Effect of Non-Darcian Flow on Time Rate of Consolidation

Elnaggar, H A; Krizek, Raymond J.; Karadi, Gabor M.

doi:10.1016/0016-0032(73)90212-3

Cited by 22 publications

(5 citation statements)

References 8 publications

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“…(10) Solutions to the new model can be given by the above linear systems of equations. The above method is an important one in evaluating scientifically accuracy of a model.…”

Section: Methods Of Solution To New Modelmentioning

confidence: 99%

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Law of nonlinear flow in saturated clays and radial consolidation

邓英尔

谢和平

黄润秋

et al. 2007

Appl. Math. Mech.-Engl. Ed.

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It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and test ones. Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow. Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius. The interaction is an important reason why nonlinear flow in saturated clays occurs. An exact mathematical model was presented for nonlinear flow in micro-scale pore of saturated clays. Dimension and physical meanings of parameters of it are definite. A new law of nonlinear flow in saturated clays was established. It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one. Darcy law is a special case of the new law. A mathematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow. Equations of average mass conservation and moving boundary, and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer, a method of steady state in stead of transient state and a method of integral of an equation. Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained. Results show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay. The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases. Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.

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“…(10) Solutions to the new model can be given by the above linear systems of equations. The above method is an important one in evaluating scientifically accuracy of a model.…”

Section: Methods Of Solution To New Modelmentioning

confidence: 99%

“…Moreover, a degree of consolidation calculated from the theory can only expressed laws of consolidation after construction be completed. Influence of non-Darcian flow on progress of consolidation of clays was researched by Elnaggar and Schmidt [10,11] . Pascal gave an approximate solution of consolidation with threshold gradients.…”

Section: Introductionmentioning

confidence: 99%

Law of nonlinear flow in saturated clays and radial consolidation

邓英尔

谢和平

黄润秋

et al. 2007

Appl. Math. Mech.-Engl. Ed.

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“…* who state that 'Since the initial tangent to the velocity-gradient relationship may assume a very small value, the argument for a threshold gradient becomes practically insignificant.' Although this statement was advanced in support of equation (2) it applies with equal validity in support of equations (1) for soils which exhibit an abrupt change in permeability to very small values at low gradients.…”

Section: Introductionmentioning

confidence: 91%

“…Under these conditions equations (1) may provide an excellent approximation to the effective flow rate. Solutions using equations (1) may also be somewhat simpler and easier to characterize than those arising from limiting processes using equations such as equation (2), or solutions such as that of Schmidt and Westmann." The writers concur with the statement of Elnagger et a1.…”

Section: Introductionmentioning

confidence: 99%

Consolidation with threshold gradients

Pascal

Murray

1981

Num Anal Meth Geomechanics

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SUMMARYEvidence for threshold gradients is reviewed. The consolidation problem, with threshold gradient, is properly formulated and solved numerically. An approximate analytical solution is also developed. The influence of a threshold gradient on the time rate of settlement is examined, and it is shown that by modifying the definition of the degree of consolidation a good approximation to the threshold gradient problem can be obtained directly from the Terzaghi solution. It is also shown that threshold gradients will have no influence on odometer testing and their effect is, therefore, to reduce the primary compression below that predicted from standard tests.

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“…The author also proposed an expression in the form of a piecewise function to describe it according to permeability test results. Since then, scholars have also proposed other classical relations, such as linear flow with threshold hydraulic gradient, 25 exponential seepage, 26 and Swartzendruber's flow, 27 etc. With the progress of the consolidation system, the above nonlinear seepage models have been widely applied to consolidation problems 28–30 .…”

Section: Introductionmentioning

confidence: 99%

Analysis of one‐dimensional nonlinear rheological consolidation of saturated clay considering self‐weight stress and Swartzendruber's flow rule

Cui

Cao

et al. 2022

Num Anal Meth Geomechanics

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Considering the nonlinear rheological properties of saturated clay, the modified unified hardening (UH) constitutive relation was introduced to describe the nonlinear rheological deformation. Meanwhile, Swartzendruber's flow law was used to simulate the non-Darcian flow of pore water in the progress of rheological consolidation. Consequently, a nonlinear rheological consolidation model (NRCM), for one-dimensional consolidation, that simultaneously incorporates nonlinear stress-strain-time relationship, Swartzendruber's flow, self-weight stress, and variable permeability coefficient has been developed here. The finite volume method (FVM) was utilized to solve the NRCM system, and its effectiveness was verified by comparing with the existing consolidation data. The parametric analysis results indicate that the soil's nonlinear rheological effect induced the excess pore water pressure (EPWP)'s accumulation in the initial loading. This phenomenon became more significant when considering the self-weight stress or as the initial overconsolidated parameter, soil thickness, and seepage parameter increased. In contrast, it weakened with the increase of external loading. Additionally, considering the self-weight stress slowed down the whole dissipation of EPWP in the initial period of loading. Nevertheless, it accelerated the nonlinear consolidation process in the middle and late loading stages.

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Effect of Non-Darcian Flow on Time Rate of Consolidation

Cited by 22 publications

References 8 publications

Law of nonlinear flow in saturated clays and radial consolidation

Law of nonlinear flow in saturated clays and radial consolidation

Consolidation with threshold gradients

Analysis of one‐dimensional nonlinear rheological consolidation of saturated clay considering self‐weight stress and Swartzendruber's flow rule

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