Influence of Water Boundary Conditions on Pore Pressure and Improvement Effect in Electroosmosis

PENG Jie( )， HUANG Mufan()， HU Jianbin()， SUN Yicheng()

1 Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering， Hohai University， Nanjing 210098， China2 Jiangsu Research Center for Geotechnical Engineering Technology， Hohai University， Nanjing 210098， China

Abstract： The influence of water boundary conditions on pore pressure was studied by one-dimensional electroosmotic consolidation test， and the effects of electroosmosis， pore water pressure， settlement and electroosmotic flow were monitored and analyzed. The results show that the boundary conditions of electroosmotic water have a significant effect on the pore water pressure and improving effect. Negative pore water pressure without auxiliary water is far greater than the replenishment. The measured data show that improvements in experiments without replenishment are also better. The calculation of Esrig solution of the pore water pressure is consistent with the measurement data in the water-supplementing test and is very different from the measurement data in the test without rehydration. Considering the impact of water boundary conditions is the key to electroosmosis experiments and applications.

Key words： consolidation; electroosmosis; pore water pressure; water boundary conditions

Introduction

The phenomenon of electroosmosis in soils was first reported by Reuss in 1809， and it was not applied to geotechnical engineering until Casagrande[1]engineered electroosmotic soil consolidation and dewatering in slope reinforcement works in 1952. It is well known that electroosmosis is effective for silt and clay-rich soils with low hydraulic conductivity. It is used not only for soil improvement but also for remediation of contaminated soils[2-5].

There are four principles in soil when electroosmosis is conducted， water， chemical， electric and heat flow[6-8]. Water flow has the most important role in geotechnical engineering applications such as seepage， consolidation and strengthening. The negative pore water pressure generated in soil between electrodes is an important factor for soil strengthening， which has been observed by several researchers. The pore pressure in soil treated by electroosmosis is affected by many factors including flow boundary conditions (i.e.， opened or closed anode)， electric field intensity and chemical properties of the system， such as the surface chemistry of the soil and chemical boundary conditions[9-12].However， the effect of a water supplement boundary condition taken into account in electroosmosis consolidation is rarely. And also neither water supplement in the anode nor cathode in most laboratory electroosmosis studies are found[13-19]. But in field research， though the permeability of soil is low， the groundwater around improvement zone can flow into the improvement zone. This water supplement boundary condition has important effects on the pore water pressure that develops in soil. The pore pressures developed under electroosmosis are negative in most instances. Negative pore pressure or suction is different from positive pore pressure on the soil. Deformation will be induced with dissipating positive pore pressure and the soil will contain saturated status even though there is no water supplement. However， the suction in soil can cause not only deformation but also an unsaturated status. The existence of a water supplement in the boundary will impact on the pore water pressure development.

This paper aims to investigate the pore pressure and mechanical processes which occurred in the soil with different water supplement boundary conditions under electroosmosis. The influence and importance of water supplement boundary conditions on the overall behavior of the soil sample is also evaluated. This could lead to a better understanding of the mechanism of electroosmosis and provide a reference for practical electroosmosis engineering.

1 Soil Preparation

The test soil used in this study is kaolinite produced from Fangshan of Nanjing in Jiangsu Province， China. Deionized water is added to form saturated samples with a water content of 60.0%. The fundamental physic-chemical and geotechnical properties of this kaolinite are shown in Table 1.

Table 1 Geotechnical properties of soil sample

Particle analysis is conducted by using a BT-9300H laser particle analyzer(Bettersize Instrument Limited Company， Dandong, China)on four samples. The measured particle size gradation curve is plotted in Fig.1. All particles within the samples are identified as fine-grained; the content of clay particles is more than 82%.

Fig.1 Grain size distribution of test soil

2 Apparatus and Test Procedure

The experimental device consists of an acrylic cylindrical cell of dimensions 25 cm high by 15 cm inner radius. Rigid and porous plastic filters are placed in the cell to hold the soil sample and minimize soil dispersion into electrolytes. Two perforated graphite tablets are used as electrodes and placed in the soil in the cell. The anode is closed and the cathode is opened with free access to water. The thickness of the test soil sample between the anode and cathode is 8 cm and the diameter is 15 cm. In Fig.2， a 6 cm thick soil is overlaid above the anode in order to

keep the anode closed, and water is added from the top and the water table is maintained at the soil surface when the water supplement is included. Figure 2(b)shows the case without the water supplement. Hydraulic seepage is neglected in this study due to the low permeability and water gradient.

