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Groundwater withdrawal can cause localized and rapid poroelastic subsidence, spatially broad elastic uplift of low amplitude, and changes in the gravity field. Constraining groundwater loss in Mexico City, we analyze data from the Gravity Recovery and Climate Experiment and its follow‐on mission (GRACE/FO) and Synthetic Aperture Radar (SAR) Sentinel‐1A/B images between 2014 and 2021. GRACE/FO observations yield a groundwater loss of 0.85–3.87 km3/yr for a region of ∼300 × 600 km surrounding Mexico City. Using the high‐resolution interferometric SAR data set, we measure >35 cm/yr subsidence within the city and up to 2 cm/yr of uplift in nearby areas. Attributing the long‐term subsidence to poroelastic aquifer compaction and the long‐term uplift to elastic unloading, we apply respective models informed by local geology, yielding groundwater loss of 0.86–12.57 km3/yr. Our results suggest Mexico City aquifers have been depleting at faster rates since 2015, exacerbating the socioeconomic and health impacts of long‐term groundwater overdrafts. Plain Language Summary Groundwater overdraft in Mexico City results from excessive freshwater demand and unsustainable water resource management in a subtropical environment with warm summers and dry winters. Groundwater depletion can result in ground surface deformation and changes in the gravity field, observable by Sentinel‐1 and GRACE satellites. Here, we examine data from both satellite missions between November 2014 and October 2021 to determine groundwater volume loss. Using GRACE, which has a footprint of ∼350 km, we quantify groundwater volume loss to a rate of 0.85–3.87 km3 per year in the broader area surrounding Mexico City. Analysis of high‐resolution Sentinel‐1 synthetic aperture radar images shows land sinks at a rate of 35 cm/yr within the city and surrounding areas uplifts at a rate of ∼2 cm/yr. While the subsidence is a consequence of aquifer compaction, the uplift represents an elastic unloading response of the Earth's crust to water mass loss. Using geophysical models informed by local geology, we show that the region loses groundwater at rates of 0.86–12.57 km3/yr. Our results emphasize the need for groundwater monitoring in Mexico City to assist with managing freshwater resources. Key Points A subsidence rate of >35 cm/yr within Mexico City, surrounded by ∼2 cm/yr of uplift, is observed using space‐borne synthetic aperture radar Groundwater loss of 0.86–12.57 km3/yr in Mexico City causes poroelastic subsidence, a broad‐scale elastic uplift, and gravity field change Mexico City aquifers have been depleting at least since 2015, exacerbating groundwater overdrafts' socioeconomic and health impacts

This study investigates the sectional loads on an elastic semi-submersible platform for a 2 MW FOWT (floating offshore wind turbine) used in the Fukushima demonstration project. A water tank test is firstly carried out with an elastic model to study the dynamic responses and sectional loads of the platform in regular and irregular waves. Numerical simulations are then performed using multiple hydrodynamic bodies connected by elastic beams. The dynamic responses of the elastic model are compared to those of a rigid model to clarify the influence of the structural stiffness on the platform motion and mooring tension. The predicted sectional loads on the deck, brace and pontoon by the proposed nonlinear hydrodynamic models show good agreement with the experimental data obtained from the water tank test and a simplified formula is proposed to evaluate the distribution of the moments on the platform. Finally, the structural optimization of the elastic semi-submersible platform is conducted. The sectional moments and fatigue loadings on the pontoons are significantly reduced using the strut between the pontoons since the horizontal wave loads on the side column are dominant and the vertical wave loads acting on the platform are relatively small due to the deep draft.

The response of a floating elastic plate to the motion of a moving load is studied using a fully dispersive weakly nonlinear system of equations. The system allows for an accurate description of waves across the whole spectrum of wavelengths and also incorporates nonlinearity, forcing and damping. The flexural–gravity waves described by the system are time-dependent responses to a forcing with a described weight distribution, moving at a time-dependent velocity. The model is versatile enough to allow the study of a wide range of situations including the motion of a combination of point loads and loads of arbitrary shape. Numerical solutions of the system are compared to data from a number of field campaigns on ice-covered lakes, and good agreement between the deflectometer records and the numerical simulations is observed in most cases. Consideration is also given to waves generated by a decelerating load, and it is shown that a decelerating load may trigger a wave response with a far greater amplitude than a load moving at constant celerity.

The contact properties of the screw-nut pair play a decisive role in the wear rate and service life of ball screws. The difficulty of the ball contact loads directly detected has resulted in the development of many flexible contact models to predict what happens inside the ball screw during its working process. However, few contact models account for nut flexibility when axial load is applied. This article proposes a screw-nut pair contact model with the flexible screw and nut, which are modeled as elastic beams with axial deformations. The geometric relationship of the centers of the raceways and balls is used to describe the variation of the contact loads with the positions of the balls. Effects of the axial, transverse, and torsional deformations of the screw and nut and the geometric error of balls on centers of the raceways and balls are taken into account in the model. For the dynamic model of the feed system, the screw is considered a continuum rod, while the worktable and bearings are treated as lamped masses. The effect of the contact stiffness of the screw-nut pair on the axial and torsional vibration modes of the screw is investigated using a numerical simulation. Moreover, the influences of the worktable position on vibration modes of the feed systems are discussed for the screw with fixed-free and fixed–fixed support modes, respectively. The load-deformation and dynamic experiments are conducted to verify the effectiveness of the proposed models.

