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This paper seeks to analyse 3D growing concrete structures taking into account the phenomenon of body accretion, necessary for the simulation of the construction sequence, and carbon dioxide attack.

A typical 3D segmental bridge made of precast concrete is studied through a fully coupled thermo‐hygro‐mechanical F.E. model. The durability of the bridge is evaluated and carbonation effects are considered. Creep, relaxation and shrinkage effects are included according to the theory developed in the 1970s by Bažant for concretes and geomaterials; the fluid phases are considered as a unique mixture which interacts with a solid phase. The porous material is modelled using n Maxwell elements in parallel (Maxwell‐chain model).

First, calibration analyses are developed to check the VISCO3D model capabilities for predicting carbonation phenomena within concrete and the full 3D structure is modelled to further assess the durability of the bridge under severe conditions of CO₂ attack.

The adopted numerical model accounts for the strong coupling mechanisms of CO₂ diffusion in the gas phase, moisture and heat transfer, CaCO₃ formation and the availability of Ca(OH)₂ in the pore solution due to its transport by water movement. Additionally, the phenomenon of a sequential construction is studied and numerically reproduced by a sequence of “births” for the 3D finite elements discretizing the bridge. The fully coupled model is here extended to 3D problems for accreting bodies (as segmental bridges) in order to gather the effects of multi‐dimensional attacks of carbon dioxide for such structures.

The objective of this paper is to develop a semi-analytical finite element method for solving chemical dissolution-front instability problems in fluid-saturated porous media.

The porosity, horizontal and vertical components of the pore-fluid velocity and solute concentration are selected as four fundamental unknown variables for describing chemical dissolution-front instability problems in fluid-saturated porous media. To avoid the use of numerical integration, analytical solutions for the property matrices of a rectangular element are precisely derived in a purely mathematical manner. This means that the proposed finite element method is a kind of semi-analytical method. The column pivot element solver is used to solve the resulting finite element equations of the chemical dissolution-front instability problem.

The direct use of horizontal and vertical components of the pore-fluid velocity as fundamental unknown variables can improve the accuracy of the related numerical solution. The column pivot element solver is useful for solving the finite element equations of a chemical dissolution-front instability problem. The proposed semi-analytical finite element method can produce highly accurate numerical solutions for simulating chemical dissolution-front instability problems in fluid-saturated porous media.

Analytical solutions for the property matrices of a rectangular element are precisely derived for solving chemical dissolution-front instability problems in fluid-saturated porous media. The proposed semi-analytical finite element method provides a useful way for understanding the underlying dynamic mechanisms of the washing land method involved in the contaminated land remediation.

The purpose of this paper is to highlight the advantages of a simplified algorithm to solve the problem of heat and mass transfer in porous medium by reducing the number of partial differential equations from four to three.

The approach of the present paper is to develop a simplified algorithm to reduce the number of equations involved in conjugate heat transfer in porous medium.

Developed algorithm/method has many advantages over conventional method of solution for conjugate heat transfer in porous medium.

The current work is applicable to conjugate heat transfer problem.

The developed algorithm is useful in reducing the number of equations to be solved, thus reducing the computational resources required.

Development of simplified algorithm and comparison with conventional method.

The 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.

Through 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.

When 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.

A 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.

Natural gas leak from underground pipelines could lead to serious damage and global warming, whose spreading in soil should be systematically investigated. This paper aims to propose a three-dimensional numerical model to analyze the methane–air transportation in soil. The results could help understand the diffusion process of natural gas in soil, which is essential for locating leak source and reducing damage after leak accident.

A numerical model using finite element method is proposed to simulate the methane spreading process in porous media after leaking from an underground pipe. Physical models, including fluids transportation in porous media, water evaporation and heat transfer, are taken into account. The numerical results are compared with experimental data to validate the reliability of the simulation model. The effects of methane leaking direction, non-uniform soil porosity, leaking pressure and convective mass transfer coefficient on ground surface are analyzed.

The methane mole fraction distribution in soil is significantly affected by the leaking direction. Horizontally and vertically non-uniform soil porosity has a stronger effect. Increasing leaking pressure causes increasing methane mole flux and flow rate on the ground surface.

