Biot Poroelasticity Research Articles

The impact of boundary conditions on the acoustical behavior of lightweight granular particle stacks

The acoustical behavior of air-saturated granular stacks can differ significantly from that of more traditional sound absorbing materials such as fibrous webs and foams when tested in a standing wave tube. The latter materials can often be modeled as equivalent fluids by using one-dimensional theory, with the further assumption that their behavior does not depend on the input signal level. In contrast, level dependence of the response of lightweight granular materials such as glass bubbles has been consistently observed in previous studies. At low input levels, the absorption coefficient of glass bubble stacks shows solid-like behavior with multiple peaks associated with radial modes of the solid phase of the edge-constrained stack: i.e., the response is two-dimensional. In contrast, at high input levels, glass bubble stacks show one-dimensional fluid-like behavior, with the quarter wave depth resonance dominating the response. It is hypothesized here that at high input levels the particles slip axially at the circumferential boundary, thus showing a one-dimensional response, while at low levels, the particles are constrained to have zero axial velocity, thus creating a two-dimensional response. It is shown here that a two-dimensional finite difference implementation of the poro-elastic Biot theory can accurately reproduce the observed level-dependent behavior.

Hyperelastic constitutive relations for porous materials with initial stress

Initial stress is widely observed in porous materials. However, its constitutive theory remains unknown due to the lack of a framework for modeling the interactions between initial stress and porosity. In this study, we construct the porous hyperelastic constitutive model with arbitrary initial stresses through the multiplicative decomposition approach. Based on the compression experiment of shale samples, the parameters in the constitutive equation are determined. Then, the explicit equations of in-plane elastic coefficients are proposed by linearizing the finite deformation formulation. The influences brought by the coexistence of initial stresses and porosity on these coefficients are revealed. Later, comparative analyses of the linearized equations between the present model, the initially-stressed models without pores, the Biot poroelasticity, and the porous hyperelastic model without initial stress are conducted to illustrate the performances of the two ingredients. As a specific example, we investigate the variation of pore sizes under external pressures and initial stresses since changes in pore sizes during deformation are crucial for understanding the accumulation and migration of shale oil and gas. The newly proposed model provides the first initially stressed porous hyperelasticity (ISPH), which is suitable for describing the finite deformation behavior of solid materials with large porosity and significant initial stress simultaneously.

Acoustic response of patchy-saturated porous media: Coupling Biot's poroelasticity equations for mono- and biphasic pore fluids.

Patchy saturation is a term used in the seismic prospecting literature to describe the state of a geological formation in which two immiscible pore fluids prevail in mesoscopic-scale clusters. If the pore fluids have contrasting compressibilities, wave-induced fluid pressure diffusion (FPD) processes may induce significant attenuation and velocity dispersion on seismic waves. Biot's monophasic poroelasticity theory is widely used to model the seismic response of rocks containing binary patches of two immiscible pore fluids. Even though effective fluid approximations may help to represent more realistic partially saturated patches using Biot's monophasic equations, the so inferred dissipation may not be representative of actual biphasic FPD phenomena. In this work, Biot's equations for mono- and biphasic fluids are combined to model FPD processes in porous media, comprising fully and partially saturated patches. An analytical solution for one-dimensional layered patchy-saturated media is presented which permits to explain some, as of yet enigmatic, experimentally observed characteristics such as increased seismic attenuation and stiffening effects occurring at low saturations. The results show that the existence of an additional diffusive wave mode within partially saturated patches may render conventional binary and effective fluid approaches incorrect and error prone.

Effect of patient-specific factors on regeneration in lumbar spine at healthy disc and total disc replacement. Computer simulation

