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The purpose of this paper to construct the fundamental solution of partial differential equations in the generalized theory of thermoelastic diffusion materials with double porosity.

The paper deals with the study of pseudo oscillations in the generalized theory of thermoelastic diffusion materials with double porosity.

The paper finds the fundamental solution of partial differential equations in terms of elementary functions.

Assuming the displacement vector, volume fraction fields, temperature change and chemical potential functions in terms of oscillation frequency in the governing equations, pseudo oscillations have been studied and finally the fundamental solution of partial differential equations in case of pseudo oscillations in terms of elementary functions has been constructed.

The evolution in developed countries has taken a role in global warming and natural disasters such as flash flood, El-Nino, earthquake and groundwater contamination. The underground storage tank leakage problems and spillage of hydrocarbon liquid leading to the contamination of non-aqueous phase liquids (NAPLs) into the groundwater could reduce the quality of groundwater. This chapter is intended to investigate the behaviour and the pattern of NAPL migrations in double-porosity soil under vibration and intact conditions. The experimental model is developed by using kaolin soil type S300 and toluene as NAPLs. The kaolin soil was mixed with 25% of moisture content to produce kaolin granules in the soil column and vibrate under 0.98 Hz of frequency within 60 seconds. As a result, both specimen liquids completely migrated to the bottom of soil column: sample 1 has higher permeability compared to sample 2. This is due to the fracture in double-porosity soil under vibration effect and loosened the soil structure in sample 1 compared to good intact soil sample 2 with stronger and compact soil structure. In conclusion, this study proves that the dangerous hydrocarbon NAPL migration in fractured double-porosity soil has very harmful effect on the environment and groundwater resources.

The purpose of this paper is to study the reflection of plane waves in thermoelastic medium with double porosity structure.

A two-dimensional model is considered of an isotropic thermoelastic half-space with double porosity. Thermoelasticity with one relaxation time given by Lord and Shulman (1967) has been used to study the problem. It is found that there exists four coupled longitudinal waves, namely, longitudinal wave (P), longitudinal thermal wave (T), longitudinal volume fractional wave corresponding to pores (PVI) and longitudinal volume fractional wave corresponding to fissures (PVII), in addition to an uncoupled transverse wave (SV).

The formulae for amplitude ratios of various reflected waves are obtained in closed form. It is found that these amplitude ratios are functions of angle of incidence. Effect of porosity and thermal relaxation time is shown graphically on the amplitude ratios with angle of incidence for a particular model.

Reflection of plane waves is of great practical importance. There are many organic and inorganic deposits beneath the earth surface. Wave propagation is the simplest and most economical technique to detect these. The model discussed in the present paper can provide useful information for experimental researchers working in the field of geophysics and earthquake engineering, along with seismologist working in the field of mining tremors and drilling into the crust of the earth.

The impact of climate change towards water surface resources is crucial, particularly in developing and non-developing countries. Groundwater as a main water resource is thus an essential. However, contamination due to hydrocarbon spills affects the groundwater as a water resource, especially as a main source of drinking water. This chapter investigates the light non-aqueous phase liquid (LNAPL) penetrations in double-porosity soil with different moisture contents and with or without vibration impact. It also explains the LNAPL penetration phenomena by employing image analysis. The physical laboratory experiments were implemented using an acrylic cylinder, a mirror, toluene and a Nikon D90 DSLR digital camera. Prepared soil was poured in an acrylic cylinder and compressed with compressor until it became 10 cm in height. LNAPL was then poured instantaneously onto the acrylic cylinder that was filled with soil sample. The LNAPL penetration patterns were recorded and monitored using a Nikon D90 DSLR digital camera. The processing technique was conducted at predetermined time intervals using Surfer software and Matlab routine to plot the LNAPL pattern. The results showed that a higher penetration rate of LNAPL occurred with higher moisture content and without vibration impact. The penetration time for LNAPL to reach the bottom of the soil sample was found to be longer for the soil that had low moisture content and with vibration impact.

The purpose of this study is to investigate the reflection of plane waves in a double-porosity (DP) thermoelastic medium.

To derive the theoretical formulas for elastic wave propagation velocities through the potential decomposition of wave-governing equations. The boundary conditions have been designed to incorporate the unique characteristics of the surface pores, whether they are open or sealed. This approach provides a more accurate and realistic mathematical interpretation of the situation that would be encountered in the field. The reflection coefficients are obtained through a linear system of equations, which is solved using the Gauss elimination method.

The solutions obtained from the governing equations reveal the presence of five inhomogeneous plane waves, consisting of four coupled longitudinal waves and a single transverse wave. The energy ratios of reflected waves are determined for both open and sealed pores on the stress-free, the thermally insulated surface of DP thermoelastic medium. In addition, the energy ratios are compared for the cases of a DP medium and a DP thermoelastic medium.

A numerical example is considered to investigate the effect of fluid type in inclusions, temperature and inhomogeneity on phase velocities and attenuation coefficients as a function of frequency. Finally, a sensitivity analysis is performed graphically to observe the effect of the various parameters on propagation characteristics, such as propagation/attenuation directions, phase shifts and energy ratios as a function of incident direction in double-porosity thermoelasticity medium.

The purpose of this study is to analyze the thermo-diffusion process in a semi-infinite nonlocal fiber-reinforced double porous thermoelastic diffusive material with voids (FRDPTDMWV) in light of the fractional-order Lord–Shulman thermo-elasto-diffusion (LSTED) model. By virtue of Eringen’s nonlocal elasticity theory, the governing equations for the considered material are developed. The free surface of the substrate is governed by the inclined mechanical load and thermal and chemical shocks.

