Terzaghi's Consolidation Theory Research Articles

Numerical Simulation of Karst Collapse in Qingling Town, Wuhan

With background information on the geological conditions of Fenghuo village, Qingling town, Wuhan, based on Terzaghi consolidation theory and GMS software, a hydrodynamic-mechanics coupling model was established. On the basis of simulating the groundwater flow field by GMS software, a mechanical calculation program was developed, and the coupling simulation of hydrodynamic mechanics was achieved. The results showed that the stress state, vertical deformation, and damage of soil are closely related to the underground water flow. The soil pressure value and effective stress value are relatively low from July to August every year. It is the result of buoyancy produced by groundwater. Soil settlement generally occurs in the dry season. When the load is not considered, the deformation value of soil settlement is generally less than 6 mm. In the wet season from July to August every year, the soil will float up, and the floating value is less than 4 mm. The groundwater table changes frequently, and the destruction around the cave body eventually leads to karst collapse.

A Study on the Production Performance of a Horizontal Shale Gas Well Using a Fully Coupled Flow and Geomechanics Modeling

Conventional petroleum reservoir simulators use constant rock compressibility to denote rock deformation. However, due to the stress-sensitive nature of the shale formations, using constant rock compressibility in reservoir simulators does not accurately capture the pressure diffusion in the reservoir, leading to a higher error margin in flow rate estimation. Fluid flow coupling with geomechanics is used to account for such a phenomenon numerically. Such an approach is important for shale numerical studies and any energy underground storage modeling (i.e., CO2 storage). Usually, when fluid flow coupling with geomechanics is studied for shale formations, the fluid, and the stimulated reservoir petrophysical properties are overlooked. This paper aims to present a study on the effect of the fluid and reservoir petrophysical properties on the performance of a gas-producing well. In addition, the results from the cases when geomechanics is coupled and decoupled with fluid flow in reservoir simulations are compared. The governing equations were discretized using the Finite Element Method. First, the model was validated against Terzaghi's consolidation theory analytical solution. After that, a history matching for the production flow rate was performed using field production data from Barnett Shale. Then a sensitivity analysis was carried out for the gas viscosity, Stimulated Reservoir Volume (SRV) porosity, and fracture conductivity. Next, the sensitivity analysis was conducted for the coupled and decoupled cases. Finally, the sensitivity analysis results were compared between the coupled and decoupled cases. The results show that lower gas viscosity, higher SRV porosity, and higher fracture conductivity improved horizontal well production performance. In addition, when the geomechanical effects were decoupled, the reservoir simulator overestimated the production flow rate and cumulative production.

Plane‐strain model for large strain consolidation induced by vacuum‐assisted prefabricated horizontal drains

AbstractVacuum‐assisted prefabricated horizontal drain (PHD) can be used to accelerate the consolidation process of dredged mud slurry with high water content, and this method exhibits advantages over traditional treatment methods that use prefabricated vertical drain (PVD). However, large‐strain model that can simulate soil consolidation induced by vacuum‐assisted PHDs is missing in the literature, although the large‐strain models for PVD‐induced radial consolidation are abundant. This study presents a piecewise‐linear plane‐strain model for large‐strain consolidation induced by vacuum‐assisted prefabricated horizontal drains. The model is called PCS, abbreviation for Plane‐strain Consolidation Settlement. PCS model can account for complex conditions including large strain, multiple layers of PHD boards, staged filling of soil layers, varying spacing of PHD boards, time‐dependent surcharge and/or vacuum loading, soil self‐weight, nonlinear compressibility, and hydraulic conductivity during the consolidation process, vertical and horizontal flows, and non‐Darcian flow. The PCS is validated using the two‐dimensional Terzaghi's consolidation theory (small strain) and a large‐scale laboratory model test (large strain), which involves multiple soil layers filled in stages, multiple PHD layers, and different horizontal spacings of PHD boards. Lastly, the proposed model is applied to a case study conducted at Shimokita Peninsula (Aomori Prefecture, Japan), where vacuum‐assisted PHDs have been used to treat the dredged mud slurry for a duration of 330 days.

