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Search Results (1,274)

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Keywords = constitutive equation

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16 pages, 5825 KB  
Article
Crystal Plasticity Simulations of Dislocation Slip and Twinning in α-Ti Single and Polycrystals
by Evgeniya Emelianova, Maxim Pisarev, Ruslan Balokhonov and Varvara Romanova
Metals 2025, 15(11), 1243; https://doi.org/10.3390/met15111243 - 13 Nov 2025
Abstract
A crystal plasticity finite element model is developed and implemented to numerically study the deformation behavior of hexagonal close-packed metals using α-titanium as an example. The model takes into account micromechanical deformation mechanisms through dislocation slip along prismatic, basal, and first-order <c [...] Read more.
A crystal plasticity finite element model is developed and implemented to numerically study the deformation behavior of hexagonal close-packed metals using α-titanium as an example. The model takes into account micromechanical deformation mechanisms through dislocation slip along prismatic, basal, and first-order <c+a> pyramidal systems, as well as tensile twinning. Twin initiation follows a two-conditional criterion requiring that both the resolved shear stress in a twin system and the accumulated pyramidal slip simultaneously reach their critical values. Three-dimensional polycrystalline models are generated using the step-by-step packing method. The crystal plasticity constitutive model describing the deformation behavior of grains is integrated into the boundary-value problem of continuum mechanics, including dynamic governing equations. The three-dimensional problem is solved numerically using the finite element method. The micromechanical model is tested for an α-titanium single crystal along the [0001] direction and a polycrystal consisting of 50 grains. The numerical results reveal that twin propagation is controlled by the critical value of accumulated pyramidal slip, emphasizing the need for experimental calibration. The agreement between numerical and experimental results provides the model validation at the meso- and macroscales. Full article
(This article belongs to the Section Computation and Simulation on Metals)
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21 pages, 5113 KB  
Article
Hysteretic Energy-Based Estimation of Ductility Demand in Single Degree of Freedom Systems
by Baykal Hancıoğlu, Murat Serdar Kirçil and Zekeriya Polat
Buildings 2025, 15(22), 4077; https://doi.org/10.3390/buildings15224077 - 13 Nov 2025
Abstract
Ductility, as a fundamental mechanical property, allows structures to undergo inelastic deformations and dissipate seismic energy while maintaining their load-carrying capacity without substantial strength degradation. Thus, the estimation of structural ductility demand has consistently constituted an essential topic of research interest in earthquake [...] Read more.
Ductility, as a fundamental mechanical property, allows structures to undergo inelastic deformations and dissipate seismic energy while maintaining their load-carrying capacity without substantial strength degradation. Thus, the estimation of structural ductility demand has consistently constituted an essential topic of research interest in earthquake engineering. In this study, an iterative procedure for estimating the ductility demand of elastoplastic single-degree-of-freedom (SDOF) systems through dissipated energy is introduced. The proposed procedure helps the determination of ductility demand by use of only elastic response spectra. It initially estimates the hysteretic energy as a proportion of the total input energy. Then, ductility demand is estimated with the help of a developed equation by performing regression analyses based on the nonlinear time history analyses results of elastoplastic single-degree-of-freedom (SDOF) systems with a certain strength. Time history analyses were carried out by using an extensive earthquake ground motion database, which includes a total of 268 far-field records, two horizontal components from 134 recording stations located on firm soil sites. Full article
(This article belongs to the Section Building Structures)
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30 pages, 3473 KB  
Article
The Impact of Ecological Public Art on Public Pro-Environmental Behavior: Evidence from a Serial Multiple Mediation Model
by Suhui Zhang, Ran Tan, Yitong Shen and Dan Wu
Sustainability 2025, 17(22), 10125; https://doi.org/10.3390/su172210125 - 12 Nov 2025
Abstract
This study examines the mechanisms through which ecological public art influences pro-environmental behavior, addressing the urgent challenges of the global ecological crisis and sustainable urban development. Using the 5th Shanghai Urban Space Art Season (SUSAS) as a case study, a serial multiple mediation [...] Read more.
