Total Vertical Stress Research Articles

Axisymmetric fundamental solutions for a finite layer with impeded boundaries.

Axisymmetric fundamental solutions that are applied in the consolidation calculations of a finite clay layer with impeded boundaries were derived. Laplace and Hankel integral transforms were utilized with respect to time and radial coordinates, respectively in the analysis. The derivation of fundamental solutions considers two-boundary value problems involving unit point loading and ring loading in the vertical. The solutions are extended to circular distributed and strip distributed normal load. The computation and analysis of settlements, vertical total stress and excess pore pressure in the consolidation layer subject to circular loading are presented.

Pore pressure/stress coupling and its implications for rock failure

Abstract Clastic dykes and sills witness that subsurface sediment mobilization is often controlled by the brittle failure of units ‘sealing’ overpressured and liquidized sediments. Brittle failure also imposes a limit on the buoyancy pressure that can be exerted by hydrocarbon columns. Conventional understanding of brittle failure induced by increasing pore pressure (P p ) assumes that total minimum horizontal stress (σ h ) is unaffected by changes in pore pressure. However, total minimum horizontal stress increases from shallow, normally pressured sequences to deeper, overpressured sequences. Data from the Canadian Scotian Shelf, the North Sea and the Australian North West Shelf demonstrate such P p /σ h coupling, with the minimum horizontal stress increasing at approximately 60–80% of the rate of pore pressure (i.e., Δσ h /ΔP p = 0.6–0.8). Hence, a greater increase in pore pressure can be sustained prior to brittle failure of units sealing overpressured compartments than would be predicted by conventional, uncoupled failure models. Furthermore, because total vertical stress is not similarly coupled to pore pressure, differential stress (σ 1 –σ 3 ) reduces as pore pressure increases in normal fault regime basins. Thus, the mode of rock failure can not be inferred from differential stress in the stable state and P p /σ h coupling promotes tensile over shear failure.

Laboratory Simulation of Field Compaction Characteristics on Sandy Soils

As a result of the development of much heavier earth-moving and vibratory roller compaction equipment, soil compaction densities in the field are reaching levels that are not attainable in the laboratory. Higher compaction efforts, routinely seen in the field, not only result in higher unit weights but also lower optimum moisture contents than those found by the modified Proctor test. An experimental study was undertaken to evaluate field and laboratory compaction characteristics and to study laboratory compaction techniques further, such as gyratory compaction, in addition to impact and vibratory compaction, for the laboratory simulation of field compaction of A-3 sandy soils. Field test sections were constructed using typical field compaction techniques of today. Earth pressure cells were installed at the base of each lift to monitor total vertical stresses. A series of laboratory gyratory compaction tests for A-3 soils were conducted. Factors including vertical pressure, gyration angle, and gyration numbers were evaluated for the effects on the dry unit weight. The gyratory compaction curves using 200-kPa (29 psi) vertical pressure, a 1.25-degree gyration angle, and 90 gyrations were close to the field compaction curves.

Éléments de couplage thermomécanique dans la consolidation de sols non saturés

Thermomechanical couplings in the consolidation of an unsaturated clayey silty sand are investigated. The couplings are analysed through the influence of the temperature (relative to the total vertical stress) on the mechanical characteristics (relative to thermal) of the consolidation. They are evidenced by means of two types of tests (thermal consolidation and mechanical consolidation). The two types of tests lead to quantitative results comparable with regards to characteristic parameters of both types of consolidation. Some elements of interpretation are proposed to integrate all of the experimental results within a framework of thinking resorting to the thermoelastoplastic behaviour of the soil under study and to the thermal and mechanical hardening phenomena.Key words: unsaturated soils, consolidation, thermal, mechanical, coupling, hardening.