A physics-informed data-driven approach for consolidation analysis

Identifying governing equations from data and solving them to acquire spatio-temporal responses is desirable, yet highly challenging, for many practical problems. Data-driven modelling has shown significant potential to influence knowledge discovery in complex geotechnical processes. To demonstrate feasibility, in this study a physics-informed data-driven approach is developed to automatically recover Terzaghi's consolidation theory from measured data and obtain the corresponding solutions. This process incorporates several algorithms including sparse regression and prior information-based neural network (PiNet), transformed weak-form partial differential equations (PDEs) (to reduce sensitivity to noisy measurement) and Monte Carlo dropout to achieve a measure of prediction uncertainty. The results indicate that consolidation PDEs can be accurately extracted using the proposed approach, which is also shown to be robust to noisy measurements. PDEs solved by PiNet are also shown to provide excellent agreement with actual results, thus highlighting its potential for inverse analysis. The proposed approach is generic and provides an auxiliary method to verify heuristic interpretations of data or to directly identify patterns and obtain solutions without the need for expert intervention.

Monitoring and Predicting the Subsidence of Dalian Jinzhou Bay International Airport, China by Integrating InSAR Observation and Terzaghi Consolidation Theory

Dalian Jinzhou Bay International Airport (DJBIA) is an offshore artificial island airport, where the reclaimed land is prone to uneven land subsidence due to filling consolidation and construction. Monitoring and predicting the subsidence are essential to assist the subsequent subsidence control and ensure the operational safety of DJBIA. However, the accurate monitoring and prediction of reclaimed subsidence for such a wide area under construction are hard and challenging. This paper utilized the Small Baseline Subset Synthetic Aperture Radar (SBAS-InSAR) technology based on Sentinel-1 images from 2017 to 2021 to obtain the subsidence over the land reclamation area of the DJBIA, in which the results from ascending and descending orbit data were compared to verify the reliability of the results. The SBAS-InSAR results reveal that uneven subsidence is continuously occurring, especially on the runway, terminal, and building area of the airport, with the maximum subsidence rate exceeding 100 mm/year. It was found that there is a strong correlation between the subsidence rate and backfilling time. This study provides important information on the reclaimed subsidence for DJBIA and demonstrates a novel method for reclaimed subsidence monitoring and prediction by integrating the advanced InSAR technology and Terzaghi Consolidation Theory modeling. Moreover, based on the Terzaghi consolidation theory and the corresponding geological parameters of the airport, predicted subsidence curves in this area are derived. The comparison between predicted curves and the actual subsidence revealed by InSAR in 2017–2021 is highly consistent, with a similar trend and falling in a range of ±25 mm/year, which verifies that the subsidence in this area conforms to Terzaghi Consolidation Theory. Therefore, it can be predicted that in the future, the subsidence rate of the new reclamation area in this region will reach about 80 mm/year ± 25 mm/year, and the subsidence rate will gradually slow down with the accumulation of reclamation time. The subsidence rate will slow down to about 30 mm/year ± 25 mm/year after 10 years.

An analytical solution for self-weight consolidation based on one-dimensional small-strain consolidation wave theory

Terzaghi's consolidation theory neglects inertial effects on the consolidation of saturated soils. To quantify the inertial effects, in this paper an original one-dimensional small-strain consolidation wave (C-wave) theory is developed, based upon a proposed modified Darcy's law with relaxation time and the equation of motion for soil ensemble. The one-dimensional governing equations were first formulated for self-weight consolidation, followed by a closed-form solution employing the method of separation of variables. The proposed model was then validated against wave velocity measurements and verified against finite-difference analysis. The half-closed self-weight consolidation behaviour was subsequently investigated, compared with Terzaghi's theory, Fillunger–Heinrich's dynamic theory and the u–p form of Biot's wave theory. This research indicates that: (a) superior to conventional models under comparison, the C-wave model enhances the predictability of the C-wave velocity; (b) the dimensionless C-wave coefficient (Cw) dominates the fundamental consolidation behaviour; (c) a wave-diffusion duality underlying the consolidation mechanism contributes qualitatively to the spatial bottom-up pattern and temporal response delay in consolidation observations; and (d) Terzaghi's theory can afford a practically accurate solution provided the Cwand time factor are below and above approximately 0·01, respectively. The C-wave theory may enrich the understanding of consolidation-related phenomena involving an appreciable Cw.

