Criticism of the Analytical Solutions to the Wave-Induced Cyclic Response of a Poro-Elastic Seabed of Finite Thickness

This paper deals with the wave-induced cyclic response of a porous seabed (by means of oscillating parameters: pore-fluid pressure, soil displacement components, effective normal stress and shear stress components) due to a surface sinusoidal water-wave propagating over a seabed of infinite thickness. The main existing analytical solutions to the governing problem are critically discussed, pointing out their meaningful errors and doubtful items. A phase-lag phenomena is particularly studied as an immanent part of any complex-valued analytical solutions having a cyclic nature.

This paper discusses the influence of different sign conventions for strains and stresses, i.e. the solid mechanics sign convention and the soil mechanics sign convention, on the form of governing partial differential equations (the static equilibrium equations and the continuity equation) used to describe the wave-induced cyclic response of a poro-elastic seabed due to propagation of a sinusoidal surface water-wave. Some selected analytical solutions, obtained by different authors and published in specialist literature in the form of complex functions describing the wave-induced pore-fluid pressure, effective normal stress and shear stress oscillations in the seabed, have been analysed and compared with each other mainly with respect to different sign conventions for stains and stresses and also with regard to different orientations of the positive vertical axis of the two-dimensional coordinate system and different directions of surface water-wave propagation. The performed analyses of the analytical solutions has indicated many inaccuracies, or even evident errors and exemplary mistakes of wrong-signed values of basic wave-induced response parameters (the shear stress in particular), thereby disqualifying these solutions and their final equations from practical engineering applications. Most of the mistakes found in the literature must be linked to authors’ lack of understanding and consistency in an uniform application of a certain sign convention for strains and stresses in the soil matrix at both stages of mathematical formulation of the governing problem and correct interpretation of equations of the final analytical solution. The present paper, based mostly on a thorough literature review, ought to draw attention and arouse interest among coastal scientists and engineers in proper identification and use of the existing analytical solutions to the wave-induced cyclic seabed response – solutions which differ very often in the applied sign convention for stresses in the soil matrix.

Quantifying and understanding friction and wear behaviour of any type of material remains a challenge to this day. This is also true for polymers that are used frequently in sliding applications. This thesis focuses on the development of quantitative measurement techniques that can be used to understand friction and wear of polymers. To understand the influence of material properties on friction and wear behaviour it is necessary to zoom in on the relevant processes in a sliding contact. A macroscopic contact between two surfaces typically consists of multiple contacts between roughness peaks. These micro-contacts make up the real contact area which is usually a small fraction of the apparent contact area, and which depends on the mechanical properties of both surfaces as well as on the loading conditions. The friction force measured in experiments is the product of this real contact area and an average effective shear stress. Because the real contact area is difficult to control and measure for macroscopic contacts such contacts are not very useful in separating the contributions to the friction force. In contrast, single asperity techniques offer the possibility to control independently the contact area and normal load and therefore offer a way forward to a critical interpretation of measured friction forces. In the work described in this thesis microscopic tribological single–asperity experiments are used to study structure-property relations. These single asperity experiments are performed using the Lateral Force Apparatus that was drastically modified to better suit this purpose. A new driving system was developed that allows friction measurements in which the sliding velocity may be varied across 5 orders of magnitude with accurate position control. This combination makes it possible to perform single–asperity measurements at widely differing speeds which are shown to be important for the interpretation of sliding friction on polymers. Accurate position control is shown to be crucial in developing advanced wear measurement techniques. In sliding friction distinction between the contribution of contact area and effective xi xii SUMMARY shear stress to the friction force is a key issue. Depending on mechanical properties and loading conditions, all materials exhibit creep on a characteristic time scale. In polymers creep is especially relevant since the associated timescales are relatively short. In single asperity friction the asperity radius and sliding speed set a contact time, during which the contact area may evolve by creep. It is shown that the contributions of contact area and effective shear stress can be distinguished from one another using single–asperity measurements at widely differing sliding velocities. In the study of wear the interpretation of measurements on macroscopic multi– asperity contacts also pose problems since they consist of a collection of microcontacts between deformed asperities. Since the strain at failure of a polymer is expected to be an important factor in determining the wear of polymers the unambiguous strain distribution of a single asperity contact is an advantage in the study of structure-wear relations. In this thesis a novel single–asperity technique to measure wear rate is developed. In this method the wear rate is measured in real time. The method is fast, uses very little material, and yet gives good statistics and a strong correlation with macroscopically measured wear rates. In a study on PE it is found that the wear rate is related to the molecular weight. Quantitative single–asperity measurements are a critical step in understanding structure-tribology relations. While macroscopic tribological experiments can only scratch the surface of structure-tribology relations, single–asperity techniques probe the material properties lying underneath.