With the aid of the normal mode technique, the solutions of the nondimensional coupled governing equations have been obtained.

The expressions of field variables are obtained analytically. By using MATHEMATICA software, various graphical implementations are presented to describe the impacts of angle of inclination, fractional-order and nonlocality parameters. The present model is also validated on the basis of some comparative studies with some preestablished cases.

As observed from the literature survey, many different studies have been carried out by taking into account the deformation analysis in nonlocal double porous thermoelastic material structures and thermo-mechanical interaction in fiber-reinforced medium under fractional-order thermoelasticity theories. However, to the best of the authors’ knowledge, no research emphasizing the thermo-elasto-diffusive interactions in a nonlocal FRDPTDMWV has been carried out. Moreover, the effect of fractional-order LSTED theory on fiber-reinforced thermoelastic diffusive half-space with double porosity has not been illuminated till now, which significantly defines the novelty of the conducted research.

The purpose of the present study is to investigate the dispersion and damping behaviors of Love-type waves propagating in an irregular fluid-saturated fissured porous stratum coated by a sandy layer.

Two cases are analyzed in this study. In case-I, the irregular fissured porous stratum is covered by a dry sandy layer, whereas in case-II, the sandy layer is considered to be viscous in nature. The method of separation of variables is incorporated in this study to acquire the displacement components of the considered media.

With the help of the suitable boundary conditions, the complex frequency relation is established in each case leading to two distinct equations. The real and imaginary parts of the complex frequency relation define the dispersion and attenuation properties of Love-type waves, respectively. Using the MATHEMATICA software, several graphical implementations are executed to illustrate the influence of the sandiness parameter, total porosity, volume fraction of fissures, fluctuation parameter, flatness parameters and ratio of widths of layers on the phase velocity and attenuation coefficient. Furthermore, comparison between the two cases is clearly framed through the variation of aforementioned parameters. Some particular cases in the presence and absence of irregular interfaces are also analyzed.

To the best of the authors' knowledge, although many articles regarding the surface wave propagation in different crustal layers have been published, the propagation of Love-type waves in a sandwiched fissured porous stratum with irregular boundaries is still undiscovered. Results accomplished in this analytical study can be employed in different practical areas, such as earthquake engineering, material science, carbon sequestration and seismology.

This paper aims to study photothermal excitation process in an initially stressed semi-infinite double porous thermoelastic semiconductor with voids subjected to Eringen’s nonlocal elasticity theory under the fractional order triple-phase-lag thermoelasticity theory. The considered substrate is governed by the mechanical and thermal loads at the free surface.

The normal mode technique is used to carry out the investigation of photothermal transportation. By virtue of the MATHEMATICA software, each distribution is exhibited graphically.

The expressions of the displacements, temperature, volume fractions of both kinds of voids, carrier density and stresses are determined analytically. With the help of the numerical data for silicon (Si) material, graphical implementations are presented on the basis of initial stress, fractional order, nonlocality and thermoelectric coupling parameters.

The present study fabricates the association of Eringen’s nonlocal theory and the stress analysis in a semiconducting double porous thermoelastic material with voids, which significantly implies the originality of the conducted work.

The material point method (MPM)is a particle-based numerical method suitable for solid–liquid simulation and large deformation problems. However, MPM is generally used in solid deformation at present, to develop a multi-physics coupling MPM; the purpose of this study is to extend the MPM to simulate the heat and fluid flow and address the thermal-hydrological (TH) coupling problems.

The porous medium was discretized into two sets of Lagrangian points, and the motion of fluid points follows the Darcy’s law. Two sets of heat transport equations were established for the heat conduction and heat exchange in the pore fluid and solid skeleton. Fractures were considered by adding the porosity gradient term in the governing equations; also a transition function was introduced to smoothen the fracture boundary.

Four cases of heat and fluid flow in porous medium and fractures were presented to verify the feasibility of the proposed method. And the effects of fractures on heat and fluid flow were investigated. Additionally, a case of geothermal extraction was solved and the importance of the interstitial convective heat transfer coefficient was analyzed.

The proposed method extends the conventional MPM, using two sets of material points and two sets of heat transport equations to simulate the heat and fluid flow and address the TH coupling problems, which can be applied in both porous medium and fractures.

The paper aims to clarify the relationship between the micro-structures of porous media and the coefficient of permeability. Most materials involve different types of defects like caves, pores and cracks, which are important characters of porous media and have a great influence on the physical properties of materials. To study the seepage mechanical characteristics of damaged porous media, the constitutive model of porous media dealing with coupled modeling of pores damage and its impact on permeability property of a deforming media was studied in this paper.

The paper opted for an exploratory study using the approach of continuum damage mechanics (CDM).

The paper provides some new insights on the fluid dynamics of porous media. The dynamic evolution model of permeability coefficient established in this paper can be used to model the fluid flow problems in damaged porous media. Moreover, the modified Darcy's law developed in this paper is considered to be an extension of the Darcy's law for fluid flow and seepage in a porous medium.

Owing to the limitations of time, conditions, funds, etc., the research results should be subject to multifaceted experiments before their innovative significance can be fully verified.

The paper includes implications for the development of fluid dynamics of porous media.

This paper fulfils an identified need to study the relationship between the micro-structures of porous media and the coefficient of permeability.