Load-bearing characteristic of methane hydrate within coarse-grained sediments – Insights from isotropic consolidation

Gas hydrate, as a solid pore constituent, can potentially share external load with sediment matrix, and critically impact geological evolution of its hosting sediments, well integration and sediment settlement during gas production depending on its contribution to support external loading. We aim to address the question of whether hydrate shares the load with the soil skeleton through isotropic consolidation experiments. Our results highlight the formation of methane hydrate does not affect the integrity of sediment skeletons if the effective stress previously applied on the skeleton remains constant, which indicates that methane hydrate would not actively support the load. Subsequent external load applied to the sediments after hydrate formation can be supported by hydrate. Secondly, hydrate as well as hydrate-bearing sediments exhibit creep behavior. As hydrate creeps, the load transfers to the sediment skeleton with time and hydrate gradually retreats from the status of load-bearing. When hydrate saturation is low and the coexisting pore fluid can percolate through sediments, the local deformation of hydrate due to sediment consolidation induces excess pore pressure, which dissipates by pushing out the pore fluid. When the coexisting pore fluid is enclosed in hydrate mass in high hydrate saturation environments, the dissipation of excess pore pressure relies on the viscous flow of hydrate. This pressure dissipation could last for millions of years according to analytical analysis based on Terzaghi's consolidation theory, during which hydrate cannot completely escape the status of load-bearing. These observations conclude that load-bearing is a dynamic status rather than a stagnant pore habit, countering conventional thinking that load-bearing joins grain-coating, cementing and pore-filling as a pore habit of gas hydrate.

Effects of calcium carbonate on hydro-mechanical properties of bentonite

To simulate characteristic changes of the bentonite mixing with CaCO3 crystals that precipitate from groundwater around the high-level radioactive waste repositories, different amounts of CaCO3 powders were mixed in the bentonite. In this study, four series of bentonite/CaCO3 mixtures were prepared with different contents of CaCO3 powders. A series of swelling, compression and direct shear tests were conducted on the bentonite/CaCO3 samples using deionized water. Terzaghi consolidation theory was adopted to compute the hydraulic conductivity of bentonite/CaCO3 mixtures. The results demonstrated that the final swelling strain decreased with increasing vertical stress and the content of CaCO3 powders. The compression index decreased slightly with increasing CaCO3 content. It was found that as the CaCO3 content increased, the hydraulic conductivity of bentonite/CaCO3 mixtures decreased. There was a peak point in the shear strength of unsaturated samples with the differences of the CaCO3 content. The cohesion of unsaturated samples increased first and then decreased, but saturated samples presented the opposite character. It could be seen from the scanning electron micrograph that the existence of CaCO3 powders filled pores of bentonite/CaCO3 mixtures and made the structure denser.

Compressibility and hydraulic conductivity of sand-attapulgite cut-off wall backfills

Soil-bentonite cut-off walls have been used widely to control pollution in landfills but their antifouling property (their ability to prevent contaminants in landfills from polluting the surrounding environment) decreases significantly over time due to a variety of factors (e.g. contaminant concentrations). In recent years, attapulgite has been considered as a backfill material for cut-off walls, but relevant studies are lacking. In this study, the compressibility and hydraulic conductivity of sand-attapulgite backfills were investigated using consolidation and hydraulic conductivity tests. In these tests, attapulgite comprised 10%, 20%, 30%, 40%, 60%, 80%, or 100% (dry weight) of the backfills. The results showed that (1) the compression (Cc) and swell (Cs) indexes of the backfills increased linearly with increasing attapulgite content (Ap); (2) both the consolidation coefficient (Cv) calculated by the Casagrande and Taylor methods and the hydraulic conductivity (ktheory) calculated according to Terzaghi consolidation theory decreased with increasing attapulgite content. In the case of an effective consolidation stress σ′<100 kPa, ktheory <10−9 m/s when Ap≥30%, which was supported by the hydraulic conductivity tests. Two methods were developed based on laboratory data, for predicting the hydraulic conductivity of sand-attapulgite backfills. We conclude that the use of sand-attapulgite backfills applied to cut-off walls as substitutes for soil-bentonite backfills is technically feasible.