A series of laboratory experiments were conducted to investigate the influence of overburden and in-situ stresses on non-Darcy gas flow behavior in Dakota sandstone. Nitrogen was flooded through cylindrical core in a triaxial core holder under specific condition of temperature at 100°F, with core outlet pore pressure at 500 psi, axial and radial stress from 2.000 to 10,000 psi, and. nitrogen reservoir pump pressure at 2.000 psi with pump flow rates from 25 to 10,000 cc/hr at 80°F. Permeability and non-Darcy coefficient were determined using Forchheimer's method. It was found that with the increase of overburden and in-situ stresses, permeability decreases while non-Darcy flow coefficient increases. Average effective normal stress and shear stress were used to quantitatively express the influence of overburden and in-situ stresses. It was found that average effective normal stress has a good linear relationship with both permeability and non-Darcy flow coefficient. In contrast, average shear stress did not appear to influence the permeability and non-Darcy coefficient.

Dynamics anisotropy in a porous solid with aligned slit fractures

Most of the widely used seismic soil liquefaction triggering methods propose cyclic resistance ratio (CRR) values valid at a reference normal effective stress ('v,0) of one atmosphere, and a zero static shear stress (st,0) state. Then a series of correction factors are applied to the CRR, to account for the effects due to variations from the reference normal effective and static shear stresses (i.e. K and K corrections). In the literature, there exist a number of stress correction factors used for seismic soil liquefaction triggering assessment. However, the presence of a wide range of them, some of which even exhibit contradicting trends, suggests that more research needs to be performed to reduce this uncertainty. Additionally, these stress correction factors are treated as being strain-independent and are applied disjointedly to CSR or CRR. The main motivation of this on-going study is defined as to develop a strain-dependent semi-empirical framework to assess combined effects of i) 'v,0, ii) st,0 acting on the plane, where cyclic shear stresses either produce iii) shear stress reversal or not. For this purpose, cyclic simple shear tests were performed on laboratory reconstituted sand samples. Additionally, cyclic test data were compiled from the available literature. On the basis of probabilistic assessment of this data, a unified correction scheme, which incorporates the interdependent effects of both overburden and static shear stresses along with the degree of cyclic shear stress reversal, has been developed.

Most of the widely used seismic soil liquefaction triggering methods propose cyclic resistance ratio (CRR) values valid at the reference normal effective stress (σ′v,0) of one atmosphere and zero static shear stress (τst,0) states. Then, a series of correction factors are applied on this reference CRR, for the purpose of assessing the variability due to normal effective and static shear stress states (i.e. Kσ and Kα corrections) acting on the horizontal plane. In the literature, a number of relationships suggested to be used as part of liquefaction triggering methodologies. However, the presence of a wide range of correction factors, some of which with even contradicting trends, suggests that more research needs to be performed to reduce this uncertainty. Additionally, these stress correction factors are treated as being strain-independent and are applied disjointedly to CSR or CRR. The main motivation of this on-going study is defined as to develop a strain-dependent semi-empirical framework to assess combined effects of i) σ′v,0, ii) τst,0 acting on the plane, where cyclic shear stresses either produce iii) shear stress reversal or not. For this purpose, cyclic simple shear tests were performed on laboratory reconstituted sand samples. Additionally, cyclic test data were compiled from the available literature. On the basis of probabilistic assessment of this data, a unified correction scheme, which incorporates the interdependent effects of both overburden and static shear stresses along with the degree of cyclic shear stress reversal, has been developed.

