EFFECT OF CHANGE IN THE COEFFICIENT OF PERMEABILITY ON CONSOLIDATION CHARACTERISTICS OF CLAYS

The settlement rate and pore water pressure dissipation rate are mainly controlled by the permeability of soil. Both laboratory and field tests show that the permeability is varied during the loading and consolidation process. It is known that consolidation process is accompanied by decrease in void ratio which leads to decrease in the coefficient of permeability. The importance of the decrease of the coefficient of permeability on the time rate of settlement and pore water pressure needs to be investigated. This paper takes into account the change in coefficient of permeability during consolidation and studies its effect on consolidation characteristics of a clay layer. The finite element method is used in the analysis and the package Geo-Slope is adopted through coupling the programs SIGMA/W and SEEP/W. The relationship between the applied pressure and permeability was determined experimentally for three samples. It was concluded that the effect of permeability is clear at later times of consolidation due to decrease in void ratio and hence slower dissipation of pore water pressure. Taking into account variable permeability leads to longer times of consolidation. At later times (after 400 days), the excess pore water pressure predicted for the case of variable permeability is greater than conventional case by about (10 – 12) %. ةصلاخلا نا لدعم يماسملا ءا ملا طغض دد بت لد عمو لوطهلا ةُبس ن نا نكمي ي رطَيْسَ ه يلع يس يئر لكش ب للاخ نم ِ ة برتلا ةِ يذافن . د قو ترهظا ةيربتخملاو ةَيلقحلا تارابتخلاإ اتلآ مامض نلااو ل يمحتلا ةِ يلمع ءا نثأ ةر يغتم ةَيذافنلا نّأ ، و فورعملا نم ً اض يا ةِ يلمع نّأ ب ضنلاا تاغارفلا ةِبسن يف نِاصقنب ةبوحصم نوكت مام و ى لإ يدّؤ تُ ي تلا ر ييغت ِ ة يذافنلا لِ ماعم يف ، دجو اذ ل يرورُ َّ ض لا نْ مَ مت يُ نْأَ يرحتلا نع ن ريثات يِماسملا ءِاملا طِغضو طوبهلل ينمزلا لدعملا ىلع ةِيذافنلا لِماعم نِاصق . يف كلذل ثِحبلا اذه مت ةسارد ريثات ف رَييغتلا يف مامضنلاا تلاماعم ىلع مامضنلاا ةيلمع ءانثأ ةِيذافنلا لِماعم ي ةبرتلا لا ةينيط ، ا مت ثيح لامعتس نعلا ةَقيرط ا حملا رِص د لِيلحتلا يف ةِد و سملا نيجمانربلا نييم SIGMA/W و SEEP/W نم نكمي يتلا و لاخ نم ريثاتلا كلذ باسح امهللاخ دامتعا ل ةقلاعلا افنلاو طِغضلا نيب ةِيذ نيجمانربلا نيذه يف اينمض ةدوجوملا تانيع ثلاثلو . ِ ةيذافنلا رَيثأت نّأب جَتنتسإ رثآا لكشب هتظحلام نكمي ضو و ح ًُ ا تلت يتلا ةرتفلا للاخ 400 لامحلاا طيلست نم موي ببسب ناصقنلا او تاغارفلا ةِبسن يف ددبتل يطبلا ئ ِ يماسملا ءِا ملا طِغض يف . نابسحلا يف نيذخا ةدا يز ى لا دو قت ةر يّغتملا ةِ يذافنلا نا يف تقو مامضنلاا . نا دجو امآ يلاوحب ةِيديلقتلا ةِلاحلا نْمِ ربآا ةِريّغتملا ةِيذافنلا ةلاح يف ضِئافلا يمِاسملا ءِاملا طغض ) 10 – 12 ( % .


