Semi-analytical Finite Element Method Research Articles

Propagation characteristics of circumferential feature guided waves propagation in a revolved topological waveguide

In our previous research, propagation characteristics and combined harmonic generation of feature guided waves (FGWs) in welded joints of plate structure, were analyzed theoretically and observed numerically. Circumferential ultrasonic guided waves find extensive applications in assessing rotating structures, highlighting the importance of investigating the propagation characteristics of circumferential feature guided waves (CFGWs) in such revolved topological waveguides. In this study, propagation characteristics of CFGW in revolved topological waveguides are investigated. Semi-analytical finite element (SAFE) method in conjunction with a perfectly matched layer (PML) within a cylindrical coordinate system is used to explore the modal and dispersion characteristics of CFGWs. Second-harmonic generation (SHG) of CFGWs is further analyzed and discussed both in theoretical and numerical manner. Cumulative SHG of selected CFGW mode pairs, propagation in the welded joint of the revolved topological waveguide, is observed successfully. The obtained results demonstrate that the energy trapping effect of CFGWs in the welded joint of revolved topological waveguide amplifies the generation of cumulative second harmonics, thereby enhancing the measurability of SHG of CFGW. This investigation reveals the potential of damage assessment in revolved topological waveguides by CFGWs.

Determination of Young’s Modulus of PET Sheets from Lamb Wave Velocity Measurement

BackgroundThe elastic modulus of polyethylene terephthalate (PET) sheets is typically measured through destructive tests that require specific sample preparation and time-consuming testing procedures.ObjectiveTo improve the efficiency of measuring the elastic modulus of PET sheets, research on a non-destructive measurement approach using guided Lamb waves was conducted.MethodsIn this approach, the group velocity of the zero-order symmetric Lamb wave mode (S0 mode) at a single frequency is first measured from PET sheets. The semi-analytical finite element method (SAFEM) is used as the forward model to calculate the corresponding numerical group velocity. Particle swarm optimisation (PSO) is used to update the elastic modulus in the SAFEM model until the numerical group velocity from the model matches the experimental results.ResultsThe results show that measuring the group velocity data at a single frequency is sufficient for elastic modulus measurement while the material thickness can be assumed as a constant, which improves the efficiency of the measurement. The identified modulus differs from the tensile modulus of the material due to the frequency dependence of the elastic modulus. However, this discrepancy could be eliminated by using a linear regression model.ConclusionsThe method mentioned above can achieve non-destructive and efficient measurement of the elastic modulus of PET sheets, which can potentially be applied for in-line quality inspection in PET bottle production processes.

Guided wave-based crack detection in U-shaped flexural plate butt welds

Based on the guided wave, a crack detection method for U-shaped flexural plate (UFP) butt welds is established to realize damage localization and quantitative identification. Firstly, the semi-analytical finite element (SAFE) method was used to obtain the dispersion curve in a plate with weld by discretizing the cross-section and then solving the characteristic equation. Subsequently, numerical studies were performed to investigate the mode conversion and energy transfer efficiency in weld bending. Then the method was determined after the wave packet analysis of voltage responses under different damage conditions. Finally, a validation experiment was conducted in an actual UFP butt weld. The result indicates that there exist 10 guided wave modes in a plate with weld at 150 kHz, while only 2 modes in a flat plate; For curvature radius of weld bending substantially greater than the weld thickness, the guided wave energy mainly passes through the bending in the form of transmitted waves and the reflected wave formed in the bending can be ignored; The damage can be located with the defect echo of the specific guided wave and the error distance only accounting for 1.5% of the total weld length. It is effective to take wavelet energy as an indicator to characterize the damage degree. The method significantly improves crack detection efficiency and provides a scientific basis for monitoring similar structures.

Exciting and Detecting Higher-Order Guided Lamb Wave Modes in High-Density Polyethylene Structures Using Ultrasonic Methods.

High-density polyethylene (HDPE) pipes are becoming increasingly popular, being used in various fields, such as construction, marine, petroleum, water transfer, process water, methane gas collection, oil and gas gathering, gas distribution systems, mining, acid and wet gas lines, offshore oil and gas and in nuclear power plants. Higher-order guided Lamb wave (UGW) modes can be used to detect various defects in complex structures. We will apply this methodology to one of the types of plastic-the structure of high-density polyethylene (HDPE). However, the excitation of UGW modes faces numerous challenges, especially when there is a need to identify which mode is excited. It is essential to note that, in the higher frequency range, multiple different higher-order modes can usually be excited. This can make it difficult to determine which modes have actually been excited. The objective of this research was to successfully excite and receive various higher-order UGW modes in high-density polyethylene structures using both ultrasonic single-element transducers and a phased array. Theoretical calculations were performed using a variety of methods: semi-analytical finite element (SAFE) method, 2D spatial-temporal spectrum analysis and finite element modeling (FEM). The results obtained from both measurements and simulations clearly demonstrate the possibility of efficiently exciting and receiving different Lamb wave modes possessing different phase velocities.