This paper investigates the time-dependent behavior of plates resting on a Pasternak elastic foundation affected by moving loads, employing the principles of the first-order shear deformation theory (FSDT). By limiting the analysis to first-order shear deformation, FSDT requires fewer degrees of freedom, making the analysis less resource-intensive compared to 3D models. The time-dependent responses of the plate on the elastic foundation were evaluated applying the Newmark direct integration method. For computational analysis, the finite element method with a serendipity (8-node) plate element is applied because the foundation equation requires second-order derivatives of the Laplace operator, and is implemented using MATLAB. Initial validation is conducted by comparing the current results with analytical approaches to demonstrate the dependability and precision of the approach. Following this, numerical examples are illustrated to illustrate the impact of various factors, covering changes in thickness and foundation properties, moving loads, velocities, and effect of boundary conditions on the behavior of the plate. The outcomes show reliable convergence, aligning well with existing research findings. These insights are applicable in numerous engineering applications involving plates on elastic foundations and provide benchmarks for future studies.

The interaction between the flow in a channel with an obstruction on the bottom and an elastic sheet representing the ice covering the liquid is considered for the case of steady flow. The mathematical model based on the velocity potential theory and the theory of thin elastic shells fully accounts for the nonlinear boundary conditions at the elastic sheet/liquid interface and on the bottom of the channel. The integral hodograph method is employed to derive the complex velocity potential of the flow, which contains the velocity magnitude at the interface in explicit form. This allows one to formulate the coupled ice/liquid interaction problem and reduce it to a system of nonlinear equations in the unknown magnitude of the velocity at the interface. Case studies are carried out for a semi-circular obstruction on the bottom of the channel. Three flow regimes are studied: a subcritical regime, for which the interface deflection decays upstream and downstream; an ice supercritical and channel subcritical regime, for which two waves of different lengths may exist; and a channel supercritical regime, for which the elastic wave is found to extend downstream to infinity. All these regimes are in full agreement with the dispersion equation. The obtained results demonstrate a strongly nonlinear interaction between the elastic and the gravity wave near the first critical Froude number where their lengths approach each other. The interface shape, the bending moment and the pressure along the interface are presented for wide ranges of the Froude number and the obstruction height.

Up to the beginning of the twenty-first century, most of quasi-brittle structures, in particular the ones composed by concrete or masonry frames and walls, were designed and built according to codes that totally ignored fracture mechanics theory. The structural load capacity predicted by strength-based theories, such as plastic analysis and limit analysis, do not exhibit size-effect. Within the framework of fracture mechanics theory, this paper deals with the analysis of the effect of non proportional loadings on the strength reduction with the structural scaling. In particular, this study investigates the size-effect of quasi-brittle materials subjected to self-weight. Although omnipresent, gravity-load is often considered negligible in most studies in the field of fracture mechanics. This assumption is obviously not valid for large structures and in particular for geometries in which the dead load is a major driving force leading to fracture and structural failure. In this study, an analytical formulation expressing the relation between the strength-reduction and the structural scaling and accounting for self-weight, was derived for both notched and unnotched bodies. More specifically, a closed form expression for size and self-weight effects was first derived for notched specimens from equivalent linear elastic fracture mechanics. Next, equivalent linear elastic fracture mechanics theory being not applicable to unnotched bodies, a cohesive model formulation was considered. Particularly, the cohesive size effect curve and the generalized cohesive size effect curves, originally obtained via cohesive crack analysis for weightless bodies with sharp and blunt/unnotched notches, respectively, were equipped of an additional term to account for the effect of gravity. All the resulting formulas were compared with the predictions of numerical simulation resulting from the adoption of the Lattice Discrete Particle Model. The results point out that the analytical formulas match very well the results of the numerical model for both notched and unnotched samples. Furthermore, the analytical formulas predict a vertical asymptote for increasing size, in the typical double-logarithm strength versus structural size representation. The asymptote corresponds to a characteristic size at which the structure fails under its own weight. For large structural sizes approaching this characteristic size, the newly developed formulas deviate significantly from previously proposed size-effect formulas. The practical relevance of this finding was demonstrated by analyzing size and self-weight effect for several quasi-brittle materials such as concrete, wood, limestone and carbon composites. Most importantly, the proposed formulas were applied to the failure of semi-circular masonry arches under spreading supports with different slenderness ratios. Results show that analytical formulas well predict numerical simulations and, above all, that for vaulted structures it is mandatory accounting for the effect of self-weight.