INTRODUCTION
Consolidation is generally related to finegrained soils such as silts and clays.Since water can flow out of a saturated soil in any direction, the process of consolidation is essentially three-dimensional.However, in most field situations, water will not be able to flow out of the soil by flowing horizontally because of the vast expanse of the soil in horizontal direction.Therefore, the direction of flow of water is primarily vertical or one-dimensional.As a result, the soil layer undergoes one-dimensional (1-D) consolidation settlement in the vertical direction.
Consolidation theory is required for the prediction of both the magnitude and the rate of consolidation settlements to ensure the serviceability of structures founded on a compressible soil layer.Terzaghi's theory of 1-D consolidation makes the following assumptions including that the soil is homogeneous and fully saturated, the solid particles and the pore water are incompressible, the flow of water and compression of soil are onedimensional (vertical), strains are small, Darcy's law is valid at all hydraulic gradients, but the most important assumption is that the coefficient of permeability and the coefficient of volume compressibility remain constant throughout the consolidation process.Terzaghi gave a theory of soil consolidation based on the effective stress principle, which was derived on several ideal assumptions to get a simplified theory.To avoid the limitations involved in Terzaghi's theory, many efforts are being made by scholars to solve the problems in practical engineering situations.
It is known that consolidation process is accompanied by decrease in void ratio which leads to decrease in the coefficient of permeability.Effect of the decrease of the coefficient of permeability on the time rate of settlement and pore water pressure needs to be investigated.Cavalcante and Assis (2002) showed the influence of the permeability gradient during the construction of tailings dams, built by the upstream method, using the hydraulic fill technique.During the hydraulic disposition, two mechanisms affect the tailings permeability: the hydraulic segregation and the consolidation due to the staged construction procedure.These mechanisms influence considerably the permeability distribution along the fill and, consequently, the behaviour of the dam.Results show that the pore pressure immediately after deposition may reach quite high values (532 kPa), but dissipates in a short period of time (1 to 10 days).Then, this effect should be taken into account in a short-term stability analysis of tailings dams.On the other hand, after pore pressure dissipation, there is a gain in the shear strength (13 %), which should also be considered, but in a long-term stability analysis of tailings dams.
The settlement rate and pore water pressure dissipation rate are mainly controlled by the permeability of soil.Both laboratory and field tests show that the permeability is varied during the loading and consolidation process.The formula proposed by Taylor (1948) and verified by Tavenas et al. (1983) can be used to represent variation of the permeability of soft clay during the consolidation: (1) where: e o : the initial void ratio, e : the void ratio at the condition under consideration, k : the permeability, k o : the initial permeability, and c k : constant which is equal to 0.5 e o (Tavenas et al., 1983).
A semi-analytical solution was presented by Ying et al. (2005) for the case of void ratio e-log effective stress p and elog permeability conductivity kv, especially.The semi-analytical results were compared with those obtained from experimental investigations with a set of advanced consolidation system.Furthermore, the behavior of nonlinear consolidation of soils is analyzed and the differences between the semi-analytical results and Davis's nonlinear theory were discussed.It was concluded that the semianalytical solution is a very effective method for solving the difficult consolidation problems taking varied compressibility and permeability into account.The degree of consolidation defined by effective stress and by settlement is different in this method.The advanced consolidation system with back pressure is an effective method for analyzing the consolidation behavior of clay.Fairly good agreement exists between theoretical results and the consolidation test results.
This paper takes into account the change in coefficient of permeability during consolidation and study its effect on consolidation characteristics of a clay layer.

DESCRIPTION OF THE PROBLEM:
The problem consists of tracing the settlement and pore water pressure changes in a clay layer under the effect of uniformly distributed load 80 kN/m 2 .The finite element method is used in the analysis and the package Geo-Slope is adopted through coupling the programs SIGMA/W and SEEP/W.