Prediction of critical strains of flexible pavement from traffic speed deflectometer measurements

Structure indicators of flexible pavements can be categorized into material moduli, deflections, distresses, or responses. Since field measurements of pavement responses, such as strains and stresses, require embedded sensors, predictions from easily measured surface deflections are desired. This study aims to predict critical strains of flexible pavements from traffic speed deflectometer (TSD) measurements. Semi-analytical finite element method (SAFEM) was developed and validated for simulation of truck-pavement system by comparison with traditional three-dimensional (3-D) FEM. Results indicated that SAFEM saved significant calculation time while ensuring the same accuracy. The efficient advantage makes it possible to develop an extensive databased of TSD measurement considering a wide rangte of pavement layer thickness, material moduli, temperature, and speed. Traditional regression analysis and artificial neural networks (ANN) models were applied to predict critical tensile, shear, and compressive strains from surface deflection parameters. The developed models were further validated with field measurements. The regression models with explicit forms are easier to understand but require asphalt layer thickness as an input for prediction of tensile or shear strains. Nevertheless, the ANN model offers greater accuracy and only requires the inputs of TSD-measured deflection slopes, which is more applicable for pavement management applications.

SOLUTION OF PHYSICALLY NONLINEAR PROBLEMS OF DEFORMATION OF MASSIVE AND THIN-WALLED PRISMATIC BODIES

The results of a numerical study on test examples of the convergence of the developed version of the semi-analytical method of finite elementsare presented. A comparison of machine time and accuracy of solving elastic and plastic problems obtained on the basis of finite elements with variableand averaged mechanical parameters was performed.The convergence of the finite element method and the semianalytical finite element method in the calculation of prismatic bodies loaded with localized and distributed external influences was studied. An effective numerical approach to the study of arbitrarily loaded massive and thin-walled prismatic bodies of complex shape, the deformation of which can pass beyond theelastic limit of the material, is being developed based on the finite element moment scheme and the semianalytical variant of the finite element method. Due to the representation of displacements by polynomials and the use of iterative methods of solving systems of equations, this approach is developed in relation to the calculation of objects with arbitrary boundary conditions on the ends, which made it possible to expand the area of effective application of the semi-analytical method of finite elements to a new class ofproblems.A number of new complex problems of elastic and elastic-plastic deformation of massive and thinwalled prismatic bodies, which have an independentapplied value, have been solved.

Quantitative assessment of corrosion-induced wall thinning in L-shaped bends using ultrasonic feature guided waves

The utilization of L-shaped bends has become widespread due to their versatility and ease of application in various industrial fields. Nevertheless, the geometric configuration of these bends makes them susceptible to stress concentration in the bending zone, which can lead to wall thinning caused by accelerated corrosion. This poses a profound challenge to the bearing capacity and reliability of L-shaped bends and highlights the urgent necessity for an effective technique to assess corrosion-induced wall thinning in the bending zone. In this study, we propose a nondestructive testing (NDT) method based on ultrasonic feature guided waves (FGWs) for the evaluation of local corrosion-induced wall thinning in L-shaped bends. Propagation characteristics of FGWs in L-shaped bends were analyzed using the semi-analytical finite element (SAFE) method and perfectly matched layer (PML) technique. Time-reversal (TR) method was employed to address the dispersion and multi-modes phenomenon of the selected guided wave modes and improve the signal-to-noise ratio (SNR) of measured FGW signals. Enhanced SNR of two types of FGW modes signals at different frequencies were verified by experimental and numerical results. Obtained results reveal that FGWs can effectively detect corrosion-induced wall thinning inside L-shaped bends, with improving the signal reflection coefficient by TR method.