Influence of recycled tyre amendment on the mechanical behaviour of soil-bentonite cut-off walls

Abstract Generation of the scarp tyre has increased in recent years, and finding innovative reusing methods is of interest to researchers. This study aims to investigate the hydraulic conductivity and one-dimensional consolidation behaviour of soil-bentonite (SB) backfill amended with powdered recycled tyre (PRT) and crumbed recycled tyre (CRT) by performing a series of oedometer consolidation and rigid-wall hydraulic conductivity tests. Three values of PRT and CRT (i.e., 2%, 5% and 10% by dry weight) were used to prepare the specimens. The investigation on vertical strain-time graphs showed that the addition of PRT and CRT caused an increase in settlement characteristics of the SB backfill. The results also showed that the addition of PRT and CRT caused an increase in the compression index (Ci) and the swelling index (Cs) of the SB specimens. The coefficient of consolidation (cv) based on the Casagrande and Taylor methods showed a consistent increasing trend by increasing the PRT and CRT. The hydraulic conductivity was computed based on the Terzaghi consolidation theory (ktheory), and the results showed that increasing the PRT and CRT caused an increase in hydraulic conductivity of the SB backfill. The hydraulic conductivity (kf) measured using a rigid-wall permeability compaction mould showed a similar increasing trend by increasing the PRT and CRT contents of the backfills.

Contaminant transport in a small deformation aquitard affected by the delayed drainage phenomenon

AbstractThis paper presents a formulation accounting for the effect of delayed drainage phenomenon (DDP) on the breakthrough of contaminant flux in an aquitard, by considering the movement of soil particles, porosity variation, hydraulic head variation, and transient flow during the consolidation. The water flow equation in an aquitard was based on the Terzaghi's consolidation theory, and the contaminant transport equation was derived on the basis of the mass balance law. Two cases were used to illustrate the effect of DDP on the contaminant transport in an aquitard of small deformation. It is found that the breakthrough time of contaminant in an aquitard is very long, which is mainly ascribed to the low permeability of aquitard and sorption of soil particles. It is also found that the increase of depletion, which is in general induced by the increase of thickness and specific storativity and the decrease of hydraulic conductivity, enhances the impact of DDP on the contaminant transport in an aquitard. A larger delay index (τ0) of DDP gives a greater delay breakthrough time (DBT) of solute transport in an aquitard, which controls the difference of the breakthrough time of contaminant transport in aquitards with and without the occurrence of DDP. For the cases where advection plays a dominant role during the process of solute transport, τ0 is almost linearly correlated with DBT, and the ratio of DBT over the breakthrough time without consideration of DDP also approximately shows a linear relationship with the ratio of specific storativity to porosity, given a fixed drawdown in the adjacent aquifer with the sorption being ignored.

Deformation behaviour of geotechnical materials with gas bubbles and time dependent compressible organic matter

Geotechnical materials may contain organic matters and gas bubbles during the process of their formation. The existence of compressible gas bubbles and organic matters may affect the excess pore water pressure distribution during compression and the deformation behaviour of the materials. Immediate settlement and creep have been observed in the early stage of consolidation curves of brown coal and peat samples, which can not be explained with Terzaghi's consolidation theory where soils are considered as fully saturated and soil particles are incompressible. A numerical model has been developed to model the consolidation behaviour of brown coal and peat considering the inclusion of gas bubbles and the time dependent compressible organic matters. In the model, the materials are assumed to contain incompressible minerals, compressible organic matters, gas bubbles and water. Consolidation of the materials is considered as a coupling process of water extrusion and volume variation of gas bubbles and organic matters. The model has been validated using the experimental results from one dimensional consolidation curves of brown coal and historical test results of peat. The gas content and the compressibility of organic matters can be obtained using the proposed model. The model can be used to analyze compression behaviour of geotechnical materials containing compressible particles and gas bubbles.

Evaluation model coupling exploitable groundwater resources and land subsidence control in regional loose sediments

The loose sediments in the Yangtze River Delta, the North China Plain, the plain of Northern Jiangsu and other districts in China are of great thickness, complex in structure and abundant in groundwater. Groundwater overexploitation easily results in geological disasters of land subsidence. Aiming at the issues, assessment models coupling exploitable groundwater resources and land subsidence control in regional loose sediments were brought up in this paper. The two models were: (1) a three dimensional groundwater seepage model with land subsidence based on the one dimensional Terzaghi consolidation theory; (2) a three dimensional full coupling model on groundwater seepage and land subsidence based on the Biot consolidation theory to simulate and calculate. It can be used to simulate and calculate the problems in real situations. Thus, the groundwater seepage and land subsidence were coupled together in the model to evaluate the amount of exploitable groundwater under the specific requirements of land subsidence control. The full coupling model, which considers the non-linear characteristics of soil mass and the dynamic changes of soil permeability with stress state based on the Biot consolidation theory, is more coincident with the variation characteristics of the hydraulic and mechanical properties of soil mass during the pumping process, making the evaluation results more scientific and reasonable.