LABORATORY WORK:
In order to define the coefficient of permeability as a function of the applied pressure, a testing program was planned on samples taken from three sites located in Baghdad city.These soil samples are named by S 1 , S 2 and S 3 .The identification and classification tests included grain size distribution, Atterberg limits and specific gravity.Table 1 shows the index properties of the soils from the three sites.Consolidation test was carried out on undisturbed soil samples according to the specification of ASTM D-2435-02.For each load increment, the coefficient of consolidation, c v , was calculated using Casagrande's procedure in addition to the coefficient of volume change, m v .Then the coefficient of permeability, k, was calculated according to the following relation: where γ w is the unit weight of waater.
The relationship between the applied pressure and permeability is plotted for each sample as shown in Figure 1.

FINITE ELEMENT ANALYSIS:
SIGMA/W is a finite element software product that can be used to perform stress and deformation analyses of earth structures.Its comprehensive formulation makes it possible to analyze both simple and highly complex problems.For example, one can perform a simple linear elastic deformation analysis or a highly sophisticated nonlinear elastic-plastic effective stress analysis.When coupled with SEEP/W (another GEO-SLOPE software product), it can also model the pore-water pressure generation and dissipation in a soil structure in response to external loads.SIGMA/W has application in the analysis and design for geotechnical, civil, and mining engineering projects.

Hydraulic Conductivity Functions
Analyzing saturated seepage processes requires establishing the hydraulic conductivity versus pore-water pressure relationship.In the case of a transient analysis, the volumetric water content function must also be defined.Both of these functions can be either measured directly in the laboratory or predicted using a variety of methods.The volumetric water content function can be predicted from the grain-size distribution curve and the hydraulic conductivity function can be predicted using the volumetric water content function and the measured saturated hydraulic conductivity.
The capacity of soil to conduct water can be viewed in terms of hydraulic conductivity (or the coefficient of permeability).The hydraulic conductivity is dependent on the water content.Since the water content is a function of porewater pressure and the hydraulic conductivity is a function of water content, it follows that hydraulic conductivity is also a function of pore-water pressure.Figure 2 presents the form of the relationship between hydraulic conductivity and pore-water pressure.This relationship is known as a conductivity function.
The variation of hydraulic conductivity with pore-water pressure makes the finite element equations nonlinear, and an iterative process is consequently required to solve the equations.Hydraulic head (pore-water pressure plus elevation) is the primary unknown computed.Since the hydraulic conductivity is related to hydraulic head, the appropriate hydraulic conductivity is dependent on the computed results.During transient processes, the amount of water entering an elemental volume of soil may be larger than the amount of water exiting the volume, or vice versa.This results in a certain amount of water either being retained or released during a particular time increment.

Elastic-Plastic Model
The eastic-plastic model describes an elastic, perfectly-plastic relationship.Stresses are directly proportional to strains until the yield point is reached.Beyond the yield point, the stress-strain curve is perfectly horizontal.

Plastic Matrix, Elastic-Plastic Model
In SIGMA/W, soil plasticity is formulated using the theory of incremental plasticity (Hill, 1950).Once an elastic-plastic material begins to yield, an incremental strain can be divided into elastic and a plastic component.Only elastic strain increments, dε e , will cause stress changes.As a result, stress increments can be written as follows.
Consequently, the yield function can be written as follows in equation form.
) , , , ( An incremental change in the yield function is given by: (5) Alternatively, this equation can be written in the following matrix form.
The theory of incremental plasticity dictates that the yield function, F < 0, and, when the stress state is on the yield surface, dF is zero.This latter condition is termed the neutral loading condition, and, can be written mathematically as: The plastic strain is postulated to be: Where: G = plastic potential function, and λ = plastic scaling factor.
Substituting the plastic strain from equation ( 8) into the incremental stress equation (equation 3) gives Substituting the stress vector, {ds}, into the neutral loading condition (equation 6), the following expression for the plastic scaling factor, λ, can be derived.
From equations ( 8) and ( 10), a relationship between stress increments and strain increments can be obtained.(12) To evaluate the plastic matrix, [Cp], the yield function, F , and the plastic potential function, G , need to be specified.
The following equation provides a common form of the Mohr-Coulomb criterion expressed in terms of principal stresses (Chen and Zhang, 1991).( 13) Figure 3 shows the finite element mesh used in this case.A layer of clay 25 m thick is modeled.The water table is assumed to be at the ground level.Eight node isoparametric elements are used.Due to symmetry, only half of the axisymmetric problem is considered.The right and left boundaries are allowed to move vertically, while the bottom boundary is restrained both horizontally and vertically.