Most existing gas diffusion models in porous media are for one- or two-dimensional simulation, which is not enough for predicting three-dimensional diffusion process after natural gas leak in soil. The heat transfer between gas and soil was also neglected by most researchers, which is very important for predicting the gas-spreading process affected by the soil moisture variation because of water evaporation. In this paper, a three-dimensional numerical model is proposed to further analyze the methane–air transportation in soil using finite element method, with the presence of water evaporation and heat transfer in soil.

Survey of period infinite element developments The first infinite elements for periodic wave problems, as stated in Part 1, were developed by Bettess and Zienkiewicz, the earliest publication being in 1975. These applications were of ‘decay function’ type elements and were used in surface waves on water problems. This was soon followed by an application by Saini et al., to dam‐reservoir interaction, where the waves are pressure waves in the water in the reservoir. In this case both the solid displacements and the fluid pressures are complex valued. In 1980 to 1983 Medina and co‐workers and Chow and Smith successfully used quite different methods to develop infinite elements for elastic waves. Zienkiewicz et al. published the details of the first mapped wave infinite element formulation, which they went on to program, and to use to generate results for surface wave problems. In 1982 Aggarwal et al. used infinite elements in fluid‐structure interaction problems, in this case plates vibrating in an unbounded fluid. In 1983 Corzani used infinite elements for electric wave problems. This period also saw the first infinite element applications in acoustics, by Astley and Eversman, and their development of the ‘wave envelope’ concept. Kagawa applied periodic infinite wave elements to Helmholtz equation in electromagnetic applications. Pos used infinite elements to model wave diffraction by breakwaters and gave comparisons with laboratory photogrammetric measurements of waves. Good agreement was obtained. Huang also used infinite elements for surface wave diffraction problems. Davies and Rahman used infinite elements to model wave guide behaviour. Moriya developed a new type of infinite element for Helmholtz problem. In 1986 Yamabuchi et al. developed another infinite element for unbounded Helmholtz problems. Rajapalakse et al. produced an infinite element for elastodynamics, in which some of the integrations are carried out analytically, and which is said to model correctly both body and Rayleigh waves. Imai et al. gave further applications of infinite elements to wave diffraction, fluid‐structure interaction and wave force calculations for breakwaters, offshore platforms and a floating rectangular caisson. Pantic et al. used infinite elements in wave guide computations. In 1986 Cao et al. applied infinite elements to dynamic interaction of soil and pile. The infinite element is said to be ‘semi‐analytical’. Goransson and Davidsson used a mapped wave infinite element in some three dimensional acoustic problems, in 1987. They incorporated the infinite elements into the ASKA code. A novel application of wave infinite elements to photolithography simulation for semiconductor device fabrication was given by Matsuzawa et al. They obtained ‘reasonably good’ agreement with observed photoresist profiles. Häggblad and Nordgren used infinite elements in a dynamic analysis of non‐linear soil‐structure interaction, with plastic soil elements. In 1989 Lau and Ji published a new type of 3‐D infinite element for wave diffraction problems. They gave good results for problems of waves diffracted by a cylinder and various three dimensional structures.

Knowledge of the behavior of concrete at mesoscale level requires, as a fundamental aspect, to characterize aggregates and specifically, their thermal properties if fire hazards (e.g. spalling) are accounted for. The assessment of aggregates performance (and, correspondingly, concrete materials made of aggregates, cement paste and ITZ – interfacial transition zone) is crucial for defining a realistic structural response as well as damage scenarios.

It is here assumed that concrete creep is associated to cement paste only and that creep obeys to the B3 model proposed by Bažant and Baweja since it shows good compatibility with experimental results and it is properly justified theoretically.

First, the three‐dimensionality of the geometric description of concrete at the meso‐level can be appreciated; then, creep of cement paste and ITZ allows to incorporate in the model the complex reality of creep, which is not only a matter of fluid flow and pressure dissipation but also the result of chemical‐physical reactions; again, the description of concrete as a composite material, in connection with porous media analysis, allows for understanding the hygro‐thermal and mechanical response of concrete, e.g. hygral barriers due to the presence of aggregates can be seen only at this modelling level. Finally, from the mechanical viewpoint, the remarkable damage peak effect arising from the inclusion of ITZ, if compared with the less pronounced peak when ITZ is disregarded from the analysis, is reported.