Pore Pressure/Stress Coupling and its Implications for Seismicity

Periodic pressure measurements made during the depletion of oil fields and virgin pressure measurements through normally- and over-pressured sequences in sedimentary basins both demonstrate that changes in pore pressure and minimum horizontal stress (σh) are coupled to one another. Pore pressure/stress coupling is predicted by poroelastic theory. Data from the North Sea (Ekofisk Field) and Texas (Travis Peak Formation of east Texas and Vicksburg Formation of south Texas) suggest that σh decreases at approximately 80% and 50% of the rate of depletion of reservoir pore pressure respectively. Virgin pressures in overpressured sedimentary basins suggest that σh increases at approximately 60-80% of the rate of increase in pore pressure in the Canadian Scotian Shelf, the Australian North West Shelf and the Gannet/Guillemot Fields area of the North Sea. The total vertical stress (σv) is given by the weight of the overburden and is unaffected by changes in pore pressure. Hence, contra to simple, uncoupled models of the effect of pore pressure on rock failure, differential stress in normal fault regime basins (σv - σh) increases as pore pressure decreases, and decreases as pore pressure increases. Increased differential stress with decreased pore pressure can account for depletion-induced seismicity, despite effective stresses increasing. Decreased differential stress with increased pore pressure implies that a greater increase in pore pressure can be withstood prior to failure than would otherwise be predicted, and increases the propensity of tensile, rather than shear failure, occurring with overpressure development.

Éléments de couplage thermomécanique dans la consolidation de sols non saturés

Thermomechanical couplings in the consolidation of an unsaturated clayey silty sand are investigated. The couplings are analysed through the influence of the temperature (relative to the total vertical stress) on the mechanical characteristics (relative to thermal) of the consolidation. They are evidenced by means of two types of tests (thermal consolidation and mechanical consolidation). The two types of tests lead to quantitative results comparable with regards to characteristic parameters of both types of consolidation. Some elements of interpretation are proposed to integrate all of the experimental results within a framework of thinking resorting to the thermoelastoplastic behaviour of the soil under study and to the thermal and mechanical hardening phenomena.Key words: unsaturated soils, consolidation, thermal, mechanical, coupling, hardening.

99/00884 In situ 1H NMR study of the fluidity enhancement for a bituminous coal by coal tar pitch and a hydrogen-donor liquefaction residue : Maroto-Valer, M. M. et al. Fuel, 1998, 77, (9/10), 921–926

This paper presents a study on reservoir-scale failure in coal seams during primary and enhanced coalbed methane production. Two sets of formulations for reservoir-scale coal failure analysis are presented: one is based on the routine effective stress definition, while the other is based on an extended definition. Two application examples – the Fruitland reservoir in San Juan Basin and a reservoir in the Sydney Basin – are investigated in terms of the approximate treatment proposed, which employs the common uniaxial strain and constant vertical total stress assumptions. The Fruitland case study found that the (reservoir-scale) friction angles fitted with the routine effective stress, at a failure pressure equal to 1.9 MPa (observed) and with the assumed weakest low-volatile–medium volatile coal, would be 22–24°. If the extended effective stress definition is used, the friction angle would be 12–15°. The former results are apparently closer to some core-scale laboratory results (usually above 30°) than the latter. However, as discussed in this paper, using the routine effective stress for coal may result in some theoretical anomalies that seem to be fundamentally against the concept of the ‘effective stress’ in a porous rock: i.e., the pore fluid pressure reduces the effective stress in the rock. In contrast, the extended effective stress invoked in this text is theoretically more plausible for coal.

Development of structure in sedimenting soils

At very low densities, a cohesive soil slurry behaves as a dense fluid, with the particles supported by the pore water, which has a pressure equal to the total vertical stress. As the soil settles ...

Consolidation of soil under depth-dependent ramp load

This technical note presents a mathematical solution for the consolidation analysis of a soil layer with a change in vertical total stress that varies linearly with depth and time and then remains unchanged after a certain period of time. The solution is described in detail. Results are presented as figures and tables for practical applications.Key words: consolidation, pore-water pressure, average degree of consolidation, total stress, clay, soil.