This study examines the mechanisms through which ecological public art influences pro-environmental behavior, addressing the urgent challenges of the global ecological crisis and sustainable urban development. Using the 5th Shanghai Urban Space Art Season (SUSAS) as a case study, a serial multiple mediation model was established, with ecological public art perception as the independent variable, environmental psychological ownership and ecological awareness as mediators, and pro-environmental behavior as the dependent variable. Based on 326 valid responses, structural equation modeling (SEM), which integrates confirmatory factor analysis (CFA) and path analysis, demonstrates that ecological public art perception significantly enhances pro-environmental behavior. Environmental psychological ownership and ecological awareness function not only as independent mediators but also jointly constitute a serial mediation pathway. The findings reveal a multidimensional process whereby ecological public art enhances pro-environmental behavior through “perceptual activation–emotional identification–cognitive enhancement–behavioral transformation”. Building on these insights, the study proposes intervention strategies focusing on multi-sensory integration, emotional narrative, digital technology application, and community-based practices to reinforce the role of ecological public art in urban environmental governance and sustainable development. Overall, this research advances the theoretical understanding of the social functions of public art and offers a valuable perspective for fostering ecological awareness and action. Full article
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34 pages, 6565 KB  
Article
A Finite Element Study of Bimodulus Materials with 2D Constitutive Relations in Non-Principal Stress Directions
by Chao Dong, Fei Wang, Tongtong Wang, Long Zhao, Penghui Qian, Mingfeng Li, Zhenglong Dai and Shan Zeng
Materials 2025, 18(22), 5126; https://doi.org/10.3390/ma18225126 - 11 Nov 2025
Abstract
This paper extends the application of bimodulus elasticity theory by formulating a constitutive relation applicable to non-principal stress directions, building upon the established framework based on principal stresses. The paper develops four full-scale finite element models—the 3-node triangular, the 4-node quadrilateral, the 6-node [...] Read more.
This paper extends the application of bimodulus elasticity theory by formulating a constitutive relation applicable to non-principal stress directions, building upon the established framework based on principal stresses. The paper develops four full-scale finite element models—the 3-node triangular, the 4-node quadrilateral, the 6-node triangular, and the 8-node quadrilateral elements—with the latter two showcasing higher precision in complex stress simulations. This formulation enables a more detailed analysis of material behavior under varying stress states. An effective iterative solution approach is introduced to address the nonlinearity of bimodulus materials, ensuring model convergence and reliability. The accuracy of the model has been verified through rigorous ANSYS 2022 R1 simulations, and the solution results have been compared with those in the existing literature, emphasizing the importance of the tension-to-compression modulus ratio in determining structural displacement and stress distribution. The developed models and methods provide useful numerical tools for the analysis and design of structures incorporating bimodulus materials. Full article
(This article belongs to the Section Materials Simulation and Design)
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27 pages, 388 KB  
Article
Thermodynamics and Nonlocality in Continuum Physics
by Claudio Giorgi and Angelo Morro
Thermo 2025, 5(4), 51; https://doi.org/10.3390/thermo5040051 - 9 Nov 2025
Viewed by 82
Abstract
This paper is devoted to the modelling of nonlocality in continuum physics through constitutive functions that depend on suitable gradients. For definiteness, the attention is addressed to elastic solids, heat conductors, and magnetic solids. Models are developed where both the requirements of the [...] Read more.