Background and ObjectiveDegenerative diseases of the spine have a negative impact on the quality of life of patients. This study presents the results of numerical modelling of the mechanical behaviour of the lumbar spine with patient-specific conditions at physiological loads. This paper aims to numerically study the influence of degenerative changes in the spine and the presence of an endoprosthesis on the creation of conditions for tissue regeneration. MethodsA numerical model of the mechanical behaviour of lumbar spine at healthy and after total disc replacement under low-energy impacts equivalent to physiological loads is presented. The model is based on the movable cellular automaton method (discrete elements), where the mechanical behaviour of bone tissue is described using the Biot poroelasticity accounting for the presence and transfer of interstitial biological fluid. The nutritional pathways of the intervertebral disc in cases of healthy and osteoporotic bone tissues were predicted based on the analysis of the simulation results according to the mechanobiological principles. ResultsSimulation of total disc replacement showed that osseointegration of the artificial disc plates occurs only in healthy bone tissue. With total disc replacement in a patient with osteoporosis, there is an area of increased risk of bone resorption in the near-contact area, approximately 1 mm wide, around the fixators. Dynamic loads may improve the osseointegration of the implant in pathological conditions of the bone tissue. ConclusionsThe results obtained in the case of healthy spine and osteoporotic bone tissues correspond to the experimental data on biomechanics and possible methods of IVD regeneration from the position of mechanobiological principles. The results obtained with an artificial disc (with keel-type fixation) showed that the use of this type of endoprosthesis in healthy bone tissues allows to reproduce the function of the natural intervertebral disc and does not contribute to the development of neoplastic processes. In the case of an artificial disc with osteoporosis of bone tissues, there is a zone with increased risk of tissue resorption and development of neoplastic processes in the area near the contact of the implant attachment. This circumstance can be compensated by increasing the loading level.

Evolutionary topology optimization approach to design multiphase soundproof systems with poroelastic media

SummaryWith the constant development of cities, noise sources have become increasingly present inside and outside living environments. Consequently, soundproof systems comprised of porous materials have been widely adopted as filling fabric of closed‐space structures, such as in the components of buildings, airplanes or automobiles. However, in many situations, simply filling spaces may not be the most effective approach. In that scenario, this work introduces a multiphase acoustic topology optimization methodology to design closed‐space structures for sound attenuation. Based on the Bi‐directional Evolutionary Structural Optimization (BESO) algorithm, the proposed approach combines Biot's poroelasticity equations, expressed in the mixed /p form, and the Unified Multiphase (UMP) technique to fully describe the multiphysics involved in the acoustic, poroelastic and elastic model relations. An objective function contemplating different combinations of structural, viscous and thermal dissipated powers is maximized over multiple frequencies. Volume constraints in each material phase and a novel material interpolation scheme are also considered. The resultant topologies present enhanced dissipated power levels and manufacturability, even when compared with various baseline configurations of similar volume fractions.

A numerical extension of White's theory of P-wave attenuation to non-isothermal poroelastic media.

Mesoscopic P-wave attenuation in layered, partially saturated thermo-poroelastic media is analyzed by combining the theories of Biot poroelasticity and Lord-Shulman thermoelasticity (BLS). The attenuation is quantified by estimating the quality factor Q. The mesoscopic attenuation effect, commonly referred to as wave-induced fluid flow (WIFF), is the process that converts fast compressional and shear waves into slow diffusive Biot waves at mesoscopic heterogeneities larger than the pore scale, but much smaller than the dominant wavelengths. This effect was first modeled in White's isothermal theory by quantifying the seismic response of a periodic sequence of planar porous layers that are alternately saturated with gas or water. This work presents a numerical extension of White's theory for the non-isothermal case in this type of sequence. For this purpose, an initial-boundary-value problem (IBVP) for the BLS wave propagation equations is solved using the finite element method, where the particle velocity field is recorded at uniformly distributed receivers. The quality factor is estimated using spectral-ratio and frequency-shift methods. The Q-estimates show that thermal effects influence the attenuation of the P-wave and the velocity dispersion compared to the isothermal case.

Opening-dependent phase field model of hydraulic fracture evolution in porous medium under seepage-stress coupling

In this paper, a seepage-stress coupling numerical analysis method is developed to simulate complex hydraulic fracturing in porous medium, in which the characteristics of hydraulic fracture evolution in porous medium under seepage-stress coupling are revealed. The classical Biot's poroelasticity theory is applied to couple the stress and fluid fields, and the crack propagation path of hydraulic fracturing is described by an opening-dependent phase field model. Potential energy caused by fluid pressure is also coupled into the governing equation of phase field evolution. The system of fracture opening affecting fluid flow is established. Staggered iterative scheme is applied to solve the above three-field coupled problem based on Newton–Raphson iterative algorithm. Three classical cases are presented to validate the proposed method: the first one is an analytical solution of pressure distribution in a fixed opening crack and the second one is a benchmark case of Sneddon analytical solution for a pressurized pre-crack and the third one is the KGD problem for hydraulic fracture propagation. Moreover, numerical simulations of hydraulic fracturing in shale block, multi-layer and natural fractures are also investigated. The numerical results agree well with the results in published literatures. It is indicated that hydraulic fracture evolution under seepage-stress coupling can be forecasted by the proposed method. The proposed method not only provides a powerful analytical tool for the oil or gas production, but also provides assessment tools for the stability of geotechnical engineering in water rich environments.

