Terzaghi's One-dimensional Consolidation Theory Research Articles

Improved analysis and design for surcharging

Surcharging or preloading is one of the oldest and most widely used in situ ground improvement techniques to strengthen weak compressible clays and to remove undesirable settlements prior to erection of permanent infrastructure. Recently, the ground improvement technique has been adopted in combination with many other techniques. The current design methodology for surcharging based on the concept of average degree of consolidation is inadequate, as all the primary consolidation settlement to be induced by the permanent load is not eliminated by the surcharging process. The problem is quantitatively analysed using Terzaghi's one-dimensional consolidation theory. The proportion of residual primary consolidation settlement is quantified, and the starting time of the re-occurrence of primary consolidation on exertion of the permanent load is determined. The effect of a change in surcharging duration on the proportion of residual settlement is quantified. The results are presented in design charts to facilitate application of the results by practicing geotechnical engineers.

Assessment of soil parameters during post-liquefaction reconsolidation of loose sand

Saturated deposits of loose sand may suffer liquefaction under earthquake shaking. Liquefaction-induced damage occurs during the earthquake loading and may continue during the post-liquefaction reconsolidation stage in which excess pore pressures gradually dissipate. An accurate evaluation of soil parameters is of great significance for the full depiction of this process. Consolidation-related problems are typically investigated using Terzaghi's one-dimensional consolidation theory, assuming a constant permeability, one-dimensional stiffness, and consolidation coefficient throughout this process. Some studies based on physical model tests suggest that an assumption of a single and constant value of soil parameter is not appropriate to study the reconsolidation of liquefied sand. This paper presents the results of three geotechnical centrifuge experiments to contribute to the current understanding of this phenomenon. The centrifuge data is combined with oedometer and fluidization test data, producing several empirical relationships to estimate the soil parameters related to the reconsolidation of liquefied sand. A simplified method is adopted to reproduce the time histories of excess pore pressure dissipation and ground surface settlement using the estimated soil parameters as the input. It is shown that the coefficient of consolidation and one-dimensional stiffness vary as a function of effective stress or excess pore pressure ratio, markedly increasing during the reconsolidation of liquefied sand. The predictions of the proposed methodology appear to match the experimental measurements reasonably well as long as appropriate soil parameters are used.

Study on the Treatment Technology of Silty Clay in Reconstruction and Expansion Project

<p>According to different geological conditions and different soft foundation thicknesses, this paper uses Terzaghi's one-dimensional consolidation theory, finite element simulation condition calculation and combined with code requirements to analyze the effects of replacement, cement mixing piles, and prestressed pipe piles on the foundation treatment of silty silty clay, and finally through the comparison and selection of plans, from the perspective of economic and technical rationality, determines the specific treatment method used.</p>

Evaluation of hydro-mechano-chemical behaviour of bentonite-sand mixtures

Bentonite-sand mixtures are widely used in engineering barrier of deep geological disposal of high-level radioactive nuclear waste and anti-seepage barrier of civil geotechnical engineering. Under the action of groundwater solution infiltration and external stress, the hydro-mechanical (HM) behaviour of bentonite-sand mixtures, i.e. the swelling characteristics and permeability, will change. Once the anti-seepage and filtration effect is weakened or lost, the pollutants will spread to the biosphere. Therefore, it is necessary to study the swelling characteristics and permeability of bentonite-sand mixtures under coupled mechano-chemical (MC) effect and to establish corresponding prediction model. For this reason, swelling tests under salt solution with different concentrations are conducted on pure bentonite and its mixtures with 30%, 70% and 90% sand contents, the compression tests are carried out on saturated samples, and the saturated permeability coefficient k of the sample under each load is calculated by Terzaghi's one-dimensional consolidation theory. The concepts of true effective stress p e , montmorillonite void ratio e m and critical sand content α s are introduced to determine the e m - p e relationship and finally the k - e m relationship of bentonite-sand mixtures. It is found that when the sand content α ≤ α s , the e m - p e relationship of the mixture is linear and independent of the salt solution concentration, and when α > α s , the e m - p e relationship of bentonite-sand mixture is bi-linear with the true effective deviatoric stress p esα as the intersection. In addition, the e m - k relationship also shows the linear trend when α ≤ α s , and the slope of the line increases with the increase of the salt solution concentration. When α > α s , the k - e m relationship will deviate from the linear relationship. Moreover, the larger the sand content is, the farther the deviation is. On the basis of summing the regularity, a model for predicting the HM behaviour of bentonite-sand mixture under the coupled MC effect is proposed. By comparing the swelling and permeability test results with model prediction results of different types of bentonite and its sand mixtures, the predictive model is verified. The study on the HM behaviour of bentonite-sand mixtures under salt solution infiltration and the model establishment can provide experimental and theoretical basis for the design and construction of anti-seepage engineering by bentonite-sand mixtures.