Fig.2 Schematic diagram of the apparatus (a) simulating the supplementary water boundary condition and(b) without the supplementary water boundary condition

At first， 5 kPa of vertical pressure was applied and maintained in the top of the soil sample during the test. After the initial consolidation， electroosmosis was conducted with a constant voltage of 10 V in EK1 and EK2， and 20 V in EK3 and EK4. The test conditions for the electroosmosis consolidation are listed in Table 2.

Table 2 Test conditions for the electroosmosis consolidation

The pore pressure， vertical deformation， water inflow and outflow were monitored in this study. The monitoring points for vertical deformation and pore pressure are indicated in Fig. 2. After the tests， the water content， void ratio and un-drained strength of the samples were determined， respectively.

3 Results

3.1 Variation of pore water pressure

The pore water pressure over time for all of the tests is shown in Fig. 3, which indicates that the water supplement boundary condition and the applied voltage both have a significant influence on the pore water pressure in soil.

There is a distinct difference between the pore pressures in the two types of water supplement boundary conditions. The pore pressure under the water supplement boundary condition decreased slowly， and reached a peak and then remained almost unchanged to the end of test. The pore pressure without the water supplement reached a peak rapidly after applying the DC voltage and declined slowly to a stable value， where it remained to the end of test. However， it showed that the time required in these tests to reach a stable status was similar between the two conditions. It took approximately 160 h to reach the stable pore pressure under 10 V in EK1 and EK3， and approximately 90 h under 20 V in EK2 and EK4. The pore pressure variation range without the water supplement was much larger than that with the water supplement boundary condition. The maximum and stable negative pore pressures in test EK1 are -64 kPa and -42 kPa， which are 3.8 times and 2.6 times as much as those in EK2， and the maximum negative pore pressure in test EK3 are -70 kPa and -49 kPa， which are 3.3 times and 2.4 times as much as those in EK4 when 20 V was applied.

The applied voltage has a relatively small influence on the pore pressure in tests EK1 and EK3 under the condition without a water supplement. The curves of pore pressure over time are similar between EK1 and EK3， as shown in Fig. 4(a). However， under the water supplement boundary condition，i.e.， EK2 and EK4， the applied voltage has a significant influence on the pore pressure， as shown in Fig. 4(b). The higher the applied voltage， the faster and higher the pore pressure developed. It took approximately 90 h to reach the peak of pore pressure in test EK4 in which 20 V was applied， and it took 145 h to reach the peak of pore pressure in test EK2 in which 10 V was applied. The stable pore pressures from the 20 V tests were noticeably higher than those of the 10 V tests， but the difference was smaller when the measured point was closer to the cathode.

Fig.3 Pore water pressure (a) 10 V test group and (b) 20 V test group

Fig.4 Pore water pressure (a) supplementary water boundary conditionand and (b) no-supplementary water boundary condition

As shown in Fig.5， from the anode to the cathode， the pore pressure shows a nearly linear decrease in both water supplement boundary conditions which is consistent with Ref.[9], and the maximum pore water pressure of every test is illustrated.

Fig.5 Pore water pressure along the direction of electroosmotic

3.2 Electrical current

The measured electrical currents between anode and cathode over time are plotted in Fig.6. The currents in all tests decrease rapidly with test time， and the water supplementing boundary condition has no significant effect on the current of these tests.

Fig.6 Electric current over time

3.3 Flow by electroosmosis

The pore water flow in an anode-to-cathode direction by electroosmosis， as shown in Fig.7， and the outflow of all tests increased significantly and then gradually decreased. The total outflow in tests EK1 and EK3 (i.e.， with water supplement) are 2.2 and 2.1 times as much as that in tests EK2 and EK4 respectively. But when the net total outflow is considered， the net total outflow in tests EK1 and EK3 were 72% and 77% of net total outflow in tests EK2 and EK4.Furthermore， the applied voltage also has significant effect on drainage. The net total outflow in test EK3 and EK4 (i.e.， with 20 V)are 27% and 18% higher than those in EK1 and EK2， respectively.

Fig.7 Electric flow over time

3.4 Vertical deformation

Figure 8 shows the variation of vertical deformation with time for all the tests. The vertical deformation behavior is similar to what can be expected in a conventional mechanical loading consolidation. The vertical deformations in EK1 and EK3 are 27% and 24%，which are less than EK2 and EK4， respectively. This means that the water supplement condition has apparent influence to the vertical deformation.