Model for the simulation of swelling-pressure measurements on expansive soils

Numerous laboratory swelling tests have been reported for the measurement of swelling pressure and the amount of swell of an expansive soil. These test methods generally involve the use of a conventional one-dimensional oedometer apparatus. Few attempts, however, have been made to formulate a theoretical framework to simulate the testing procedures or to visualize the different stress paths followed when using the various methods. The simulation of the oedometer tests on expansive soils is required to fully understand the prediction of heave. The correct measurement of swelling pressure is required for an accurate prediction of heave. It is further anticipated that some information on unsaturated soils property functions may be approximated from the back-analysis of the data. A theoretical model is proposed to describe the pore-water pressures with time and depth in a specimen as well as the volume changes during various oedometer swell tests. The model is formulated based on equilibrium considerations, constitutive equations for an unsaturated soil, and the continuity requirement for the pore fluid phases. The transient water flow process is coupled with the soil volume change process. The model can be used to describe the volume-change behaviour, pore-water pressure, and vertical total stress development in an unsaturated soil during an oedometer test performed by any one of several test procedures. The model has been put into a finite element formulation using the Galerkin technique. All the parameters required to run the model can be obtained by performing independent, common laboratory tests. The proposed model was used to simulate the results from free-swell, constant-volume, constant water content, and loaded-swell oedometer tests. Computed values of volume change, vertical total stress, and pore-water pressure are in good agreement with measured values.Key words: unsaturated soil, expansive soil, swelling pressure, theoretical simulation, constant-volume oedometer test, free-swell oedometer test, loaded-swell oedometer test.

Evaluation of Collapse Potentials Using Single Oedometer Test Results

Collapsibility is a property of some soils and constructed fills whose volume suddenly decreases with an increase in moisture content under practically unchanged total vertical stress. This phenomenon, associated with unpredictable breakdown of soil and/or fill structure, has always been a topic of hot discussions and tough decisions. The necessity to evaluate and control collapsible soils and fills has brought to life different laboratory and field methods of collapse potential measurements. Single and double ring oedometer tests became the most popular and relatively inexpensive source of collapse potential information all over the world. Numerous graphs, charts, and empirical formulas introduced for different regions summarize engineering laboratory and field experience in this area. This paper presents an analytical method for a conservative estimation of soil collapsibility utilizing oedometer test results. Simple formulas are offered for the prediction of maximum additional settlement of water saturated natural soils and fills under practically unchanging total vertical stresses. Derived formulas are illustrated with test results published in literature.

The caprock of the Snorre Field, Norway: a possible leakage by hydraulic fracturing

The Snorre Field, located on the Tampen Spur in the west of the Viking graben, presents a 300 m oil column in Triassic and Lower Jurassic reservoirs, and it is characterized by high pressures. The caprock is formed by thick shale of Cretaceous and Palaeocene age. Some oil shows are found in the caprock up to a few hundred metres above the reservoir and have the same origin as the oil in the reservoirs. The secondary migration process seems to be linked to high overpressures within the reservoir. The pore pressure at the top of the reservoir reaches about 82% of the total vertical stress, which is close to the minimum horizontal stress according to leak off test data. Hydraulic fracturing probably occurs, increasing the shale permeability so that some oil escapes from the reservoirs. The Snorre Field can be considered as a dynamic trap where a constant pressure regime is maintained by several processes linked to the local conditions and particularly to its structural situation, and where regulation of the system occurs at the top of the reservoirs. The pressure regime and the in situ stress conditions are the key factors in the prospectivity of the traps in this area.

In situ measurement of total natural horizontal stresses in an expansive clay

Vibrating-wire earth pressure cells were installed in a highly expansive, unsaturated lacustrine clay deposit, to measure the natural in situ horizontal pressure. The work was part of a project to investi- gate the design of retaining structures in expansive clay. Care was taken in the placement of the cells, to ensure that the soil was disturbed as little as possible, and the pressures were monitored for several years. Total horizontal earth pressures of two or three times the total vertical stress were recorded, and a seasonal fluctuation related to rainfall and evapo-transpiration was noted. Des cellules de pression du sol à fil vibrant ont été installés dans un dépôt d'argile lacustre non-saturée et très expansive afin de mesurer la pression horizontale naturelle en place. Ce travail faisait partie d'un projet pour étudier la construction de soutènement dans l'argile expansive. Les cellules furent positionnées soigneusement, pour que le sol soit remanie le moins possible et les pressions ont été enregistrées pendant plusieurs années. On enregistra des pressions horizontales totales due sol deux ou trois fois supérieures à celle de la contrainte totale verticale et une variation fut notée en function des précipitations et de l'évapotranspiration.