A fusion model used in subsidence prediction in Taiwan

Abstract. The Taiwan Water Resources Agency uses four techniques to monitor subsidence in Taiwan, namely data from leveling, global positioning system (GPS), multi-level compaction monitoring wells (MCMWs), and interferometry synthetic aperture radar (InSAR). Each data type has advantages and disadvantages and is suitable for different analysis tools. Only MCMW data provide compaction information at different depths in an aquifer system, thus they are adopted in this study. However, the cost of MCMW is high and the number of MCMW is relatively low. Leveling data are thus also adopted due to its high resolution and accuracy. MCMW data provide compaction information at different depths and the experimental data from the wells provide the physical properties. These data are suitable for a physical model. Leveling data have high monitoring density in spatial domain but lack in temporal domain due to the heavy field work. These data are suitable for a black- or grey-box model. Poroelastic theory, which is known to be more conscientious than Terzaghi's consolidation theory, is adopted in this study with the use of MCMW data. Grey theory, which is a widely used grey-box model, is adopted in this study with the use of leveling data. A fusion technique is developed to combine the subsidence predicted results from poroelastic and grey models to obtain a spatially and temporally connected two-dimensional subsidence distribution. The fusion model is successfully applied to subsidence predictions in Changhua, Yunlin, Tainan, and Kaohsiung of Taiwan and obtains good results. A good subsidence model can help the government to make the accurate strategies for land and groundwater resource management.

Analysis of nonlinear settlement for an unsaturated soil under stage continuous loading

A new approach was proposed to describe settlement behavior of an unsaturated soil with subgrade filling for high-speed railway. Firstly, based on Terzaghi consolidation theory, equations considering the variation coefficient of consolidation with void ratio and saturation for consolidation of an unsaturated soil under stage continuous loading were derived, and according to analytical solutions of equations, a formula for settlement computation under stage continuous loading was obtained. Then, combined with the width-to-height ratio of subgrade to compute ground reaction, and by means of in-situ plate loading curves, a correctional approach was presented for the analysis of nonlinear settlement of foundation. Also, the comparison between calculated and measured load-settlement behavior for an unsaturated soil in Qingdao-Ji’nan high-speed railway was given to demonstrate the effectiveness and accuracy of the proposed approach. It can be noted that the presented solution can be used to predict the settlement of an unsaturated soil foundation under stage continuous loading in engineering design.

Flow slides run-out prediction using a sliding-consolidation model

The estimation of maximum travel distance of flow slides is an important topic to assess the consequence of natural disasters caused by landslides. During debris transportation, dissipation rules of pore-water pressure determine movement properties of flow slides. Based on 1-D Terzaghi consolidation theory, expressions of excess pore-water pressure with three cases of initial conditions are deduced and are programmed using Mathematica® language. Furthermore, the factors affecting the distribution of pore-water pressure are studied using nondimensional method interactively, such as z/h, ub/ua, and Tv, which are fairly significant to investigate soil consolidation during the movement of flow slides. On the basis of the sliding-consolidation model first provided as reported by Hutchinson (Can. Geotech. J. 23(2):115-126, 1986), equations of pore-water pressure, velocity, and travel distance of flow slides are obtained and the physical quantities are coded as mathematical functions using Mathematica® language characterized by its user-friendly interfaces to study run-out properties of flow slides very easily. The program can be used to compute velocity of flow slide, time, and pore-water pressure at a certain position, and thus judge automatically when and where flow slide will stop on slopes with different slope angles, solving the computing difficulties encountered during the Hutchinson's model application, especially in the last decades when computing technique with computers did not develop so rapidly as at present. At last, back analysis for properties of the 1966 flow slide at Aberfan, South Wales is done to test the model and the program, whose results are compared with those as reported by Hutchinson (Can. Geotech. J. 23(2):115-126, 1986). The results show that the program developed by the authors makes the application of Hutchinson's model more correct and easier.