Investigation of the coefficient of consolidation of fine-grained soils using combined apparatus

The scope of this investigation is to compare the coefficient of consolidation (cv) values defined by the Taylor's Square Root of Time Fitting Method, which is obtained from the conventional oedometer tests, with the cv values calculated by Terzaghi's One-Dimensional Consolidation Theory, which is obtained from the permeability-consolidation tests performed with a combined apparatus specifically designed for this study. In addition, an empirical relation is developed to determine cv using the coefficient of permeability (k) and index properties of the soils. The cv values obtained from the permeability-consolidation tests using the combined apparatus were found to be larger than the cv values defined by the Taylor's Method, which is one of the oedometer tests. The findings showed that the difference was more prominent in the soil samples with a high plasticity. It was also found that the cv calculated by the Taylor's Method exhibited a distribution in a wide range with the increased load depending on the degree of plasticity of the soil. The cv obtained from the combined apparatus it decreased with low load values and increased with higher loads levels. The cv obtained by the proposed empirical relationship showed good agreement with the cv defined by permeability-consolidation relationships.

Determination of Bearing Capacity of Single Pile based on Seismic Piezocone Penetration Tests

Based on the similar characteristics of installation about the penetrometer of seismic piezocone penetration tests(SCPTu) and the single pile, a theoretical relationship between ultimate bearing capacity of single pile, time-effect of shaft bearing capacity of single pile, excess pore water pressure around the pile during pile driven and the data measured from SCPTu is developed according to the cavity expanded theory, the Terzaghi one-dimensional consolidation theory and effective stress theory. The result of field test in KunShan and the calculated result which used the theoretical relationship mentioned above are compared. The results indicate that the analytical solutions agree well with the in-situ tests, which show that the applications of seismic piezocone penetration tests have wide range in the design of pile foundation.

Consolidation analysis of composite foundation with partially penetrated cement fly-ash gravel (CFG) piles under changing permeable boundary conditions

Based on the double-layered foundation theory, the composite ground with partially penetrated cement fly-ash gravel (CFG) piles was regarded as a double-layered foundation including the surface reinforced area and the underlying untreated stratum. Due to the changing permeability property of CFG piles, the whole consolidation process of the composite ground with CFG piles was divided into two stages, i.e., the early stage (permeable CFG pile bodies) and the later stage (impermeable pile bodies). Then, the consolidation equation of the composite foundation with CFG piles was established by using the Terzaghi one-dimensional consolidation theory. Consequently, the unified formula to calculate the excess pore water pressure was derived with the specific solutions for the consolidation degree of composite ground, reinforced area and underlying stratum under instant load obtained respectively. Finally, combined with a numerical example, influencing rules by main factors (including the replacement rate m, the treatment depth h1, the permeability coefficient Ks1, Kv2 and compression modulus Es1, Es2 of reinforced area and underlying stratum) on the consolidation property of composite ground with CFG piles were discussed in detail. The result shows that the consolidation velocity of underlying stratum is slower than that of the reinforced area. However, the consolidation velocity of underlying stratum is slow at first then fast as a result of the transferring of effective stress to the underlying stratum during the dissipating process of excess pore water pressure.

A Review and Update of Analytical and Numerical Solutions of the Terzaghi One-Dimensional Consolidation Equation

Practical resolution of consolidation problems that we often face requires an extensive and solid knowledge of the different parameters highlighted by the Terzaghi one-dimensional consolidation theory. This theory, with its assumptions, leads to a partial differential equation of second order in space and first order in time of pore water pressure. Analytical and numerical resolutions of this equation allow determining the water pressure variation before and after the application of a charge. Numerical modeling has enabled the simulation of the whole results obtained by the two methods of resolution (pressure, degree of consolidation, time factor, among others) to have a physical analysis and a lawful observation that lead to a suitable understanding of the phenomenon of Terzaghi one-dimensional consolidation.

