrastructures and Transport in 2020. The guidelines outline procedures and tools for safety assessments and maintenance interventions: a mandatory step is the analysis of original documents (concerning the design, the construction process and the maintenance interventions) in order to acquire robust knowledge of the structure. As noted in recent works in the literature, non-invasive structural monitoring approaches play a crucial role in the safety assessment of existing bridges. One such approach is multi-temporal differential synthetic aperture radar interferometry (DInSAR). This paper presents a cross-disciplinary process for the structural monitoring of modern existing bridges, based on integration of DInSAR measurements, exploiting Cosmo-SkyMed measurements collected during the period 2011–2019, and accurate knowledge of the structures derived from analysis of original documents conserved in historical archives. The procedure is applied to two reinforced concrete Gerber bridges in Rome, designed in the 1930s.

Secondary silane grafting on aramid fibers improves the interfacial bonding performance in textile composite materials

To improve the chemical and physical surface features of aramid fibers and the bonding quality at the interface, carbon nanotubes, dopamine and silane coupling reagent KH560 were used to modify the surface of aramid fibers. The fiber surface was characterized by FTIR, XPS, SEM and AFM. The single-fiber specific strength, surface roughness, wettability and interfacial shear strength of the modified fiber were quantified. Finally, the uniaxial tensile behaviour of the textile composite laminate with the modified fibers was tested. The experimental results show that: after the grafting of silane coupling reagent as a second modification step, the amount of oxygen-containing groups on the surface of aramid fibers, and the surface roughness, and the ability to impregnate resin are further improved. The single-fiber specific strength, the interfacial shear strength by fiber pull-out tests, and the tensile strength of the laminate are increased by 21.62%, 73.57%, and 51.60%, respectively. This work demonstrates a general surface modification strategy working for diverse types of fibers, synthetic or natural. The present findings help to develop a broad range of high-performance textile composites to address long-term challenges in structural engineering.

Deformation of unsaturated collapsible soils under suction control

Abstract Collapsible soils present significant geotechnical and structural engineering challenges worldwide. They can be found in arid or semi-arid regions and are directly affected by the multi-step wetting procedure due to the reduction of soil suction. The main objectives of this paper are to investigate the volume change behaviour, collapse mechanism and deformation characteristics under the control of suction and net vertical stress. In this study, three types of collapsible soils were investigated such as natural soils of sandy gypseous, silty loess, and artificial soil of gypsum–sand mixture. A series of constant net stress-suction control (wetting and drying) tests using a combination of axis-translation and vapor equilibrium techniques were deployed to cover a wide range of applied suction. The test results show that large volume change and collapse deformation occur upon a stepwise suction decrease. On the other hand, shrinkage behaviour resulting from increases in imposed suction is observed during the drying path. The collapse deformation depends on the stress path and is a function of net normal stress, suction, dry density, and degree of saturation. The water content and the degree of saturation dramatically increase as the applied suction decreases from the initial high to zero values at the drying path.