Consolidation Process and Triaxial Shear Test of Consolidation Coefficient for Saturated Soft Soil in Marsh

The consolidation coefficient is the important parameters for soft soil foundation to predict its consolidation settlement. At present, one-way compression test is mainly used to study consolidation process and consolidation coefficient of soft soil. For saturated soft soil in marsh, through triaxial shear test, the dissipation of pore water pressure and consolidation process can be observed during the course of soil sample drainage. This study got test result bellow through above triaxial test. Firstly, pore water pressure has hysteresis effect during the consolidation process, and the reason for this is analyzed. Secondly, consolidation degree in different consolidation time can be got according to the change of discharged water volume. Thirdly, according to Terzaghi consolidation theory, consolidation coefficients can be got under different consolidation pressures. Consolidation coefficient first increases with the increasing of consolidation degree, when consolidation degree is between 40% and 80%, saturated soft soil has larger consolidation coefficient, consolidation coefficient of saturated soft soil in marsh is between 2Ч10-4 cm2 / s and 10Ч10-4cm2 / s.

Methods for determination of the coefficient of consolidation and field observations of time rate of settlement — an overview

The main objective of this paper is to review the state-of-the-art for determining coefficient of consolidation (<i>c_v</i>), which is required for predicting the rate of settlement of structures founded on cohesive soil deposits in order to check the settlement criteria of foundation design. In the past five to six decades, attempts have been made to propose methods for determining more reliable values of <i>c_v</i>. All these methods are critically reviewed in this paper in terms of their limitations and practical use. It is found that most of the current methods attempt to fit the characteristic features of average degree of consolidation (<i>U</i>) versus time factor (<i>T</i>) relationship from the Terzaghi consolidation theory to the observed compression versus time data obtained in the laboratory oedometer test with incremental loading. The two conventional methods, namely the Casagrande logarithm of time fitting and the Taylor square root of time fitting methods, are still having much greater acceptance and use in geotechnical engineering practice as the standard methods in spite of their limitations. Other alternative methods such as inflection point (Cour, 1971), velocity (Perkin, 1978), rectangular hyperbola fitting (Sridharan and Rao, 1981) and revised logarithm of time fitting (Robinson and Allam, 1996) methods are also based on rational approaches and have potential for predicting reliable values, sometimes even better than the values obtained by standard methods. Mainly, due to lack of comparisons with field observations of time rate of settlement, and also to some extent because of more data reduction effort and sophistication of the method, the alternative methods have not been found suitable for routine applications. These alternative methods do not appear to offer apparent advantages as expected in geotechnical engineering at the cost of extra effort. Among the methods available for estimating the field values of <i>c_v</i>, the Asaoka method is preferred, mainly because of its rational and simple procedures. A comparison of <i>c_v</i> values obtained from the laboratory data and the field observations are required for assessing the suitability of all the proposed methods, but unfortunately it has not been reported extensively. However, the limited comparisons in this paper clearly show that <i>c_v</i> from the field is an order of magnitude higher than that from the laboratory. This overview will be useful to engineering students and practicing engineers, and at the same time, it highlights the need for further research.

Lateral and consolidation behaviors of seabed-type breakwater for very soft ground

A seabed-type of breakwater applicable to very soft ground without the need for soil improvement is newly developed. This type of soft-ground breakwater is expected to ensure sufficient lateral resistance and prevent excessive consolidation settlement due to self-weight of the breakwater. In this paper, lateral and consolidation behaviors of soft-ground breakwater were investigated by performing model tests and finite element simulations. The results revealed that the bottom wall and buoyant box, which are the main features of soft-ground breakwater, contribute to the increase in lateral resistance and to the control of the consolidation settlements, respectively, and that Terzaghi's consolidation theory could be conservatively adopted in deriving the consolidation settlements of soft-ground breakwater proposed herein.

A model for contaminant mass flux in capped sediment under consolidation

The paper presents a model for contaminant transport and flux through a consolidating subaqueous sediment and overlying cap. The formulation is based on the effect of consolidation and excess pore pressure dissipation on transient, nonlinear advective component of transport through sediment and the cap. The consolidation is induced by the buoyant weight of the cap when it is placed on the contaminated sediments. One equation is presented for advective–diffusive transport through the sediment that is dependent upon soil/contaminant properties and transient advective velocity, which is calculated from a second equation based on the Terzaghi consolidation theory. A third equation is provided to describe the transport of contaminants in the cap. The parameters, including advective velocity, and boundary conditions used for contaminant transport through the cap are derived from the solution of the first two equations. The finite difference method is used to solve the system of equations for consolidation and contaminant transport. A hypothetical case is analyzed to demonstrate the formulation, and the results show that advection due to consolidation can accelerate breakthrough of contaminant through the cap by orders of magnitude. The derivation and results show that consolidation should be included for cap design, and that reactive caps are essential for delaying and reducing dissolved contaminant flux.