Determination of internal efforts in the base finite elements of SAFEM

The principles of calculating the internal efforts of a circular finite element in the semi-analytical finite element method (FEM) based on the obtained components of the stress tensor and the peculiarities of the approach associated with the use of the moment scheme of the finite element (FEM) are considered. Formulas for determining longitudinal, shear forces, bending and torque moments have been obtained.
 A special place, among the variety of objects considered with the help of analytical and numerical methods, is occupied by bodies of revolution of complex shape and cross-sectional structure, formed by the movement of some creative surface along a closed or opened line without breaks. The selected geometric class is used as natural structures of nodes and details in construction of mechanical engineering. The sufficiently wide distribution of the specified forms in the construction and machine-building industries, on the one hand, and the possibility of significantly simplifying the solving relationships by taking into account their geometric features, on the other hand, provide a basis for the development and use of various modifications of the finite element method (FEM). The semi-analytical finite element method (SAFEM) is one such approach that has gained widespread use for solving problems whose objects are prismatic bodies and bodies of revolution of complex shape and cross-sectional structure. Due to the introduction of additional hypotheses that do not reduce the accuracy of the approximation, the representation of deformations and stresses in physical terms and in accordance with the moment scheme of the finite element (MSFE), on the one hand, it is possible to avoid the time-consuming procedure of numerical integration over the cross-sectional area of the finite element (FE), on the other hand - maintain the high efficiency of 3D discretization.
 Despite the large number of publications devoted to the semi-analytical method of finite elements, the question of determining internal forces, which are often component factors of the strength criteria laid down in state building codes, is inappropriately neglected. The use of SAFEM in combination with МSFЕ creates some mathematical features of calculating internal longitudinal, shearing forces and moments.

Analysis of structures with arbitrary kinematic boundary conditions by the semi-analytical finite element method

The successful application of FEM to the analysis of structures is largely due to the efficiency of the use of modern software packages, in connection with which the role of program systems that implement the solution process increases. The correct organization of the computing complex, the choice of optimal algorithms for solving systems of linear and nonlinear equations largely determine the possibilities of the method in terms of the structural complexity of the objects under consideration, the accuracy of the results obtained, and the complexity of setting nonlinear problems. Therefore, there is an increased interest in the development of fairly universal computing complexes based on FEM. One of the effective software complexes is the "Strength" system, designed to conduct comprehensive research in the field of mechanics of a deformable solid, the basic principles of construction of which are used in this work in the implementation of a semi-analytical version of the FEM.
 In this work, solutions of a significant number of control problems of deformation of massive and thin-walled prismatic bodies under different boundary conditions and loads are obtained. In the process of solving new problems, the estimation of the convergence of results was carried out on the basis of a sequential increase in finite elements and contained terms of decomposition, an increase in the accuracy of systems of linear and nonlinear equations, and the accuracy of satisfaction with natural boundary conditions was checked. The developed effective method for solving new complex problems of deformation of prismatic bodies is implemented in the form of complex programs and can be used in design and construction practice in construction, mechanical engineering and other fields of technology.

Implementation and analysis of viscoelastic damping in a 2D + 1D model of railway track vibrations

One of the most important technological challenges in the railway context nowadays is reducing the noise produced by the interaction between the train wheels and the track surface, that is the rolling noise. Introducing viscoelastic damping in the railway structure is one method to mitigate this rolling noise. In the paper, we investigate the impact of damping in the vibrational response of railway tracks using different viscoelastic models and parameters available in the literature. For this purpose, the main focus here is on developing an advanced numerical model in which viscoelastic models representing the rail foundation and/or pad are implemented in the framework of the Semi-Analytical Finite Element (SAFE) method. Linear or nonlinear viscoelastic models are considered, compared and effectively implemented for accelerance computation. The obtained numerical strategy leads to affordable and accurate predictions on dynamic features of the railway structure compared to classical methods.

Investigation of energy trapping effect for nonlinear guided waves in a topographical structure

Cumulative second harmonic generation (SHG), where the amplitude of the generated second harmonic increases with propagation distance, is commonly utilized to enhance the measurability of nonlinear guided waves by providing a sufficient signal-to-noise ratio. Investigating and confirming the cumulative SHG of feature guided waves (FGWs) in topographical waveguides is crucial for accurately assessing material nonlinearity in such structures. This study examines the cumulative SHG of FGWs propagating in a typical topographic structure of a welded joint through both numerical simulations and experimental investigations. A theoretical model is developed using the semi-analytical finite-element (SAFE) method and perfectly matched layer (PML) to analyze the propagation characteristics of FGWs in a welded joint. The numerical and experimental results provide verification of the “trapping effect” of FGWs within the welded joint. Furthermore, the “cumulative effect” of SHG of FGWs is observed. Remarkably, both the experimental and numerical findings demonstrate that cumulative SHG of FGWs can be achieved by employing suitable mode selection and frequency tuning in the topographic structure, which aligns well with the theoretical predictions. This investigation contributes to advancing our understanding of cumulative SHG in FGWs propagated within topographical structures. These findings have practical implications for accurately characterizing material nonlinearity in topographic waveguides.