Regions in the vasculature exposed to steady laminar flow have a lower likelihood for atherosclerosis than regions exposed to disturbed flow with low shear stress. We previously found that laminar flow of short duration inhibited tumor necrosis factor (TNF)-alpha-mediated proinflammatory signaling in cultured endothelial cells (ECs). However, mechanisms responsible for the atheroprotective effects of physiological shear stress remain undefined. Therefore, we examined the effects of chronic shear stress on TNF-alpha-induced inflammatory responses using an ex vivo perfusion organ culture system. Rabbit aortas were exposed to low or normal shear stress (0.4 or 12 dyne/cm2) at a constant pressure for 24 to 26 hours. EC and vascular smooth muscle cell (VSMC) proteins were selectively purified. After exposure to low shear stress, TNF-alpha (50 ng/mL, 6 hours) specifically stimulated vascular cell adhesion molecule (VCAM)-1 expression in ECs but not VSMCs. TNF-alpha-stimulated VCAM expression was inhibited significantly by preexposure to normal shear stress. Normal shear stress inhibited TNF (15 minutes) activation of mitogen-activated protein (MAP) kinases (c-Jun NH2-terminal kinase [JNK], p38, extracellular signal-regulated kinase [ERK]) in ECs. Specific pharmacological inhibitors of JNK and p38 but not ERK significantly inhibited TNF-induced VCAM expression. Normal shear stress prevented the association of TNF receptor (TNFR)-1 with TNFR-associated factor (TRAF)-2. There was no effect of low or normal shear stress on TNF-alpha-induced nuclear factor-kappaB activation. A nitric oxide synthesis inhibitor, NG-nitro-l-arginine methyl ester, did not reverse the inhibitory effects of shear stress on VCAM expression. These results suggest that physiological shear stress is antiinflammatory by specifically inhibiting MAP kinase signaling and inhibiting TRAF-2 interaction with TNFR-1.

The wave-induced pore pressures and effective stresses in a saturated submarine sediment are treated by means of the finite element method. By using the general theory of behaviour of the saturated poro-elastic media presented by Biot (1972, 1973), field equations of motion are established. By introducing a valid approximation for very slow phenomena, the full formulation is simplified and the well-known equations of consolidation are obtained. Stability conditions and accuracy of the process of solution are discussed. A verification of the written finite element program is made by a comparative study with the infinite depth solution given by Yamamoto (1978) and Madsen (1978). The effects of bed thickness, permeability and soil stiffness on the wave-induced pore pressures, effective normal stresses, shear stresses, horizontal and vertical displacement at the mud line and with depth are investigated by various examples. The response of a heterogeneous sea bed to a harmonic wave loading is compared with a homogeneous case. As an example of application, the vertical distribution of wave-induced pore pressures and effective stresses within the submarine sediments limited by a sloping surface are considered. La méthode par éléments finis est employée pour traiter les pressions interstitielles induites par les vagues et les contraintes effectives dans un sédiment saturé sous-marin. Les équations de mouvement dans le champ sont établis à l'aide de la théorie générale présentée par Biot (1972, 1973) pour le comportement des matières poroélastiques saturées. La formulation complète est simplifiée et les équations connues de consolidation sont obtenues par l'introduction d'une approximation valable pour des phénomènes très lents. L'article discute les conditions de stabilité et la précision de la méthode de solution. Le programme écrit en elements finis est vérifié par moyen d'une comparaison avec la solution à profondeur infinie donnée par Yamamoto (1978) et Madsen (1978). Des examples sont donnés pour étudier les effets de l'epaisseur de la couche, de ia perméabilité et de la rigidité du sol sur les pressions interstitielles induites par les vagues, les contraintes normales effectives, les contraintes de cisaillement et le déplacement horizontal et vertical à la surface du fonds marin et avec la profondeur. La réponse d'un fonds marin hétérogène au chargement harmonique par les vagues est comparée avec un cas homogène. L'article présente comme exemple pratique d'application la distribution verticale des pressions interstitielles induites par les vagues et des contraintes effectives à l'intérieur de sédiments sous-marins limités par une surface en pente.