Total Stress Probe Determination of Clay Slurry Density

Abstract The progress of sedimentation, self-weight consolidation, and gain in surface strength of a hydraulic clay fill were observed by monitoring the density improvement of the clay slurry with time. A practical method of measuring the in situ slurry density profile with depth is to employ a submersible gamma-source, backscattertype nuclear density gauge. A slurry consolidation test in the laboratory has demonstrated that above 1.5 times the liquid limit, the horizontal and vertical total stresses are equal. Hence, from the horizontal total stress measurements with a vertical probe, the in situ vertical total stress profile of the slurry can be obtained. In principle, the integration of the density profile with depth gives the vertical total stress profile. Therefore, an estimate of the density can be made from the gradient of the vertical total stress with depth. Comparisons of field measurements of the total stress profile of a clay slurry in a reclamation project using the total stress probe and the density profile by the nuclear density gauge demonstrates this principle, thus confirming that the total stress probe with appropriate data interpretation can be used to measure the density of an in situ clay slurry around its surface.

An instrumented steep reinforced soil embankment at Åndalsnes, Norway

The design and construction of an instrumented steep reinforced soil embankment built over a competent foundation is described. The embankment, which is intended to act as a snow avalanche barrier, was constructed from a uniformly graded medium sand and ‘Tensar’ SR2 geogrid was used as the primary reinforcement. Reinforcement strains were measured using ‘Bison’ strain coils and measurements were also made of stresses and lateral displacements occurring in the soil. The measured values of reinforcement strain are shown to be substantially less than those obtained from a limit equilibrium analysis of the embankment in which the mobilized friction angle is based on pressure cell measurements of vertical and horizontal total stress. This result is consistent with other published field trials and indicates an excessive conservatism in the limit equilibrium methods currently used for design.

Preconsolidation pressure from piezocone tests in marine clays

Piezocone penetration tests were carried out at five sites in marine clay with overconsolidation ratios ranging from 1·3 to 4·8 A simple model for the behaviour of these clays indicates that the effective vertical yield stress mobilized along the cone axis during penetration is equal to the difference between the actual induced total vertical stress in the soil and the total porewater pressure. The actual induced total vertical stress can he derived from piezocone test data. Theoretically the ratio of the vertical yield stress inferred from piezocone results and the preconsolidation pressure should correlate with the overconsolidation ratio. This hypothesis is supported by the field and laboratory investigations presented in this study. Des essais de pénétration avec un piezocone ont été effecté sur cinq sites d'argile marine ayant des rapports de surconsolidation variant de 1,3 à 4,8. Un modèle simple de comportement de ces argiles indique que la contrainte effective verticale à l'état limite mobilisée durant la pénétration est égale à la différence entre la contrainte totale verticale et la pression interstitielle générées dans le sol. La contrainte totale verticale peut être déterminée à partir des réultats des essais de piezocone. En théorie, le rapport de la contrainte verticale à l'état limite, calculée à partir des résultats du piezocone, et de la pression de surconsolidation devrait être une fonction du rapport du surconsolidation. Cette hypothése est vérifiée par les essais in situ et de laboratoire présentés dans cet article.

Theoretical One-Dimensional Water to Soil Impact Pressures

ABSTRACT THEORETICAL equations which describe the pressures caused by one-dimensional impact of water onto soil surfaces were derived from basic mechanics. The pressures of impact on the soil skeleton and in the soil pores were shown to be functions of the densities and volume fractions of the soil pores and skeleton, a dynamic coupling coefficient, and the compressional wave velocities in the two soil fractions. Theoretical or empirical relationships between the dynamic parameters and soil matric potential, porosity, and degree of saturation were presented, and the total and effective vertical stresses and pore water pressures caused by impact were calculated as a function of those static soil properties. The calculated total vertical stresses were of the order of 0.05 to 0.16 the value for impact on rigid surfaces, and were largely a function of soil matric potential and porosity. The calculated pore water pressures were primarily dependent upon the degree of saturation. At high saturation levels and low matric suctions, calculated pore water pressure exceeded calculated effective vertical stress, indicating a liquified and unstable state for that soil condition. The results will be useful in providing input functions for numerical or analytical studies of soil response to waterdrop impacts.