Flood impact on structural response of asphalt pavement: A finite element modeling approach

The frequency and intensity of floods have increased due to climate change. These natural events negatively affect asphalt pavements, submerging their layers and reducing structural resistance. This work introduces a computational finite element model suitable for investigating the impact of floods on asphalt pavement response. Unlike previous works, which consider a multi-layer analysis, in this research, the resilient modulus varies locally as a function of moisture, which could be variable in the transverse direction of the cross-section. The moisture distribution in the pavement structure is found by solving the Richards’ equation through non-linear finite element analysis. This moisture distribution is coupled to the three-dimensional elasticity problem to find the structural response to traffic loads. The structural problem was solved using the semi-analytical finite element method. Results show that the reduction of the resilient modulus in the unbound and subgrade layers is heterogeneous, with the areas near the edges of the pavement being the most affected. It was also found that the increase in elastic surface deflection depends on both the load position and time, which suggests the damage caused by vehicles could be different for each wheel path, depending on the time in which the vehicles circulate. This research presents a valuable tool for evaluating the impact of flooding on asphalt pavement structures.

Validation of zero-group-velocity feature guided waves in a welded joint

Extensive research has been conducted on zero-group-velocity (ZGV) Lamb waves in elastic plates, demonstrating significant progress in the field of nondestructive testing. However, there is a scarcity of studies focusing on ZGV modes in complex structures. In this paper, we present our research investigating the presence of ZGV feature guided waves (FGWs) in a welded joint. Our approach follows a similar methodology used to study ZGV Lamb waves in elastic plates. By employing two-dimensional (2D) finite element (FE) modeling, we analyze the response spectra of the welded joint when subjected to a force source, revealing the occurrence of resonance in the response spectra. To investigate resonance modes in the welded joint, we employ the three-dimensional (3D) time-step FE method. By applying spatial 2D and short-time Fourier transforms to the received time-domain signals, we analyze the frequency content and spatial distribution of the signals. This analysis allows us to verify the existence of non-propagation and propagation modes in the welded joint. The non-propagation mode refers to the presence of signals with a zero wavenumber, indicating that they do not propagate or travel along the welded joint. These signals are typically associated with local resonances or vibrations within the welded joint itself. On the other hand, the propagation mode corresponds to signals with nonzero wavenumbers, suggesting that they propagate or travel along the welded joint. Furthermore, by further analyzing the propagation mode in the welded joint, similar to the analysis of ZGV modes in solid plates, we have observed that it also exhibits ZGV characteristics based on the wavenumber-frequency spectra. To further analyze acoustic field distributions at resonance frequencies, we utilize the semi-analytical finite element method in conjunction with the perfectly matched layer method. The results obtained from this analysis are consistent with those obtained from the 2D FE method and 3D time-step FE method, thereby confirming that propagation modes with ZGV characteristics at resonance frequencies correspond to FGWs, which we refer to as ZGV-FGWs. Through this step-by-step analysis, we ultimately establish the existence of ZGV-FGWs in the welded joint. This study introduces fresh ideas and serves as a point of reference for future research on ZGV-FGWs in complex structures.

Investigation of acoustoelastic surface acoustic waves in prestressed media

Dispersion of broadband surface acoustic waves (SAWs) is often used for the nondestructive evaluation of near-surface elastic properties of materials. The accurate forward model of SAW propagation is essential for inversion. In this paper, we present a combining semi-analytical finite element (SAFE) and perfectly matched layer method for accurately predicting the phase velocity dispersion, attenuation and polarization modes of SAWs in any prestressed anisotropic layered half-space. Equations of motion are formulated based on the Biot's theory of small deformations influenced by initial stress, so it does not matter whether the residual stress results from hyperelastic transformations. The simulated results are firstly validated by the solutions from the exact three-dimensional elasticity theory-based method. The SAFE method is then used to discuss the effect of material anisotropy and residual stress on the SAWs. Finally, the method is applied to two practical examples. The differences and similarities of two common types of acoustoelastic theories are also discussed.