The shale oil resource is growing in offshore basins of China and considered to be a prosperous substitution for shale oil/gas on land. Unlike on land shale oil reservoir, the offshore shale oil play is featured by younger stratigraphy, lower diagenetic compaction, and higher-pressure coefficient. Strong heterogeneity, complex mineralogical composition, and unstable tectonic activities, and more naturally developed fractures are the main challenges for evaluating offshore shale oil. The common integration of geological and engineering evaluation on shale oil is not adequate, as natural fracture effectiveness can’t be verified without geomechanical analysis. To get more accurate petrophysical evaluation, the advanced logging spectroscopy log and nuclear magnetic resonance (NMR) log are indispensable. The oil-bearing potential, storage capacity, and fluid movability are analyzed by NMR log and total organic carbon (TOC), mineralogical composition, and matrix density are calculated by spectroscopy log. Core photos, thin sections together with spectroscopy log were used to characterize shale lithofacies. Borehole imaging log was utilized for geological evaluation especially for fracture identification. Based on the electrical resistivity image and standoff image, fractures are categorized into three types: fully open fractures, partially open fractures and closed fractures. Based on Coulomb failure function, these fractures are further integrated with effective normal stress and shear stress in Mohr-Coulomb for fracture stability analysis to geomechanically verify whether the fractures are critically stressed or stable. The fracture stability analysis shows the fractures dip azimuth from 280 to 330 deg are more stable (black) than other azimuthal directions, most of the effective fractures (fully open fractures and partially open fractures based on image logs) are tending to be critically stressed, the result of which is over 85% consistent to the fracture identification from borehole image log. The fractures that are both open and critically stressed are considered as effective fractures which will contribute more permeability to the shale oil reservoir, and on the contrary, the fractures that are partially open/closed and stable are considered as non-effective fractures.

The instability region in anisotropic seabed to water waves has investigated to estimate from the five independent elastic parameters of anisotropic materials and coefficient of permeability. Especially, the phase delay, pore water pressures, effective normal stresses and shear stresses have been discussed. As the results of the analysis of the 2- and 3- dimensional stresses distribution, we have to not only judge the instability of the seabed by the area where the vertical effective stresses is negative. We also have to examine the conditions leading to the formation of non-vertical pulling destruction and shear destruction.

Quasi‐static field equations for fully saturated porous elastic media, based on Biot's theory (1972‐1973), established in the writer's previous works (1989‐1990) are used in order to describe the behavior of such materials under wave ocean loading. A brief description of cross anisotropy with a vertical axis of symmetry (orthotropy) is given. The five independent elastic parameters of anisotropic materials are clarified. The field equations are modified and adapted for application to anistropic cases. A numerical procedure (finite element discretization) for the motion equations of an orthotropic saturated poro‐elastic seabeds is presented. The accuracy of the chosen algorithm is discussed. The wave‐induced pore pressures, effective stresses and displacements in an anisotropic submarine sediment are investigated. The results illustrate a significant influence of elastic anisotropic parameters on the wave‐induced pore pressures, effective normal stresses, shear stresses, horizontal and vertical displacemen...

The behaviour of a real case of geosynthetic reinforced embankment slope (GRES) over soft cohesive soils with a prefabricated horizontal drains system (PHDs) was studied by two-dimensional finite element method, considering both small and large displacement assumptions. In order to determine the input geotechnical parameters accurately, laboratory tests and finite element back analysis were carried out. Coupled mechanical and hydraulic analysis was conducted to predict time-dependent behaviour of GRES under staged loading applied in the undrained conditions. The main objective of this study is to assess the effects of changes in geometry on deformation and stress behaviour during the consolidation process. Indeed, the developments of the settlement, horizontal displacement, excess pore pressures, normal effective stress and shear stress during and after construction periods were investigated. According to the large displacement computation results, the combined use of geosynthetic reinforcement with PHDs significantly reduces both the settlement and horizontal displacement but increases pore pressures. Therefore, the required number of construction stages can be reduced. The results of small and large displacement analyses show that the shear strength improvement in the upper embankment part is induced by the combination of surface roughness (skin friction) and arching effects within the embankment fill, while in the lower part it is mainly due to the confinement effect.