This paper is devoted to the modelling of nonlocality in continuum physics through constitutive functions that depend on suitable gradients. For definiteness, the attention is addressed to elastic solids, heat conductors, and magnetic solids. Models are developed where both the requirements of the second law of thermodynamics and the balance equations are satisfied for the constitutive functions that involve gradients of strain, temperature, heat flux, and magnetization. Concerning elastic and magnetic solids, it is shown that, depending on the chosen variables, the standard symmetry property of the stress holds identically. The models so developed are free from any hyperstress tensor frequently considered in the literature. Full article
24 pages, 3428 KB  
Article
Numerical Analysis of Critical Embedment Depth of Offshore Monopile Foundations in Clay
by Ali Khezri, Hongbae Park and Daeyong Lee
J. Mar. Sci. Eng. 2025, 13(11), 2118; https://doi.org/10.3390/jmse13112118 - 8 Nov 2025
Viewed by 195
Abstract
The design of offshore monopile foundations typically follows an iterative process aimed at optimizing key geometric parameters—namely, pile diameter, wall thickness, and embedded length. Among these, selecting an appropriate embedded length is a critical step in geotechnical design, as it must satisfy both [...] Read more.
The design of offshore monopile foundations typically follows an iterative process aimed at optimizing key geometric parameters—namely, pile diameter, wall thickness, and embedded length. Among these, selecting an appropriate embedded length is a critical step in geotechnical design, as it must satisfy both stability and serviceability requirements. The critical pile length is defined as the embedment depth beyond which additional penetration yields no significant improvement in lateral capacity and at which the pile reaches its critical lateral capacity. From a design standpoint, extending the pile beyond this length offers no further gain in resistance, rendering such an approach both inefficient and uneconomical. To evaluate and characterize the critical length of offshore monopile foundations, three-dimensional finite element (3D FE) analyses were performed on laterally loaded monopiles using the NGI-ADP constitutive model. The analyses considered a wide range of pile geometries, load eccentricities, and soil properties. This study first investigate how geotechnical parameters affect lateral response, then characterizes the critical lateral capacity (Hcrit) and critical pile length (Lcrit) based on the analyzed cases. Finally, an empirical equation was developed to estimate the critical embedment depth of monopiles in clay. Results indicate that higher undrained shear strength (Su) or lower ultimate plastic shear strain (γf) considerably reduce the critical pile length, whereas it is increased with greater pile head rotation. The normalized critical length is largely independent of pile diameter and load eccentricity. These insights provide practical guidance for geotechnical design by offering an efficient method to estimate critical pile length, supporting informed decisions on the required embedment depth. Full article
(This article belongs to the Section Ocean Engineering)
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26 pages, 8457 KB  
Article
Low Cyclic Fatigue Properties and Cyclic Constitutive Modeling of SS275 Steel for Seismic Applications
by Hubdar Hussain and Dong-keon Kim
Buildings 2025, 15(21), 3997; https://doi.org/10.3390/buildings15213997 - 5 Nov 2025
Viewed by 200
Abstract
Steel energy dissipation devices are integral to seismic design, as they help reduce structural deformations during strong earthquakes by absorbing and dissipating energy through large inelastic deformations. This research provides new insights into the cyclic behavior and constitutive modeling of carbon steel SS275, [...] Read more.