Sound transmission reduction of double walls using porous and viscoelastic materials

Double-walled structures separated by an acoustic cavity are widely used in many applications for sound insulation purposes. Their sound transmission loss is estimated by calculating the ratio between the incident sound power on the first wall and the radiated sound power by the second. The introduction of a melamine foam associated with heavy masses brings a better sound insulation against external noise. In this context, this work deals with the numerical prediction of the sound transmission of a roller shutter box equipped with porous and viscoelastic materials. Such system can be modeled, at first approximation, as a double-walled structure. The proposed approach is based on the use of the finite element method for the modeling of the different solid and fluid domains of the problem. A mixed displacement pressure formulation of the Biot poroelasticity equations is used to model the poroelastic domain. The structure is excited by a diffuse field represented by a superposition of plane waves with random phases and directions. The acoustic power radiated by the second wall is calculated by applying the Rayleigh integral method. The results show the importance of optimizing the position of the porous and the heavy layers to maximize the sound insulation.

Broadband surface wave attenuation in porous soil by elastic metasurfaces

To mitigate surface waves in ambient vibration, a novel broadband elastic metasurface is proposed by periodically burying the layered in-filled pipes below the ground surface. The present metasurface is a simple structure and can be easily implemented. In contrast to the existing studies of metasurfaces in single-phase elastic soil, the coupling of elastic metasurfaces with saturated porous soil is investigated within the framework of Biot's theory. Note that Biot's poroelasticity can capture the complexity of soils in the presence of fluids. Both dispersion and transmission analysis are comprehensively conducted. The present investigation shows that the elastic metasurfaces are suitable for a wide range of fluid-saturated porous soil, and a significant surface wave attenuation is observed within the attenuation zone of elastic metasurfaces. In addition, the burying depth is the key point of the design of elastic metasurfaces. Specifically, the surface wave attenuation zone (SWAZ) will vanish when the depth is larger than three times the periodic constant. Besides, the SWAZ will be widened by stacking the layers of elastic metasurfaces. Three layers is enough for the metasurface to attenuate more than 80 % surface wave energy. Due to the similar dynamic characteristics of elastic metasurface in the fluid-saturated porous half-space compared to dry half-space, single-phased soil can be used to simplify the analysis of saturated soil with ideal fluids. To widen the scope of application in elastic metasurfaces, the feasibility of ambient vibration mitigation by elastic metasurfaces is experimentally and numerically verified. The experimental results confirm an obvious wave attenuation within the SWAZ, and the average insertion loss (IL︸) is 9.8 dB. Last but not least, the performance of elastic metasurfaces to mitigate ground-borne vibration induced by trains is numerically studied in time domain. Elastic metasurfaces outperform traditional trenches within the main frequency range, and IL︸ is increased by 3.9–7 dB. Thanks to the excellent wave attenuation performance and subwavelength thickness, these novel elastic metasurfaces are expected to open new avenues in ambient vibration mitigation in the costal area of saturated soil.

Numerical and experimental investigation of sound transmission through roller shutter boxes

Roller shutter boxes are essential components of building facades, providing crucial thermal and acoustic insulation. Conventional laboratory tests have been traditionally used to evaluate the sound transmission of roller shutter boxes. However, these tests can be expensive and lack repeatability and reproducibility, especially in the low-frequency range. To overcome these limitations, this study aims to introduce an advanced numerical model capable of accurately predicting the vibroacoustic response of roller shutter boxes and optimizing their acoustic insulation performance. The proposed numerical approach utilizes the finite element method to model the various solid and fluid domains within the roller shutter box structure. To capture the behavior of the poroelastic layers, a mixed displacement–pressure formulation of the Biot poroelasticity equations is employed. Excitation of the structure is achieved using a diffuse field comprising a superposition of plane waves with random phases and directions, while the resulting sound radiation is computed utilizing the infinite elements method. To validate the proposed numerical model, a comparison is made with results obtained from laboratory tests, and the experimental protocol is thoroughly described. The practical application of the proposed numerical method extends to the investigation of several influential factors on the acoustic behavior of roller shutter boxes, including assembly conditions, the positioning of poroelastic layers, and the inclusion of heavy masses.