Fig.8 Vertical deformation over time

3.5 Measurement after electroosmosis

Once the electroosmosis was completed， the applied voltage was removed， the testing apparatus surrounding the top and sides of the soil was dismantled. And the un-drained strength， water content and the void ratio of the soil were measured.

When testing was completed， the un-drained shear strength was measured by using the miniature vane device(ASTM D4648). Compared to the initial soil in which the un-drained strength was 4 kPa， the strength of the treated soil is shown in Fig.9， and is significantly increased. The influence of the water supplement boundary condition is clear. The un-drained strength near the anode in test EK2 was 44%higher than that in EK1 and in test EK4 was 45%higher than that in EK3 respectively. The influence of voltage is also obvious. The un-drained strength near the anode in tests EK3 and EK4 were 16% higher than in EK1 and EK2 respectively. Closer to the cathode， however， the influence of the water supplement boundary condition and voltage became smaller.

Fig.9 Un-drained shear strength after test

The water content after testing is shown in Fig. 10. The water content of the soil decreases significantly after treatment， and the water content of every position in tests EK2 and EK4 is less than those in tests EK1 and EK3. In addition， the higher the applied voltage is， the lower the water content obtains.

Fig. 10 Water content after test

The void ratio after the tests is illustrated in Fig. 11. The void ratio of the soil decreases after electroosmosis， and the magnitude of these decreases under the condition without water supplementation being more than that under water supplementation.

Fig.11 Void ratio after test

Fig.12 Saturation degree after test

According to the water content and void ratio after the tests， the saturation degree in the soil can be obtained， which is shown in Fig.12. All of the soil samples in this study became unsaturated after electroosmosis. This occurred even though the saturation degree of every position in tests EK2 and EK4 with the water supplement was less than those in tests EK1 and EK3. The higher the applied voltage was， the lower the saturation degree obtained.

From the data of saturation degree， the difference between positive and negative pore water pressures can be obtained. Deformation and increasing strength will be induced with both positive and negative pore pressures， but under the application of positive pore water pressure， the soil will remain saturated even though there is no water supplement. When a soil is under a negative pore water pressure induced by electroosmosis， the volume of net electroosmosis flow is more than volume of void compression. As a result， the soil will become unsaturated regardless of the existence of a water supplement condition.

In general， the treatment effect in the case without the water supplement boundary condition is better than that with the water supplement boundary condition， when other conditions of electroosmosis remain the same.

4 Discussion

4.1 Theoretical calculation of pore water pressure of electroosmosis

When the pore fluid at a point in the soil is removed under electroosmosis， the pore fluid demand due to the electroosmotic pore fluid flux will increase. If the soil within the zone due to low hydraulic conductivity， pore fluid mass can only be balanced by the generation of negative pore water pressure[19]. Therefore， the pore water pressure in the soil under electroosmosis is significantly affected by hydraulic conductivity. The pore water pressure can be estimated by Eq.(1) when the anode is closed and the cathode is opened with free access to water[9].

(1)

whereuis the pore water pressure(kPa)，xis the distance from the anode(m)，tis time of electroosmosis(s)，keis coefficient of electroosmosis permeability(m2/sV)，kis coefficient of hydraulic permeability(m/s)，Vmis electric field strength between anode and cathode(V)，V(x) is electric field strength between pointxand cathode(V)，γwis unit weight of water(kN/m3)，misn+1/2;Tv

The maximum negative pore pressure in the soil can be determined by Eq. (2).

(2)

The coefficient of electroosmosis permeability can be calculated from Eq. (3).

(3)

whereQeis velocity of electroosmosis flow (m/s).Vmis voltageand andLis the distance acting along an electric field line.

The calculated maximum coefficient of electroosmosis permeability.kefrom the maximum flow rates of test EK1， EK2， EK3 and EK4 are 2.29×10-9， 2.56×10-9， 1.07×10-9， 2.20×10-9(m2/s·V)， respectively. The average coefficient of electroosmosis permeability，ke， from the total cumulative flow rates test EK1， EK2， EK3 and EK4 are 1.30×10-9， 1.46×10-9， 1.00×10-9， 1.19×10-9(m2/sV). When the effective electric field strength between anode and cathode is considered. The coefficient of electroosmosis permeability is 1×10-9-1×10-8(m2/sV) in common kaolinite[6]. The calculated coefficient of electroosmosis permeability in this study falls within this range， but decreases over time.