Steel energy dissipation devices are integral to seismic design, as they help reduce structural deformations during strong earthquakes by absorbing and dissipating energy through large inelastic deformations. This research provides new insights into the cyclic behavior and constitutive modeling of carbon steel SS275, a domestically manufactured material in Korea specifically used for seismic energy dissipation applications. To characterize its mechanical response, monotonic and strain-controlled cyclic loading tests are conducted on nine machined coupons. The cyclic tests are performed under constant strain amplitudes ranging from ±0.5% to ±3.0%. Experimental strain–life data obtained at these amplitudes are used to determine the Coffin–Manson parameters, while the cyclic stress–strain relationship is defined using the Ramberg–Osgood equation. Furthermore, material parameters for the Chaboche nonlinear hardening model are extracted from the experimental results and validated through finite element simulations of coupon tests in ABAQUS, ensuring close agreement with the measured cyclic response. Following the coupon-level analysis, a member-scale test is performed on a buckling-restrained brace (BRB) fabricated from SS275 steel. The calibrated Chaboche parameters are then applied in numerical simulations of the BRB, and the results are compared with experimental data to assess the model’s predictive capability for seismic performance. Full article
(This article belongs to the Special Issue Seismic Performance of Seismic-Resilient Structures)
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19 pages, 11365 KB  
Article
Hot Deformation Behavior and Dynamic Recrystallization Mechanism of GH3230 Superalloy
by Shichong Yuan, Yanhui Liu, Hua Zhang, Hao Li, Qing Li and Jinshan Li
Metals 2025, 15(11), 1220; https://doi.org/10.3390/met15111220 - 4 Nov 2025
Viewed by 292
Abstract
An isothermal hot compression test of GH3230 was carried out under deformation conditions with deformation temperatures ranging from 1020 to 1110 °C and strain rates ranging from 1 to 0.001 s−1. On this basis, the corresponding constitutive equation of the alloy [...] Read more.
An isothermal hot compression test of GH3230 was carried out under deformation conditions with deformation temperatures ranging from 1020 to 1110 °C and strain rates ranging from 1 to 0.001 s−1. On this basis, the corresponding constitutive equation of the alloy was established. ε˙=exp36.123sinh0.00587σ4.7946exp451.507/RT. At the same time, a power dissipation diagram and thermal processing diagram were created. The peak value η can reach 0.36, and the optimum hot working parameter window of the GH3230 superalloy is 1020~1110 °C/0.1~0.001 s−1. The microstructure evolution of the alloy under different conditions was studied by EBSD. With an increase in deformation temperature and a decrease in strain rate, the grain size significantly improved; the average grain size of the GH3230 alloy increased from 16.86 to 35.06 μm, and the degree of recrystallization of the alloy also improved. The maximum recrystallization volume fraction is 75.2%. At low temperature and high strain rate, the recrystallization mechanism of the microstructure is mainly CDRX, and DDRX is the auxiliary mechanism. At high temperature and low strain rate, the main corresponding recrystallization mechanism gradually transforms into DDRX. Full article
(This article belongs to the Special Issue Deformation Behavior and Microstructure Evolution of Alloys)
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21 pages, 2842 KB  
Article
Robust Optimal Reinsurance and Investment Problem Under Markov Switching via Actor–Critic Reinforcement Learning
by Fang Jin, Kangyong Cheng, Xiaoliang Xie and Shubo Chen
Mathematics 2025, 13(21), 3502; https://doi.org/10.3390/math13213502 - 2 Nov 2025
Viewed by 242
Abstract
This paper investigates a robust optimal reinsurance and investment problem for an insurance company operating in a Markov-modulated financial market. The insurer’s surplus process is modeled by a diffusion process with jumps, which is correlated with financial risky assets through a common shock [...] Read more.
This paper investigates a robust optimal reinsurance and investment problem for an insurance company operating in a Markov-modulated financial market. The insurer’s surplus process is modeled by a diffusion process with jumps, which is correlated with financial risky assets through a common shock structure. The economic regime switches according to a continuous-time Markov chain. To address model uncertainty concerning both diffusion and jump components, we formulate the problem within a robust optimal control framework. By applying the Girsanov theorem for semimartingales, we derive the dynamics of the wealth process under an equivalent martingale measure. We then establish the associated Hamilton–Jacobi–Bellman (HJB) equation, which constitutes a coupled system of nonlinear second-order integro-differential equations. An explicit form of the relative entropy penalty function is provided to quantify the cost of deviating from the reference model. The theoretical results furnish a foundation for numerical solutions using actor–critic reinforcement learning algorithms. Full article
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28 pages, 903 KB  
Article
Encourage Online Consumers to Embrace Voice Shopping: Roles of Tasks, Technology, and Individual Characteristics
by Li Wang and SungMin Bae
J. Theor. Appl. Electron. Commer. Res. 2025, 20(4), 293; https://doi.org/10.3390/jtaer20040293 - 1 Nov 2025
Viewed by 396
Abstract
Voice shopping brings consumers convenience and retailers a new channel to reach buyers, which is an important component of online shopping. However, it has received a tepid response recently. Two issues must first be addressed to promote voice shopping: why consumers have a [...] Read more.