Analysis Results:
Finite element analysis was carried out for two cases; in the first case, the coefficient of permeability is considered constant during the consolidation process while in the second case, the coefficient of permeability is changed with the applied pressure (effective stress) during consolidation.Figure 4 shows a comparison of the total surface settlement calculated after 1000 days for the two cases.It can be noticed that the maximum effect of permeability occurs below the center of the problem.A decrease in the maximum surface settlement of the order of (12 -15) % can be predicted when the permeability change is considered.Another comparison is made in Figure 5 at time 450 days.The figures show that during consolidation, the effect of permeability is clear, then the difference decreases at the end of consolidation (after 1000 days).
The same results are also noticed in Figure 6 which displays the percent of settlement at the end of load application to the final (total) consolidation settlement.
Figure 7 shows the distribution of the final consolidation settlement with depth along the centerline.It can be noticed that the effect of change of the permeability increases with depth.The maximum difference between the settlements predicted in these cases is in the percentage of (16 -22) %.Similar relations are shown in Figure 8 after 450 days of consolidation, but also the difference between the two cases is greater Figure 9 presents the variation of horizontal displacement along sec.(a-a), (shown in Figure 3), 5 meters away from the problem centerline.It can be noticed that the effect of changing the coefficient of permeability is pronounced at the ground surface and a difference of about (12 -14) can be noticed.Similar results are presented in Figure 10 which shows that the effect of permeability is greater at time 450 days.
The effect of permeability on the time rate of settlement is explained in terms of consolidation ratio (degree of consolidation) as shown in Figure 11.The degree of consolidation of the clay layer at any time is calculated as the ratio between the excess pore water pressures dissipated at that time to the initial excess pore water pressure.It is evident that the effect of permeability is clear at later times of consolidation due to decrease in void ratio and hence slower dissipation of pore water pressure.Taking into account variable permeability leads to longer times of consolidation.
Figure 12 traces the dissipation of pore water pressure at point (a) 12 m deep with time.It is noticed that the pore water pressure predicted in the case of variable permeability is greater than in conventional constant permeability case due to smaller rate of dissipation.
Figure 13 shows the isochrones of excess pore water pressure at different times.At early stages, the effect of permeability is not clear, while at later times (after 400 days), the excess pore water pressure predicted for the case of variable permeability is greater than conventional case by about (10 -12) %.

CONCLUSIONS:
1.The maximum effect of permeability occurs below the center of the problem.A decrease in the maximum surface settlement of the percentage of (12 -15) % can be predicted when the permeability change during consolidation is considered.2. The effect of permeability is clear at later times of consolidation due to decrease in void ratio and hence slower dissipation of pore water pressure.Taking into account variable permeability leads to longer times of consolidation.At later times (after 400 days), the excess pore water pressure predicted for the case of variable permeability is greater than conventional case by about (10 -12) %.
• User's Guide Manual of SIGMA/W, (2002), GEO-SLOPE International Ltd, Calgary, Alberta, Canada.• Ying, Z., Kang, X., Xi, L., ( 2005 of consolidation, and then decreases at the end. Fig.(1) Variation of the coefficient of permeability with pressure for the three soils.

Fig. 10 :Fig. 13 :
Fig. 10: Effect of different conditions of permeability on the distribution of horizontal displacement with depth along the foundation centerline at (450 days).

Table 1 : Index properties of the three soils.
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