Case Studies of PSDDF for Phased Placement of Dredged Soils

Use of Terzaghi's one-dimensional consolidation theory is not suitable for consolidation of highly deformable soft clays such as dredged soils. To model this condition, it is necessary to consider non-linear finite strain consolidation behavior, i.e., changes in compressibility and permeability with increasing stress. A one-dimensional non-linear finite strain numerical model, Primary Consolidation, Secondary Compression, and Desiccation of Dredged Fill (PSDDF), has been used to predict the stress-dependent settlement of fine-grained dredged materials. In this paper, two case studies of using PSDDF are discussed to illustrate the applicability and accuracy of PSDDF. The first case study involves PSDDF simulations of laboratory-phased placement of a marine clay dredged from Busan, Korea. PSDDF results are in good agreement with the corresponding results of the laboratory large strain consolidation tests. The other involves estimating the service life of the Craney Island Dredged Material Management Area near Norfolk, Virginia, in the United States. The excellent agreement between measured and calculated values shows that PSDDF is a reliable tool for predicting settlement of dredged material.

Consolidation Behavior of Soils Subjected to Asymmetric Initial Excess Pore Pressure Distributions with One-Way Drainage

A consolidating clay layer can be singly or doubly drained. The degree of consolidation is a function of the initial excess pore pressure distribution and the drainage conditions. Traditional geotechnical engineering practice assumes a uniform initial excess pore pressure distribution, for which the singly drained and doubly drained solutions to Terzaghi's one-dimensional consolidation theory are available in most textbooks. In this paper, several symmetric and asymmetric initial excess pore pressure distributions are studied using a series solution method. Excess pore pressure isochrones and average degree of consolidation plots are generated for all cases, assuming an impervious boundary at the base of the clay stratum. These plots enable users to determine the average degree of consolidation and pore pressure at a specific depth for a variety of loading scenarios. Pore pressure redistribution is also clearly more prevalent in singly drained clays, where pore-water pressures at certain depths increase at certain times, a phenomenon not generally expected during consolidation.

Study on Consolidation Mechanism of Debris Flow Deposit

The damage of debris flow effected on highway subgrade, pavement, protective structure, bridge and culvert laid on debris flow impact fracture and buried damage. Thus far, research on debris flow burying mechanism is still fuzzy. According to the two-phase flow theory of debris flow deposit, analyzed the consolidation mechanical mechanism of highway debris flow deposit. On the basis of Terzaghi one-dimensional consolidation theory, established the consolidation formula, which described the change process of excess pore water pressure, consolidation degree, settlement and compression with the consolidation time and deposit size, and then verified the correctness and feasibility of the formula by the indoor consolidation test. It adopted these results and combined it with the field survey data, it could develop a proper program for emergency mitigation of highway debris flow buried disaster more quickly and accurately.

Study on Consolidation Mechanism of Debris Flow Deposit

The damage of debris flow effected on highway subgrade, pavement, protective structure, bridge and culvert laid on debris flow impact fracture and buried damage. Thus far, research on debris flow burying mechanism is still fuzzy. According to the two-phase flow theory of debris flow deposit, analyzed the consolidation mechanical mechanism of highway debris flow deposit. On the basis of Terzaghi one-dimensional consolidation theory, established the consolidation formula, which described the change process of excess pore water pressure, consolidation degree, settlement and compression with the consolidation time and deposit size, and then verified the correctness and feasibility of the formula by the indoor consolidation test. It adopted these results and combined it with the field survey data, it could develop a proper program for emergency mitigation of highway debris flow buried disaster more quickly and accurately.