Numerical investigation of convergence of Fourier series, poly-nomials, and method of finite elements

Purpose. To compare the efficiency of using finite elements with variable and averaged mechanical and geometric parameters and to investigate the convergence of results obtained by the semi-analytical finite element method (SAFEM) using Fourier series and polynomials with the results obtained by the finite element method (FEM). The methods. The construction and development of an algorithm for studying the stress-strain state of spatial bodies with variable and averaged mechanical and geometric parameters were carried out based on SAFEM. Findings. Solvability indicators of SAFEM were obtained for calculating nodal reactions and stiffness matrix coefficients of finite elements with variable and averaged mechanical and geometric parameters. Numerical convergence studies of results obtained using SAFEM with Fourier series, polynomials, and the finite element method were conducted for a benchmark example, which was the Boussinesq problem for a half-space subjected to a concentrated force. The results indicate that the convergence of the investigated coordinate functions in the considered problem is of the first order. The originality. The obtained solvability indicators of SAFEM for calculating nodal reactions and stiffness matrix coefficients of finite elements with variable and averaged mechanical and geometric parameters allow for the study of various classes of problems. Numerical convergence studies using Fourier series, polynomials, and the finite element method were conducted for the benchmark example. Practical implementation. The practical significance lies in the development of a methodology for determining the stress-strain state of relevant spatial elements of structures with variable and averaged mechanical and geometric parameters subjected to arbitrarily distributed spatial loads.

Modelling guided waves in acoustoelastic and complex waveguides: From SAFE theory to an open-source tool

Guided wave (GW)-based techniques have been extensively investigated and applied in material characterization, damage detection, and structural health monitoring. A comprehensive understanding of GW is the cornerstone for the development of such techniques. Based on the semi-analytical finite element (SAFE) method, an open-source dispersion calculator of GW propagating in acoustoelastic and complex waveguides with both isotropic and anisotropic material properties is developed. First, by assuming the simple harmonic motion along the propagation direction and discretizing along the thickness direction, 1D-GLL-SAFE (one-dimensional Gauss-Lobatto-Legendre SAFE) is adopted for the solution of GW in plate waveguide, which is attributed to its superior performance in terms of computational accuracy and efficiency. Different theories on acoustoelasticity are adopted to calculate GWs under loading. Then 2D-Gauss-SAFE (two-dimensional Gauss SAFE) with triangular meshes filling the cross section is adopted for GW in general waveguides considering the ease of convenience in meshing. Finally, based on the 1D-GLL-SAFE and 2D-Gauss-SAFE algorithms, an open-source tool SAFEDC (SAFE-based dispersion calculator) is developed, which not only provides the solution of GW in pre-stressed isotropic waveguide and general cross section, but also extends to GW in laminates with arbitrary layer stacking configurations and hybrid stacking including multiple materials. Most of the GW features, including phase velocity, group velocity, wave number, wave structure in terms of displacement, stress, and strain, and animation of wave propagation are all offered in SAFEDC, which helps the researchers and engineers to understand and utilize GW.

An ultrasonic scanning system for the inspection of composite stiffened panels from elastic constant identification via inversion of guided waves

This paper describes an ultrasonic scanning system for the inspection of stiffened composite panels used in modern aircraft construction based on elastic constant identification. Conventional ultrasonic scanning systems track individual features of the propagating waves (e.g. amplitude, arrival time, etc.) to detect damage by tracking the associated wave scattering. An ability to map the elastic constants of the composite part can greatly enhance the sensitivity of the scan to structural damage that can be detected and quantified by a corresponding reduction in the stiffness components. Elastic constants can be also correlated to residual strength. The proposed scanning system utilizes a “single-input-dual-output“ (SIDO) scheme whereby ultrasonic guided waves are excited by an impact and detected by two air-coupled ultrasonic sensors. The phase velocity dispersion curves of the waves are experimentally measured under a single excitation at each scanning line using a phase-spectrum technique. These curves are then inverted using a Semi-Analytical Finite Element (SAFE) method as the wave propagation forward model and Simulated Annealing as the optimization routine. This approach yields estimates of several elastic effective constants of the composite panel at each scanning line. These constants are then related to impact damage in stiffened stringer-skin composite panels.