Voice shopping brings consumers convenience and retailers a new channel to reach buyers, which is an important component of online shopping. However, it has received a tepid response recently. Two issues must first be addressed to promote voice shopping: why consumers have a low acceptance of voice shopping and how to motivate their use. Since technology is intended to serve practical purposes, it is necessary to achieve a fit among voice shopping, online shopping tasks, and consumers. Accordingly, this study elaborates on fit and integrates the task-technology fit (TTF) theory (for objective fit) and the technology acceptance model (TAM, for subjective fit) to build a research model in which task, technology, and individual characteristics affect fit that will stimulate voice shopping intention. Using Structural Equation Modeling to analyze the data collected from 425 consumers who do not accept voice shopping, the results show that both objective fit and subjective fit can determine voice shopping intention; however, some critical task, technology, and individual characteristics cannot affect either aspect of fit, indicating that consumers still do not believe voice is workable in online shopping. These findings make suggestions for a purposeful upgrade of the voice shopping experience, which helps promote voice shopping and ultimately contributes to the prosperity of online shopping. This study also offers insights into what constitutes fit and its roles in the integrated model of the TTF theory and TAM. Full article
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14 pages, 1559 KB  
Article
Investigating Dew Trends and Drivers Using Ground-Based Meteorological Observations at the Namib Desert
by Sara Javanmardi, Na Qiao, Eugene Marais and Lixin Wang
Atmosphere 2025, 16(11), 1257; https://doi.org/10.3390/atmos16111257 - 31 Oct 2025
Viewed by 281
Abstract
In arid environments such as the Namib Desert, non-rainfall water sources—including dew and fog—constitute indispensable yet understudied components of the regional hydrological cycle. These moisture inputs play a critical role in sustaining ecological functionality and biogeochemical processes, but remain among the least quantified [...] Read more.
In arid environments such as the Namib Desert, non-rainfall water sources—including dew and fog—constitute indispensable yet understudied components of the regional hydrological cycle. These moisture inputs play a critical role in sustaining ecological functionality and biogeochemical processes, but remain among the least quantified facets of desert ecohydrology. The present study investigates multi-year trends in morning dew formation within the Namib Desert, utilizing observations from the Gobabeb–Namib Research Institute between 2015 and 2022. Meteorological data from the Southern African Science Service Centre for Climate and Adaptive Land Management (SASSCAL), in conjunction with direct field observations of dew, were used to develop an empirical equation to estimate dew occurrence. A sensitivity analysis verified the robustness of this formulation, and subsequent validation using field data confirmed its reliability (84.84% accuracy). During this eight-year period, the annual number of days with morning dew decreased from 170 in 2015 to 140 in 2022, representing an overall decline of approximately 18%. However, the total daily dew occurrence across 24 h remained relatively constant, indicating that the observed decline is confined primarily to morning condensation events. Dew formation was most prevalent during the wet season (December–May). Both monthly and annual analyses revealed a discernible declining trend in morning dew occurrence across this hyperarid ecosystem (p < 0.05). This decline corresponded with a gradual increase in both air and soil temperatures (approximately +0.03 °C yr−1) and a slight but consistent decrease in relative humidity (approximately −0.26% yr−1) between 2015 and 2022. The principal drivers of this decline include rising soil and air temperatures and decreasing atmospheric humidity. The analysis further identified an inverse relationship between air temperature and dew formation, implying that climatic warming intensifies evaporative demand and thereby suppresses dew condensation. Random forest analysis identified soil temperature, air temperature, and relative humidity as the most important predictors influencing dew occurrence, whereas wind speed and direction played lesser roles. Collectively, these findings underscore the vulnerability of dew-dependent ecosystems to anthropogenic climate change and highlight the imperative to continue investigating non-rainfall moisture dynamics in desert environments. Full article
(This article belongs to the Special Issue Analysis of Dew under Different Climate Changes)
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13 pages, 3612 KB  
Article
Hot Deformation Behavior and Microstructure Evolution of Mg-9Li-5Al-2Sn-1.5Y (Wt%) Alloy
by Xiaochen Huang, Lin Yuan, Yue Du, Debin Shan and Qijun Li
Metals 2025, 15(11), 1212; https://doi.org/10.3390/met15111212 - 31 Oct 2025
Viewed by 243
Abstract
The hot deformation behavior of the duplex structured Mg-9Li-5Al-2Sn-1.5Y alloy is investigated via hot compression tests in the temperature range of 200–350 °C and strain rate range of 0.001–1 s−1. The flow behavior of the Mg-9Li-5Al-2Sn-1.5Y alloy is defined by hyperbolic [...] Read more.