Coupled hydro-mechanical-chemical simulation of CCUS-EOR with static and dynamic microscale effects in tight reservoirs

Tight reservoir can be potentially stimulated via CO2 injection and serves as potential sites for CO2 storage. However, simplifying flow mechanisms in hydro-mechanical-chemical coupling simulations can cause significant deviations in forecasting productivity and storage performance. In this study, a coupled hydro-mechanical-chemical model with both static and dynamic microscale effects was established for the first time. We characterized the impact of micro- and nanopores on the multicomponent thermodynamics and multiphase flow of CO2 and in-situ oil by considering the critical property shift, capillary pressure, and boundary slip. The matrix and hydraulic fracture system were constructed based on the embedded discrete fracture model (EDFM). The effect of mineral reaction in the matrix and time-varying width and permeability of propped fractures were also involved in the model to address practical field-scale problems. An iteratively coupled scheme was used in a more comprehensive model to compute the flow and mechanical parameters at each time step, with the impact of different degrees of microscale effects studied by changing the proportions of micropores and nanopores. Two fluid models with different minimum miscible pressures (MMPs) were used to simulate the miscible and immiscible production processes. The stress sensitivity was analyzed based on the Biot poroelasticity theory and time-varying fracture conductivity, with the results suggesting that stress sensitivity can reduce overall production by slower outward pressure movement but can inhibit gas channeling and breakthrough to a certain extent. The detailed analysis of microscale effects, miscibility, and stress sensitivity in this work is of practical significance for tight reservoir development and CO2 geological storage.

Equal Lower-order Finite Elements of Least-squares Type in Biot Poroelasticity Modeling

Equal Lower-order Finite Elements of Least-squares Type in Biot Poroelasticity Modeling

A novel hydraulic fracturing model for the fluid-driven fracture propagation in poroelastic media containing the natural cave

Hydraulic fracturing is an efficient technology to extract hydrocarbon within natural caves. However, these caves can markedly affect the fracture propagation behavior. This paper proposes a novel hydraulic fracturing model to simulate the fracture propagation in poroelastic media containing the natural cave, utilizing the strengths of the phase-field method. By coupling the Reynolds flow with cubic law in fracture domain, free flow in cave domain, and low-permeability Darcy flow in reservoir domain, the fracture-cave-reservoir flow governing equations are established. The Biot poroelasticity theory and fracture width are the links of hydro-mechanical coupling. The smooth phase-field is introduced to diffuse not only the sharp fracture but also the sharp cave edge. The fully coupling model is solved by a staggered scheme, which independently solves the pressure field and displacement field in inner cycle, and then independently solves the phase field in outer cycle. The proposed model is verified by comparing with the Khristianovic–Geertsma–de Klerk (KGD) model and Cheng's hydraulic fracturing model. Then, the interaction between hydraulic fracture and natural cave is investigated through several two-dimensional and three-dimensional cases. The result shows that the cave effect can make the hydraulic fracture deflect and raise its propagation velocity. Increasing the fracture-cave distance, injection rate, and in situ stress difference can all decline the cave effect. The displayed cases also substantiate the capability and efficiency of the proposed model.

3D coupled hydro-mechanical modeling of multi-decadal multi-zone saltwater disposal in layered and faulted poroelastic rocks and implications for seismicity: An example from the Midland Basin

Knowledge of subsurface coupled pore pressure and stress perturbations due to saltwater disposal (SWD) is crucial for understanding and managing induced seismicity. Current studies choose Biot poroelasticity to implement fluid-rock coupling and perform numerical modeling in relatively simple settings. In this study, we first introduce a general poromechanical framework to capture a broader range of hydro-mechanical coupling and then apply it to model real-world SWD problems with geological and operational complexities. We demonstrate a viable workflow through the case study of a 2500 km2, layered, faulted, and recently seismically awaken area that has undergone multi-decadal multi-zone injection by nearly 200 SWD wells in the Midland basin. The example provides a unique opportunity to study the respective impact of shallow and deep injections across depths and the role of inter-zone interactions, among others. Our modeling suggests over 500 and 250 psi increases in pore pressure and Coulomb stress, respectively, in the deep disposal zone in the last decade, which were 5 to 10 times greater than those accumulated over the past four decades in the two shallower disposal zones. Vertically, shallower injections impacted mostly shallower zones, whereas the deep injection produced changes across depths and dominated especially in the deep zone and the upper segment of the basement. Towards the mid-segment of the basement, changes due to shallow and deep injections were comparable, with the latter 2 to 5 times higher. Laterally, in-zone changes were dominated by pore pressure diffusion in the near field and poroelastic stressing in the far field in shallower zones but were dominated by pore pressure diffusion everywhere in the deep zone, owing to their different hydraulic diffusivities. Faults acted as pore pressure and Coulomb stress sinks for disposal zones and sources for non-disposal zones, and fault-zone permeability structure had a minor impact. Finally, seismological modeling suggests that seismicity in the area was most likely driven by the deep injection.