Research on Application of Seismic Piezocone Penetration Tests in Pile Foundation

According to the characteristics of installation about the penetrometer of seismic piezocone penetration tests (SCPTu) and the pile, a theoretical relationship between ultimate bearing capacity of single pile, time-effect of shaft bearing capacity of single pile, excess pore water pressure around the pile during pile driven and the data measured from SCPTu is developed based on the cavity expanded theory, the Terzaghi one-dimensional consolidation theory and effective stress theory. The result of field test in KunShan and the calculated result which used the theoretical relationship mentioned above are compared. The results indicate that the analytical solutions agree well with the in-situ tests, which show that the application of seismic piezocone penetration tests have wide range in the pile foundation.

Experimental evaluation of nonlinear Kelvin model constants from triaxial test data

Kelvin body, comprised of a spring and a dashpot and connected in a parallel arrangement, is quite widely used for the representation of visco-elastic behavior of soils. Parameters of the Kelvin model include a spring constant and a dashpot constant. These constants are usually required in any time dependent soil-foundation-structure interaction analysis which helps in predicting the variation of stress resultants in the foundation and structure with time. In the present paper, an attempt has been made to estimate these material parameters of a non-linear Kelvin body using the triaxial test data. The conceptual background of the material constants has been presented and the procedure for analysis of triaxial test data to obtain these constants has been laid down. Triaxial tests were conducted under — i) constant total stress condition and ii) the hydrostatic stress condition and the test data were analyzed by employing the proposed approach. Hydrostatic and the deviatoric stresses have been related to the material parameters. An example for analysis of a pile-raft system has been worked out and it has been found that the settlement from the present study is higher than that obtained from Terzaghi's one-dimensional consolidation theory. Application of the proposed approach in finite element analysis has also been mentioned.

Consolidation Behavior of Soils Subjected to Asymmetric Initial Excess Pore Pressure Distributions

Although the consolidation settlements beneath foundations and embankments are rarely one dimensional, Terzaghi's one-dimensional consolidation theory is often applied to these situations to approximate consolidation behavior. This paper investigates the consolidation behavior of a soil stratum subjected to various initial excess pore pressure distributions which occur under one-dimensional loading. The results show that analysis in terms of average degree of consolidation provides an incomplete representation of the consolidation behavior. While the average degree of consolidation curves for all uniform and linearly varying initial distributions are identical, the degree of consolidation isochrones for each distribution are unique. Furthermore, the application of a bottom-skewed initial excess pore pressure distribution results in a redistribution of pore pressures toward the skewed region so that an increase in excess pore pressure occurs at some depth after consolidation has already commenced. As a result, conventional consolidation relationships are considered inappropriate for these cases, and an alternative method of consolidation analysis in terms of normalized pore pressures is proposed.

Fully Coupled Numerical Modelling of Ground Surface Uplift in Steam Injection

Abstract In enhanced oil recovery, steam injection involves high stresses, pressures, temperatures and volume changes. Traditional reservoir simulation fails to predict associated transient ground surface movements because it does not consider coupled geomechanical effects. We present a fully-coupled, thermal half-space model using a hybrid DDFEM method, in which a simultaneous finite element method (FEM) solution is adopted for the reservoir and the surrounding thermally affected zone, and a displacement discontinuity (DD) method used for the elastic, non-thermal zone. This approach provides transient ground surface movements in a natural manner. Introduction Enhanced oil recovery (EOR) methods involving high pressures and steam injection (steamflooding, cyclic steam stimulation, steam-assisted gravity drainage) are accompanied by large volume changes in the reservoir horizon. Ground movements in excess of 300 mm heave or subsidence are registered during injection and production cycles. Reservoir simulation cannot address this phenomena without due consideration of geomechanical effects. The earliest theory to account for coupled pore fluid behaviour and soil deformation was the Terzaghi one-dimensional consolidation theory, still used in soil mechanics. Since Biot's theory of consolidation(1) was introduced to petroleum engineering by Geertsma(2) with the coined term "poroelasticity,?? coupled analysis of petroleum geomechanics effects has been widely advocated(3-5). Coupled reservoir simulation can be carried out in a loosely coupled fashion(6, 7) or with a tightly coupled scheme(8-10), and comparisons of different coupling techniques can be found (11, 12). In reservoir simulation, a coupled analysis demands simultaneous solution of changes in (p,T) and fluid flow as well as stress and strain. Computing challenges persist in large-scale 3D applications to real cases where there are a huge number of equations to solve iteratively; e.g. thermo-poro-elasto-plastic analyses involving several simultaneous diffusion processes (Darcy, Fourier, Fick). In regions of large pressure, temperature, concentration or stress gradients, accurate solution requires small-scale discretization. If the problem has strong non-linearity, such as changes in permeability, compressibility, or other properties arising from changes in pressure and effective stress, the computational effort increases by several orders of magnitude because multiple iteration loops are needed. These issues mean that accurate analysis of realistic complex 3D problems is challenging, and will so remain as we seek to solve larger and larger coupled problems involving non-linear responses.