The hot deformation behavior of the duplex structured Mg-9Li-5Al-2Sn-1.5Y alloy is investigated via hot compression tests in the temperature range of 200–350 °C and strain rate range of 0.001–1 s−1. The flow behavior of the Mg-9Li-5Al-2Sn-1.5Y alloy is defined by hyperbolic constitutive equation. The Zener–Hollomon parameter Z is used in the hyperbolic-sine-type equation to express the relationships between the peak stress, deformation temperature, and strain rate. Dynamic recovery and dynamic recrystallization are the main characteristics that affect deformation behaviors. The activation energy Q is calculated as 127.89 kJ/mol. Based on the dynamic materials model, the processing maps at strains of 0.6 and 0.8 are constructed, and the optimum processing parameters are determined as the temperature range of 320–350 °C and strain rate range of 0.001–0.007 s−1. Full article
(This article belongs to the Special Issue Novel Insights into Wrought Magnesium Alloys)
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17 pages, 1053 KB  
Article
Symmetry-Guided Numerical Simulation of Viscoelastic Pipe Leakage Based on Transient Inverse Problem Analysis
by Tian-Yu Zhang, Ying Xu, Yu-Chao Ma and Jian-Feng Qian
Symmetry 2025, 17(11), 1805; https://doi.org/10.3390/sym17111805 - 26 Oct 2025
Viewed by 311
Abstract
In this study, numerical simulations were performed, and leaks in viscoelastic pipelines were detected. Based on the transient flow equations derived from the continuity and momentum equations, the Kelvin–Voigt model was used to describe the viscoelastic constitutive relationship and derive the strain equation, [...] Read more.
In this study, numerical simulations were performed, and leaks in viscoelastic pipelines were detected. Based on the transient flow equations derived from the continuity and momentum equations, the Kelvin–Voigt model was used to describe the viscoelastic constitutive relationship and derive the strain equation, further establishing a one-dimensional transient flow model for viscoelastic pipelines. A frequency-domain analysis of the transient flow was performed by deriving the Fourier transform and transfer matrix. An inverse problem analysis method for transient flow leak detection was proposed to identify the leak location and rate by minimizing the objective function. To verify the effectiveness of the proposed model, an experimental platform was built, and the pressure head frequency-domain data under working conditions of no leak, experimental leak, and simulated leak were compared. The results showed that the experimental data were consistent with the simulated data under leakage conditions, thus proving that the model was accurate and reliable. Under leak-free conditions, the frequency-domain characteristics of transient pressure waves exhibit significant symmetrical features, whereas when a leak exists in the pipeline, the leak point acts as a localized non-uniform disturbance source, disrupting the symmetry of the frequency-domain characteristics. Moreover, the leak point can be determined by the difference in the peak heights between the no-leak and leak conditions, and the leak parameters can be accurately identified using the inverse problem method. Full article
(This article belongs to the Section Engineering and Materials)
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19 pages, 6718 KB  
Article
Mapping Soil Erosion and Ecosystem Service Loss: Integrating RUSLE and NDVI Metrics to Support Conservation in El Cajas National Park, Ecuador
by Diego Portalanza, Javier Del-Cioppo Morstadt, Valeria Polhmann, Gabriel Gallardo, Karla Aguilera, Yoansy Garcia and Fanny Rodriguez-Jarama
Hydrology 2025, 12(11), 279; https://doi.org/10.3390/hydrology12110279 - 25 Oct 2025
Viewed by 665
Abstract
Mountain protected areas in the tropical Andes experience localized yet severe soil erosion that threatens erosion-regulating services and downstream water–energy security. We mapped soil loss at 30 m using the Revised Universal Soil Loss Equation (RUSLE) and quantified the erosion-control service in El [...] Read more.