Biot-consistent framework for wave propagation with macroscopic fluid and thermal effects

SUMMARY In principle, wave propagation in porous media can simultaneously trigger macroscopic fluid flow and thermal flow, which can be described by Biot's poroelasticity and Lord–Shulman thermoelasticity, respectively. The physical processes of those effects are significantly different, but phenomenologically, they can lead to identical wave attenuation and dispersion and are hard to be distinguished. By using Biot's virtual concept entropy flow, the Biot-consistent General Linear Solid (the GLS) framework and matrix notation, a rigorous and convenient tool is provided to reveal the similarities and disparities between poroelasticity and thermoelasticity. By using the same framework, a Biot-consistent thermo-poroelastic model is proposed to consider macroscopic effects of fluid and thermal flows simultaneously in an elegant way. These similarities allow us to directly translate many of the available results in poroelasticity to thermoelasticity and vice versa by a simple change of notation. The disparities indicate a fundamental difference in physical mechanisms. Plane-wave analysis shows that the primary P-wave modes of thermoelasticity and poroelasticity are all GSLS-equivalent (Generalized Standard Linear Solid) and can be identical if the model parameters are selected properly. However, the corresponding slow-wave modes have significantly different phase velocity dispersion although the attenuation spectra of which are identical. Such a surprising result can be explained by the GSLS non-equivalence of the slow-wave modes and the fundamentally different mechanisms. As expected, the thermo-poroelastic model predicts four wave modes, which are the fast- and slow-P, temperature (T wave) and S waves. Two attenuation peaks due to, respectively, the thermal- and fluid-flow effects are predicted for the fast-P wave. The slow-P wave mode due to fluid flow is influenced by the thermal effects, but the T wave seems unaffected by the fluid flow. The thermo-poroelastic model is then applied to laboratory observations at 200–106 Hz for the brine-saturated tight sandstone under 35 MPa effective pressure. The unified model provides a convenient framework for studying geothermal exploration, thermal-enhanced oil recovery and other applications involving temperature variations within the porous rock.

Twofold Saddle-Point Formulation of Biot Poroelasticity with Stress-Dependent Diffusion

Twofold Saddle-Point Formulation of Biot Poroelasticity with Stress-Dependent Diffusion

Theoretical, experimental, and numerical studies of flow field characteristics and incipient scouring erosion for slope with rigid vegetations

Under the action of continuous rainfall, the coupling linkage between runoff and seepage can cause erosion of non-cohesive soil particles on vegetated slopes. A nonlinear turbulent-seepage coupling model is established to study the flow field characteristics and incipient scouring erosion of the vegetated slope. The fluid in the turbulent region is governed by the Reynolds averaged Navier-Stokes. Biot's poroelasticity theory describes the flow in the vegetation region. The seepage in the soil region obeyed the Darcy-Brinkman equation. Analytical solutions of the vertical velocity profile and safety factor (sliding and rolling) of the particle incipient motion are derived based on the coupling between turbulence and seepage. The velocity expression is found to be in good agreement with the existing experimental data of both emerged and submerged vegetation conditions, respectively. The velocity distribution above the surface follows a logarithmic pattern, while below the surface, non-linear seepage occurs with a transition layer that deviates from Darcy seepage. In addition, the particle incipient motion is verified by the physical flume souring test under none, sparse, and dense vegetation, respectively. The absolute error between the theoretical calculation and the physical test is within 5%. Furthermore, the critical water depth is nonlinearly negatively correlated with the energy slope. Finally, a CFD-DEM coupling numerical model is employed to further observe the scouring erosion of the sparse and dense vegetated slopes with the same conditions as the physical test. The numerical results show that the scouring erosion exhibits discontinuous behavior and the soil particles between the two vegetation are more vulnerable to scouring than those in other locations. After scouring, the inertial porosity of the vegetated soil slope decreases while the porosity in the surface area increases.