Estimation of Land Subsidence Based on Groundwater Flow Model

This article presents an approach for estimating land subsidence due to withdrawal of groundwater. The proposed method calculates the groundwater seepage in 3-D-condition and calculates the land subsidence one-dimensionally. The governing equation on groundwater seepage is based on the three-dimensional mass conservation law and the principle of effective stress. The land subsidence calculation method is derived based on the following assumptions: (1) displacements occur only in the vertical direction, and (2) in vertical direction the total stresses do not change. The governing equation is solved by numerical method, i.e., finite element method (FEM) in spatial discretization and finite difference method (FDM) in time series discretization. In FEM Galerkin method is adopted and in FDM, lumped matrix method is employed. The proposed method is calibrated via analyzing 1-D consolidation problem and the results are compared with those from Terzaghi's one-dimensional consolidation theory and oedometer test. The proposed method is employed to analyze the consolidation of a soft layer due to withdrawal of groundwater from an aquifer under it. Moreover, this method is also applied to a field case of land subsidence due to groundwater pumping in a gas production field in Japan. The analytical results are compared with the field observed data. The results show that this approach simulates the field case well.

Discussion on “A Study on the Beginning of Secondary Compression of Soils” by R. G. Robinson

R. G. Robinson has suggested an approach for studying the beginning of secondary consolidation. Secondary compression is defined as any extra compression other than primary compression [1]. The primary consolidation occurs due to the dissipation of excess pore water pressure. Terzaghi's one-dimensional consolidation theory [2] has been used widely to analyze the time-compression data but is valid only in the primary consolidation phase. Non-linear stress-strain curves, time-dependent loading, impeded drainage, stratified soils multi-dimensional flow, large strains, effective stress-dependent (void ratio dependent) hydraulic conductivities, anisotropy, and other such effects are included and can lead to a response that deviates widely from that predicted using Terzaghi's theory. Remaining effects may loosely be termed initial and secondary. Secondary effects are then defined as all effects except these classified as initial and primary [1].

Application of Terzaghi's consolidation theory to nearly saturated soils

Terzaghi's one-dimensional consolidation theory is modified to account for the compressibility of fluid and solid phases. The proposed modified equations can be used to analyze the consolidation response of unsaturated soils over the saturation range where the gases remain in an occluded form (generally within a range between 80 and 100aturation); however, such applications are subject to the same limitations and idealizations implicit in Terzaghi's classical consolidation theory. The purpose of this note, therefore, is to offer a simple solution and not to unravel the complexities involved in general analysis of flow and deformation response of unsaturated soils. The proposed approach involves defining the consolidation coefficient, and hence the time factor, in terms of an equivalent fluid compressibility. This equivalent fluid is assumed to represent the compressibility characteristics of all the compressible phases that constitute the soil skeleton. The proposed generalized form of Terzaghi's consolidation equations is shown to qualitatively capture the consolidation behaviour of unsaturated soils. To test the validity of the formulations presented, one-dimensional oedometer tests were performed on specimens of Lantz clay that had been prepared at different saturation levels; satisfactory agreement was achieved between the theoretical and measured data at two states of saturation. Key words : consolidation, theoretical solutions, oedometer test, compressible fluid, occluded gas.

Critical analysis of Terzaghi's one-dimensional consolidation theory (in French) : Tavenas, F; Brucy, M; Magnan, J P Rev Fr Geotech, N7, May 1979, P29–43

Critical analysis of Terzaghi's one-dimensional consolidation theory (in French) : Tavenas, F; Brucy, M; Magnan, J P Rev Fr Geotech, N7, May 1979, P29–43