Mountain protected areas in the tropical Andes experience localized yet severe soil erosion that threatens erosion-regulating services and downstream water–energy security. We mapped soil loss at 30 m using the Revised Universal Soil Loss Equation (RUSLE) and quantified the erosion-control service in El Cajas National Park, Ecuador (28,544 ha) using an NDVI-based index. Replacing categorical land cover C factors with a continuous NDVI surface increased the park-wide soil loss estimate by ∼58%, yielding an area-weighted mean of 5.3 t ha−1 yr−1 and local maxima of 120 t ha−1 yr−1 on steep and sparsely vegetated escarpments. Relative to a bare soil scenario, existing páramo grasslands, shrub mosaics, and scattered Polylepis woodlots avert 95% of potential erosion, quantifying the service supplied by vegetation. Between 2023 and 2024, a ∼60% rise in mean NDVI more than doubled the area delivering moderate-to-high erosion control. A hot-spot analysis further identified ∼30 km2 (≈5% of the park) where high modeled soil loss coincides with low protection; these clusters generate ∼80% of predicted sediment and constitute priority targets for restoration or visitor use regulation. The integrated RUSLE–NDVI–EC approach provides a concise and transferable screening tool for aligning conservation investments with Ecuador’s restoration pledges and for safeguarding critical hydrological services in Andean protected areas. Full article
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20 pages, 1574 KB  
Article
Analysis of Torsional Vibration of Single Pile in Orthotropic Layered Soil
by Zixin Lian, Yanzhi Zhu and Yongzhi Jiu
Buildings 2025, 15(21), 3834; https://doi.org/10.3390/buildings15213834 - 23 Oct 2025
Viewed by 282
Abstract
To address the difficulty in obtaining analytical solutions for the torsional vibration response of pile foundations in orthotropic layered soil foundations subjected to torsional excitation at the pile top, this study investigates a layered recursive algorithm based on the Hankel transform. An integral [...] Read more.
To address the difficulty in obtaining analytical solutions for the torsional vibration response of pile foundations in orthotropic layered soil foundations subjected to torsional excitation at the pile top, this study investigates a layered recursive algorithm based on the Hankel transform. An integral transformation method is employed to reduce the dimensionality of the coupled pile–soil torsional vibration equations, converting the three-dimensional system of partial differential equations into a set of ordinary differential equations. Combining the constitutive properties of transversely anisotropic strata with interlayer contact conditions, a transfer matrix model is established. Employing inverse transformation coupled with the Gauss–Kronrod integration method, an explicit frequency-domain solution for the torsional dynamic impedance at the pile top is derived. The research findings indicate that the anisotropy coefficient of the foundation significantly influences both the real and imaginary parts of the impedance magnitude. The sequence of soil layer distribution and the bonding state at interfaces jointly affect the nonlinear transmission characteristics of torque along the pile shaft. Full article
(This article belongs to the Section Building Structures)
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