A model linking subaqueous dune migration to the effective (grain related) shear stress is calibrated by means of flume data for bedform dimensions and migration rates. The effective shear stress is calculated on the basis of a new method assuming a near‐bed layer above the mean bed level in which the current velocity accelerates towards the bedform crest. As a consequence, the effective bed shear stress corresponds to the shear stress acting directly on top of the bedform. The model operates with the critical Shields stress as a function of grain size, and predicts the deposition (volume per unit time and width) of naturally‐packed bed material on the bedform lee side, qbcrest. The model is simple, built on a rational description of simplified sediment mechanics, and its calibration constant can be explained in accordance with estimated values of the physical constants on which it is based. Predicted values of qbcrest correlate with measured values of bedform height multiplied by bedform migration rate with R2 = 0·83. Copyright © 2010 John Wiley & Sons, Ltd.

For a safe and efficient reservoir development, it is important to understand if, how, when and where faulting and fracturing will occur as a function of reservoir production or stimulation operations, or in case of a dumpflood or an internal blow-out situation. This paper describes 1) the making of a numerical geomechanical model to achieve this understanding, 2) the uncertainty in geomechanical model results, and 3) how the model results were applied in operational decisions for production and on reservoir fluid containment. The case study presented here is one of deep-gas production from stacked thin (few meters) sandstone reservoirs vertically separated by shale layers and laterally cut by steeply-dipping sealing normal faults, with pore pressure differences of several MPa across the faults in many sand-shale and sand-sand juxtapositions. We calculated the effective normal stress (sn) and maximum shear stress (tmax) along the faults and in the country rock as a function of pore pressure changes documented in the field development plan. The sn - tmax data were compared with fault slip and fracture-opening criteria based on Mohr-Coulomb frictional slip and tensile fracturing laws using fault cohesion, fault-friction-angle, and tensile strength as input. The geomechanical model results indicate that the current operational criterion of a maximum pore pressure difference of 7 MPa across the faults can be increased to 10 MPa without creating shear failure or tensile fracturing. This would lead to greater operational flexibility, cost reduction (less wells), and accelerated yet safe production. Introduction Reservoir rocks deform when their pore pressure is changed due to hydrocarbon production or because of fluid injection. A pore pressure reduction (depletion) increases the average effective stress on the rock, and leads to compaction (densification) and porosity reduction. A pore pressure increase, on the other hand, decreases the average effective stress on the rock, and leads to a bulk-volume increase (dilation) and to a porosity increase. Because the compacting or dilating reservoir remains connected to the rock around it, there will be deformation, displacements and total stress changes in these rocks too (Teufel et al. 1991, Zoback 2007). These total stress changes in the non-reservoir rock do not "stop" at the boundary of the reservoir, but are transmitted to the reservoir as well, interacting with the total stress changes within the reservoir proper. Therefore, pore pressure changes in the reservoir are typically accompanied by changes in the total stress in and around the reservoir. Together, they make up the operation-induced change in effective stress in and around the reservoir, also known as the stress path (Addis et al. 1996, Hettema et al. 2000, Nelson et al. 2006, Sayers and Schutjens 2007, Davison et al. 2013). Particularly strong total stress changes (due to depletion or injection) are expected in fault-bounded reservoir compartments, because of the (often) strong fault-position-controlled lateral variation in operation-induced pore pressure change. Hence, rather than the common "pancake"-model where the overburden acts like a dead weight (see Figure 1a), in pore pressure compartments.