“… Figure 3 ( a ) Shows the 2D triangular mesh element with three nodes showing six deformations, 3 in each direction. ( b ) shows the schematic diagram of classical creep 72 . …”
A promising option for storing large-scale quantities of green gases (e.g., hydrogen) is in subsurface rock salt caverns. The mechanical performance of salt caverns utilized for long-term subsurface energy storage plays a significant role in long-term stability and serviceability. However, rock salt undergoes non-linear creep deformation due to long-term loading caused by subsurface storage. Salt caverns have complex geometries and the geological domain surrounding salt caverns has a vast amount of material heterogeneity. To safely store gases in caverns, a thorough analysis of the geological domain becomes crucial. To date, few studies have attempted to analyze the influence of geometrical and material heterogeneity on the state of stress in salt caverns subjected to long-term loading. In this work, we present a rigorous and systematic modeling study to quantify the impact of heterogeneity on the deformation of salt caverns and quantify the state of stress around the caverns. A 2D finite element simulator was developed to consistently account for the non-linear creep deformation and also to model tertiary creep. The computational scheme was benchmarked with the already existing experimental study. The impact of cyclic loading on the cavern was studied considering maximum and minimum pressure that depends on lithostatic pressure. The influence of geometric heterogeneity such as irregularly-shaped caverns and material heterogeneity, which involves different elastic and creep properties of the different materials in the geological domain, is rigorously studied and quantified. Moreover, multi-cavern simulations are conducted to investigate the influence of a cavern on the adjacent caverns. An elaborate sensitivity analysis of parameters involved with creep and damage constitutive laws is performed to understand the influence of creep and damage on deformation and stress evolution around the salt cavern configurations. The simulator developed in this work is publicly available at https://gitlab.tudelft.nl/ADMIRE_Public/Salt_Cavern.
“… Figure 3 ( a ) Shows the 2D triangular mesh element with three nodes showing six deformations, 3 in each direction. ( b ) shows the schematic diagram of classical creep 72 . …”
A promising option for storing large-scale quantities of green gases (e.g., hydrogen) is in subsurface rock salt caverns. The mechanical performance of salt caverns utilized for long-term subsurface energy storage plays a significant role in long-term stability and serviceability. However, rock salt undergoes non-linear creep deformation due to long-term loading caused by subsurface storage. Salt caverns have complex geometries and the geological domain surrounding salt caverns has a vast amount of material heterogeneity. To safely store gases in caverns, a thorough analysis of the geological domain becomes crucial. To date, few studies have attempted to analyze the influence of geometrical and material heterogeneity on the state of stress in salt caverns subjected to long-term loading. In this work, we present a rigorous and systematic modeling study to quantify the impact of heterogeneity on the deformation of salt caverns and quantify the state of stress around the caverns. A 2D finite element simulator was developed to consistently account for the non-linear creep deformation and also to model tertiary creep. The computational scheme was benchmarked with the already existing experimental study. The impact of cyclic loading on the cavern was studied considering maximum and minimum pressure that depends on lithostatic pressure. The influence of geometric heterogeneity such as irregularly-shaped caverns and material heterogeneity, which involves different elastic and creep properties of the different materials in the geological domain, is rigorously studied and quantified. Moreover, multi-cavern simulations are conducted to investigate the influence of a cavern on the adjacent caverns. An elaborate sensitivity analysis of parameters involved with creep and damage constitutive laws is performed to understand the influence of creep and damage on deformation and stress evolution around the salt cavern configurations. The simulator developed in this work is publicly available at https://gitlab.tudelft.nl/ADMIRE_Public/Salt_Cavern.
“…More details about the line-search technique and iterative procedures can be found elsewhere. 47,48 Figure 4 shows the comparison between the numerical and experimental load-deflection responses. The peak load obtained by the simulation was 156.6 kN, while the load obtained in test was 148 kN.…”
This paper describes a numerical study of the punching shear resistance of unbonded post-tensioned slabs without shear reinforcement. This research aimed to develop a methodology for modeling unbonded tendons and numerically evaluate the prestressing effects on the punching shear capacity. To validate the modeling approach, a series of well documented experimental tests were simulated using the finite element software DIANA. The nonlinear analyses were performed using three-dimensional solid elements, incorporating the cracking behavior of concrete by the smeared crack approach. In addition, interface elements were included, providing bond-slip properties to simulate the friction between tendons and concrete. A good agreement was found between the numerical results and experimental data. Load capacity, cracks patterns, and the prestressing effects were accurately simulated. After the validation, a parametric study was conducted to analyze the influence of distribution, force and profile of prestressing tendons. Finally, the numerical results were compared with current design code provisions and the approach provided by the Critical Shear Crack Theory.
“…It is noted that the Newton–Raphson iterative method is used to solve the non‐linear governing equations. Therefore, Equation is linearized to obtain the tangent stiffness matrix, and consequently, the quadratic convergence in the Newton–Raphson iterative solution can be attained . The Newton equation is written as where K T,p is the tangent matrix, is the internal load vector whereas f ext corresponds to the external load vector.…”
SUMMARYThe production of new composite laminates with variable stiffness within the surface of plies was enabled by tow-placement machines. Because of the variation of stiffness, these materials are called variable stiffness composite laminates (VSCL). Recently, many attempts were made to investigate their structural behaviour. In this contribution, a first-order shear deformation theory is selected to model the multilayered composite laminates. The adopted theory is enhanced by the extended finite element method (XFEM) to describe discontinuities at element level of any interface of interest. To predict the location of the delamination onset, a traction-separation law is developed that is consistent with the XFEM topology. An exponential softening behaviour is implemented within the interface to model the delamination growth in a mixed-mode direction. In order to solve the non-linear equations of the delamination propagation, an arc-length method is applied. The effect of the curvilinear fibre orientation on the location of the delamination onset is investigated. Subsequently, the structural response of the laminates is computed. According to the simplicity of the new approach using the XFEM; and based on the computational cost for calculating the stiffness of VSCL, the method is able to determine structural response of VSCL with less computational effort.
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