The fully coupled 3D F.E. code NEWCON3D has been adopted to perform fully coupled thermo‐hygro‐mechanical meso‐scale analyses of concrete characterized by aggregates of various types and various thermal properties. The 3D approach allows for differentiating each constituent (cement paste, aggregate and ITZ), even from the point of view of their rheologic behaviour. Additionally, model B3 has been upgraded by the calculation of the effective humidity state when evaluating drying creep, instead than using approximate expressions. Damage maps allows for defining an appropriate concrete mixture to withstand spalling and to characterize the coupled behaviour of ITZ as well.

The purpose of this paper is to solve non‐linear parametric thermal models defined in degenerated geometries, such as plate and shell geometries.

The work presented in this paper is based in a combination of the proper generalized decomposition (PGD) that proceeds to a separated representation of the involved fields and advanced non‐linear solvers. A particular emphasis is put on the asymptotic numerical method.

The authors demonstrate that this approach is valid for computing the solution of challenging thermal models and parametric models.

This is the first time that PGD is combined with advanced non‐linear solvers in the context of non‐linear transient parametric thermal models.

The purpose of this paper is to systematically investigate the fluid lag phenomena and its influence in the hydraulic fracturing process, including all stages of fluid-lag evolution, the transition between different stages and their coupling with dynamic fracture propagation under common conditions.

A plane 2D model is developed to simulate the complex evolution of fluid lag during the propagation of a hydraulic fracture driven by an impressible Newtonian fluid. Based on the finite element method, a fully implicit solution scheme is proposed to solve the strongly coupled rock deformation, fluid flow and fracture propagation. Using the proposed model, comprehensive parametric studies are performed to examine the evolution of fluid lag in various geological and operational conditions.

The numerical simulations predict that the lag ratio is around 5% or even lower at the beginning stage of hydraulic fracture under practical geological conditions. With the fracture propagation, the lag ratio keeps decreasing and can be ignored in the late stage of hydraulic fracturing for typical parameter combinations. On the numerical aspect, whether the fluid lag can be ignored depends not only on the lag ratio but also on the minimum mesh size used for fluid flow. In addition, an overall mixed-mode fracture propagation factor is proposed to describe the relationship between diverse parameters and fracture curvature.

In this study, relatively simple physical models such as linear elasticity for solid, Newtonian model for fluid and linear elasticity fracture mechanics for fracture are used. The current model does not account for such effects like leak off, poroelasticity and softening of rock formations, which may also visibly affect the fluid lag depending on specific reservoir conditions.

This study helps to understand the effect of fluid lag during hydraulic fracturing processes and provides numerical experience in dealing with the fluid lag with finite element simulation.

The purpose of this work is to propose the generalized integral transform technique (GITT) for the investigation of two-dimensional steady-state natural convection in a horizontal annular sector containing heat-generating porous medium.

GITT was used to investigate steady-state natural convection in a horizontal annular sector containing heat-generating porous medium. The governing equations in stream function formulation are integral transformed in the azimuthal direction, with the resulting system of nonlinear ordinary differential equations numerically solved by finite difference method. The GITT solutions are validated by comparison with fully numerical solutions by finite difference method, showing excellent agreement and convergence with low computational cost.

The effects of increasing Rayleigh number are more noticeable in stream function, whereas less significant for temperature. With decreasing annular sector angle from π to π/6, a reduction in the maximum temperature and stream function was noticed. While the two counter-rotating vortical structure is common for all annular sector angles investigated, the relative size of the two vortices varies with decreasing sector angle, with the vortex near the outer radius of the cavity becoming dominant. The annular sector angle affects strongly the maximum temperature and the partition of heat transfer on the inner and outer surfaces of the annular sector with heat-generating porous medium.

The strong effects of the annular sector angle on natural convection in annular sectors containing heat-generating porous medium are investigated for the first time. The proposed hybrid analytical–numerical approach can be applied in other convection problems in cylindrical or annular configurations, with or without porous medium. It shows potential for applications in practical convection problems in the nuclear and other industries.