Dispersion curves of acoustoelastic borehole waves: the perturbation method with the correct formulation of the stresses around the borehole

SUMMARY The acoustoelastic model has been widely used to investigate the influence of formation stresses on the dispersion curves of borehole waves. The analytical perturbation method (PM), the finite-difference time-domain (FDTD) and the semi-analytical finite element (SAFE) are three common-used methods to calculate the dispersion curves. However, due to different interpretations of the PM and plane strain assumptions, the obtained dispersion curves are incompatible among existing PMs, which may misguide the interpretation of formation stresses. It is therefore necessary to untangle the applicability and limitations of PM. Considering that the conventional PMs are usually inaccurate at the low frequency or inconsistent with Hamilton’s principle, we develop a revised PM to obtain the dispersion curves of borehole waves propagating along a borehole surrounded by the triaxially stressed formation assumed as a monoclinic medium. The revised PM is more accurate, reasonable and logical than existing PMs. When the formation is subjected to low stresses, our finding is of great benefit for quickly computing dispersion curves, since the revised PM is much more efficient than the FDTD method; and there are small discrepancies between the flexural dispersions obtained by the revised PM and those obtained by the FDTD method. Nevertheless, the revised PM has two limitations. The first limitation is that the revised PM cannot be used to compute the Stoneley dispersion curves, which have been validated by comparison with SAFE and FDTD methods. The second limitation is that flexural dispersion curves show significant discrepancies in the high-frequency domain when the low-stress assumption does not hold, as compared to those obtained by the FDTD method.

Numerical analysis of the stressed-deformed state of a tubular element under thermal loading

In articles [2-5] solving relations and the block iteration method algorithm for solving linear and nonlinear equations by the semi-analytical finite element method for curvilinear heterogeneous prismatic bodies are implemented. In article [1], a numerical study of the convergence of the solution was performed, a wide range of test problems for bodies with smoothly and abruptly changing physical and geometric characteristics in elastic and elastic-plastic settings were considered. In [6], to confirm the reliability of the results obtained on the basis of the semi-analytical method of finite elements, the effectiveness of the application of this approach for the calculation of curvilinear inhomogeneous prismatic objects is shown. Solving control problems of the theory of elasticity, thermoelasticity, and thermoplasticity, as well as shape change problems, makes it possible to draw a conclusion about the reliability of the results of the research of a selected class of objects based on the developed methodology and implements its application program package.
 In this paper, using the methodology outlined in the above works, the results of the numerical solution of the problem, which have an applied value, were presented. The stress-strain state of a tubular element with a rectangular cutout under conditions of thermoforce loading was studied. As a rule, solving similar problems is carried out in a flat setting without taking into account the bending load. This approach greatly simplifies the formulation of the problem, but leads to very significant errors in the results. At zero value of the bending load, a good agreement of the planar and spatial solutions is observed. The presence of a bending load leads to deviation of the curves from their initial position. The maximum discrepancy of the results is almost 50%.
 The analysis of this structure from the standpoint of the spatial problem of thermoplasticity, which ensures taking into account the dependence of the physical and mechanical characteristics of the material on temperature and taking into account the bending load on the section of the cut, allowed us to reveal the real features of its deformation.

Simulating dual solutions of coupled pore-fluid flow and chemical dissolution problems in fluid-saturated heterogeneous porous media

PurposeThe objective of this paper is to establish a solution strategy for obtaining dual solutions, namely trivial (conventional) and nontrivial (unconventional) solutions, of coupled pore-fluid flow and chemical dissolution problems in heterogeneous porous media.Design/methodology/approachThrough applying a perturbation to the pore-fluid velocity, original governing partial differential equations of a coupled pore-fluid flow and chemical dissolution problem in heterogeneous porous media are transformed into perturbed ones, which are then solved by using the semi-analytical finite element method. Through switching off and on the applied perturbation terms in the resulting perturbed governing partial differential equations, both the trivial and nontrivial solutions can be obtained for the original governing partial differential equations of the coupled pore-fluid flow and chemical dissolution problem in fluid-saturated heterogeneous porous media.FindingsWhen a coupled pore-fluid flow and chemical dissolution system is in a stable state, the trivial and nontrivial solutions of the system are identical. However, if a coupled pore-fluid flow and chemical dissolution system is in an unstable state, then the trivial and nontrivial solutions of the system are totally different. This recognition can be equally used to judge whether a coupled pore-fluid flow and chemical dissolution system involving heterogeneous porous media is in a stable state or in an unstable state. The proposed solution strategy can produce dual solutions for simulating coupled pore-fluid flow and chemical dissolution problems in fluid-saturated heterogeneous porous media.Originality/valueA solution strategy is proposed to obtain the nontrivial solution, which is often overlooked in the computational simulation of coupled pore-fluid flow and chemical dissolution problems in fluid-saturated heterogeneous porous media. The proposed solution strategy provides a useful way for understanding the underlying dynamic mechanisms of the chemical damage effect associated with the stability of structures that are built on soil foundations.