Integrated thermo-poro-mechanical characterization for CO2 Sequestration at deep aquifer conditions

Modelling and forecasting of injected CO2 plume behaviour is an essential step in the baseline, monitoring, and verification [BMV] process in the CO2 sequestration lifecycle. The goal of reduction of uncertainty through forecasting models, can be better realized by accounting for the thermo-poro-mechanical nature of the deep subsurface reservoir systems. The current study focusses on developing and refining a laboratory workflow which will help in generating representative static and dynamic datasets at ambient and deep aquifer conditions. The workflow involves characterizing the poroelastic Biot coefficient and mechanical properties at ambient, high temperatures and at reservoir representative stress conditions. This information will be combined with the dataset from a CO2 flood experiment which replicates the displacement of brine by super critical CO2 at ambient and high temperatures and at reservoir representative stresses. Resistivity and acoustic signals will be monitored throughout the flood experiment. Existing analytical models for fluid substitution such as the Biot-Gassmann-Brie populated with representative data will be evaluated for finding the best description of the experimental observations. The integrated results of the workflow are meant to help develop better informed static and dynamic models improving the confidence in the BMV process of CCUS.

Transverse penny-shaped hydraulic fracture propagation in naturally-layered rocks under stress boundaries: A 3D phase field modeling

The ground (tectonic) stress and layered structures of rocks are the among the main factors that influences the hydraulic fracturing behavior. The purpose of this study is to examine the suitability of the phase field model (PFM) in simulating transverse penny-shaped hydraulic fracture propagation and to investigate the phase field feature for the transverse penny-shaped hydraulic fracture in layered rocks under stress boundaries. A phase field model for 3D transverse penny-shaped hydraulic fracture propagation in naturally-layered rocks considering the effect of initial stress field is established. The mathematical model is based on Biot poroelasticity theory and the phase field fracture theory, while the governing equations are solved by using the finite element method in a staggered manner. The established PFM is validated experimentally and analytically by 2D and 3D examples. At last, the influences of the initial stress field, stiffness contrast and inclination angle of the layer interface on the penny-shaped fracture evolution in naturally-layered rocks are investigated by using the PFM. The study indicates that the phase field model has excellent feasibility and practicability in predicting penny-shaped hydraulic fractures. The layer inclination has nearly no effect on the penny-shaped fracture evolution in naturally-layered rocks. The stress ratio Sv/Sh on the boundaries has a significant effect on propagation of the penny-shaped hydraulic fracture. With the increase in Sv/Sh, the hydraulic fracture deflects and propagates along the direction of the maximum in-situ stress. For a high Sv/Sh, branching scenarios can be observed. The stiffness contrast of the rock layers determines whether the penny-shaped hydraulic fracture can penetrate into the adjacent layer. The predictions on the effects of the initial stress field, stiffness contrast and inclination angle of the layer interface provide new understanding of penny-shaped hydraulic fracture propagation in underground geological environment.

Theoretical investigation on characteristics of field reactions of saturated ground subjected to vibrations of inclined pile groups

Inclined pile groups have been adopted in engineering practice (e.g. offshore wind turbines) to withstand strong horizontal environmental loads that are repetitive in nature. Field reactions including the additional stresses and excess pore water pressures are responsible for the cyclic degradation of foundation soil, which may induce the accumulative deformation and fundamental frequency shifting of the marine structure. In this study, a theoretical model incorporating an inclined pile group and a saturated half-space was established, wherein the pile and saturated soil were described by the E–B beam and Biot poroelasticity theories, respectively. The pile and soil were coupled through the receptance matrix, which was established at the pile–soil interaction points in the transform domain. The dynamic impedances of the inclined pile group are first obtained, and then the field responses, including stresses and excess pore water pressure in the saturated ground, are evaluated for different types of loads applied to the pile cap. The frequency response function and spatial distributions of the field responses were obtained for varying rake angle of pile and permeability of soil. It was found that the horizontal force induces the largest responses in the ground when compared to the vertical force and the overturning moment applied to the inclined pile group. It is beneficial to employ an inclined pile group to withstand the horizontal force and overturning moment because the foundation stiffness increases, and the additional stresses in the ground decrease with increasing rake angle.