Excess Pore Water Pressure Due to Undrained Strip Loading on a Cross-Anisotropic Elastic Soil Deposit

The characteristics of the excess pore water pressure developed in a saturated cross-anisotropic elastic soil deposit immediately after the application of a load are theoretically examined. It is indicated that the excess pore water pressure is quantitatively equivalent to the increase in total vertical stress only when the elastic constants of soil skeleton have the relation of μh + μvEh/Ev = 1 and to the increase in mean normal stress only when the soil skeleton satisfies the zero-dilation condition of μh + μvEh/Ev = 1 and μv = 0.5. Moreover, it can be found from numerical results that the excess pore water pressure is exceedingly affected by the anisotropy of Young’s modulus of soil skeleton.

Relationship Between Horizontal Stress and Depth in Sedimentary Basins

Summary Previous work on establishing a relationship between in-situ stress and depth is reviewed. On the basis of data from literature, supplemented by available field data, equations are proposed to describe the trend of horizontal stress with depth for normally pressured formations in the U.S. gulf coast region. A separate correlation between horizontal stress and pore pressure allows this trend to be extended to formations containing abnormal pore pressures. Having achieved a good correlation for data from this well-documented region, we repeat the process for other parts of the world, using data from hydraulic fracture treatments and formation integrity (leakoff) tests. Similar relationships between horizontal stress and depth are found to hold for normally pressured areas that are geologically and tectonically similar to the U.S. gulf coast. Coupled with regional correlations between horizontal stress and pore pressure, these relationships enable horizontal stress levels to be estimated for a given depth, provided the pore pressure also is known. Introduction The instantaneous shut-in pressure (ISIP) recorded during or after a fracturing job or during a minifracture test provides a good approximation to the minimum principal in-situ total stress components sHmin. The vertical total stress or overburden stress sV (normally the maximum principal in-situ stress) can be derived by integration of the formation density, compensated (FDC) log. In tectonically inactive areas, the intermediate principal stress, sHmax, can be assumed approximately equal to the minimum principal stress: sHminsHmax<sV. In the more general case, when sHmax>sHmin, the value of sHmax in principle can be derived from the formation breakdown pressure pb as measured at the start of a fracturing job. For a fully plastering fluid, for instance, pb 3sHmin-sHmax-Pc where Pc is the pore pressure. In practice, however, sHmax cannot be determined accurately because the breakdown value will be influenced by hole geometry, hole integrity, mud-cake properties, and the extent to which the fluid penetrates into and pressurizes the pore space around the borehole. Also, hydraulic fracturing data are often lacking in many areas of the world. The only remaining way, then, to obtain information relation to in-situ stresses is to analyze the results of formation integrity tests (leakoff tests and casing-seat tests). In these tests, the pressure at which the formation starts taking fluid may range from sHmin to 2sHmin-Pc. Therefore, it is the lower end of the range of values from formation-integrity tests that is of interest for in-situ stress determination. Review of Previous Work The majority of hydraulic fracturing/formation-integrity test data quoted in literature are from the U.S. gulf coast and Santa Barbara Channel (CA). From these data, a number of authors have derived fracture gradient correlations to be used in planning drilling programs.

Principal Stress Ratios in Cretaceous Limestones from Texas Gulf Coast

Study of calcite twin lamellae abundance in cores of low-porosity limestones indicates that the average number of lamellae per millimeter increases by 10 for every 5,500 ft of depth through the 20,800-ft interval sampled. The conditions of lamellae formation have been determined by creep tests on a representative limestone at several differential stress levels and loading durations at appropriate confining pressures and temperatures. Results show that (1) twin lamellae do not form when the specimens are subjected to a uniform confining pressure alone, (2) the lamellae increase in abundance with increasing differential stress, and (3) the abundance of lamellae increases with the duration of loading. Creep tests at differential stresses of 1,450-5,800 psi over durations of ,000 minutes indicate that the average number of lamellae per millimeter increases by 10/510 psi differential stress. From these results, we infer that the differential stress gradient in situ could not have exceeded about 510 psi/5,500 ft of burial and, because of the much longer time intervals in nature, this gradient probably was much less. Assuming a total vertical stress gradient of 1 psi/ft and a pore-pressure gradient of 0.5 psi/ft, we conclude that the probable maximum ratio of vertical-to-horizontal effective stresses (^sgrv/^sgrh = ^sgr1/^sgr3) in the Texas Gulf Coast is about 1.2.