Mechanical behavior and energy evolution of rock around the tunnel are critical for evaluating the instability of geotechnical engineering. To reveal the influence of tunnel section shape on deformation, stress distribution, and fracturing mechanism of rock around the tunnel, a series of physical model shear tests for rock around prefabricated rectangular and circular tunnels were carried out, and corresponding fracturing and energy evolution analysis were also presented. In the shear test, the cracking evolution of rock around tunnel specimens was monitored and recorded by a high-speed camera and acoustic emission monitor to reveal the macro- and meso-fracture features. In addition, to examine the continuous-discontinuous shear process, four typical numerical models of rock around the tunnel were exploited to explore meso-mechanical behavior and fracturing mechanism. In light of the first law of thermodynamics, energy conversion process, damage characteristics and rockburst tendency of rock around tunnel specimens were investigated. The test results manifested that fracturing evolution, energy characteristic conversion, and micro-cracks evolution of rock around tunnel specimens generally were classified as four unified stages. In terms of fracturing evolution, rock around tunnel specimens experienced shearing compression stage (stage I), elastic stage (stage II) dominated by crack initiation, shearing fracture stage (stage III) dominated by crack propagation, coalescence and shear-induced rockburst, and shearing friction stage (stage IV). In the aspect of energy characteristic conversion, rock around tunnel specimens were mainly elastic deformation before peak shearing load, and the plastic deformation was relatively small. Partial dissipated strain energy acted on closing hole and crack initiation, and the rest was stored as elastic strain energy. After peak shearing load, the shear strength dropped rapidly, and a large amount of strain energy was converted into dissipated strain energy for crack propagation, coalescence and shear-induced rockburst. In the evolution of micro-cracks, the specimens underwent crack quiet period (stage I), crack initial increase stage (stage II), crack rapid increase stage (stage III), and crack stable stage (stage IV). Interestingly, the damage stress and rockburst tendency of rock around prefabricated rectangular tunnels were superior to those of rock around prefabricated circular tunnels, indicating that the bearing capacity of rock around prefabricated rectangular tunnels was superior to that of rock around prefabricated circular tunnels, related to the deviatoric stress distribution and confining pressure. In addition, a novel impact tendency index (Sp et) was presented for evaluating shear-induced rockburst tendency, which carved the proportional relationship between elastic strain energy and dissipative strain energy at peak shearing load. The research results were conducive to recognize the fracturing mechanism of rock around a tunnel subjected to shear condition and provided a theoretical basis for the prevention and control of geotechnical engineering.HighlightsShear characteristic, energy characteristic conversion and micro-cracks number evolution of rock around tunnel specimens generally were classified as four unified stages.Bearing capacity of rock around a prefabricated rectangular tunnel was superior to that of rock around a prefabricated circular tunnel, related to the deviatoric stress distribution and confining pressure.A novel damage variable was proposed to quantify the damage degree of rockA novel impact tendency index (Sp et) was presented for evaluating the shear-induced rockburst tendency

This paper aims to investigate the size scale effect on the buckling and post-buckling of single-walled carbon nanotube (SWCNT) rested on nonlinear elastic foundations using energy-equivalent model (EEM). CNTs are modelled as a beam with higher order shear deformation to consider a shear effect and eliminate the shear correction factor, which appeared in Timoshenko and missed in Euler–Bernoulli beam theories. Energy-equivalent model is proposed to bridge the chemical energy between atoms with mechanical strain energy of beam structure. Therefore, Young’s and shear moduli and Poisson’s ratio for zigzag (n, 0), and armchair (n, n) carbon nanotubes (CNTs) are presented as functions of orientation and force constants. Conservation energy principle is exploited to derive governing equations of motion in terms of primary displacement variable. The differential–integral quadrature method (DIQM) is exploited to discretize the problem in spatial domain and transformed the integro-differential equilibrium equations to algebraic equations. The static problem is solved for critical buckling loads and the post-buckling deformation as a function of applied axial load, CNT length, orientations and elastic foundation parameters. Numerical results show that effects of chirality angle, boundary conditions, tube length and elastic foundation constants on buckling and post-buckling behaviors of armchair and zigzag CNTs are significant. This model is helpful especially in mechanical design of NEMS manufactured from CNTs.

In this paper, the time-dependent properties of the elastic modulus of fly ash concrete under sustained compressive load were studied. An experiment was conducted and showed an increment of elastic modulus for two types of fly ash concrete (20% and 40% fly ash replacement) under sustained load. The mechanisms of this increment were analyzed, and two Representative Volume Elements (RVEs) were established to represent the micro-heterogeneous space of binder and concrete based on continuum mechanics. The shrinking core models of hydration and pozzolanic reaction were adopted to quantify the volume fraction of each phase within the binder RVE. A prediction model was proposed by incorporating the effects of extra hydration and time-dependent aggregate concentration rate under sustained load. Finally, parameter analysis including the influences of initial loading age and the loading level was conducted.