The coefficient of hydraulic permeability and consolidation factor of the soil sample are illustrated in Table 1. The calculated pore water pressure curves over time from Eq. (1) and measured data are presented in Fig. 13. It shows that the calculated values agree with the measured data obtained in test EK1 and EK3 (i.e.， with water supplement)， but there is a large gap between the calculated values and the measured data obtained in test EK2 and EK4 (i.e.， without water supplement). The measured maximum negative pore water pressure is much higher than the calculated value， and the shape of curve is also different. This may be due to the unsaturated status of the soil after electroosmosis.

Fig.13 Calculated and measured pore water pressure in point a

After the pore fluid in soil is removed by electroosmosis without the water supplement， the soil became unsaturated. In unsaturated soil， the coefficient of hydraulic permeability is significantly affected by the degree of saturation (or water content) of the soil. As a soil becomes unsaturated， air first replaces some of the water in the large pores， and this causes the water to flow through the smaller pores with an increased tortuosity to the flow path. A further increase in the matric suction of the soil leads to a further decrease in the pore volume occupied by water. As a result， the coefficient of hydraulic permeability with respect to the water phase decreases rapidly as the space available for water flow reduces[20]. When most of the pore water is discharged due to electroosmosis， the negative pore water pressure reaches a peak. After this point， pore water and air enter the negative pore pressure zone， and the negative pore water pressure recovers gradually to a stable value.

4.2 Negative pore water pressure and effective stress

The vertical deformation of the sample is calculated through layer a summation method in order to investigate the relationship between negative pore water pressure and effective stress. Isotropic compression of the test sample occurs when a negative pore water pressure is generated inside the soil in electroosmosis. The isotropic compression status is different from the stress state used in the layer summation method， which is confined compression. However， it is similar to the soil status under EK3 preloading in which a negative pore water pressure is also generated. As a result， the settlement calculation method for vacuum preloading in the technical code for ground treatment of building of China (JGJ79—2012)[21]is adapted in this study. The equation is shown as below[9].

(4)

whereSfis the final vertical deformation(m);e0iis the void ratio corresponding to the initial vertical stress in thei-th layer， which is determined by e-p laboratory compress curve;e1iis the void ratio corresponding to the final vertical stress in thei-th layer， which is determined by e-p laboratory compression curve;hiis the thickness of thei-th layer;ξis the experience factor.

The laboratory compression curve of kaolinite in this study is shown in Fig. 14. The sample is stratified to 4 layers in which the measured maximum negative pore water pressure in the middle of layer is used as the final vertical effective stress. The initial vertical stress is 5 kPa. The calculated results and measured data are listed in Table 2.

Table 3 shows that the measured vertical deformation is much less than the computation in EK2 and EK4， while the measured vertical deformation of EK1 and EK3 are close to the calculated values， in which the same method is used. This reveals that the negative pore water pressure in EK2 and EK4 cannot be directly treated as effective stress.

Fig.14 Relation between pressure and void ratio (e-p) of original soil

CodeMeasured vertical deformation/mmCalculated vertical deformation/mmEK13.73.8EK25.18.9EK34.24.0EK45.610.1

5 Conclusions

The water boundary conditions for electroosmosis have a significant influence on the pore water pressure generated during electroosmosis. The range of negative pore water pressure generated without the water supplement is much more than that with the water supplement. It is apparent that the shape of the curve of pore water pressure over time is different from the two water boundary conditions. The pore water pressure in the test with the water supplement decreases gradually over time， and reaches a peak and remained unchanged to the end of test. The pore pressure without the water supplement reaches a peak rapidly after the application of the DC voltage and declined slowly to stable value， where it remains to the end of test.

The water boundary condition for electroosmosis has an apparent influence on the improvement effect of soil from electroosmosis. The measured vertical deformation， net electroosmosis flow， un-drained strength and water content show that the treatment effect in the tests without the water supplement is better than the tests with the water supplement， when other test conditions remain the same.

The calculated pore water pressure of Esrig’s solution agreed well with the measured data in tests with the water supplement and was very different from the measured data in tests without the water supplement， including the maximum value and the shape of the pore water pressure over time curve.

Although the range of negative pore water pressures generated without the water supplement is much higher than that with the water supplement， the effective degree of the negative pore water pressure in tests without the water supplement is less than the effective degree of the negative pore water pressure in tests with the water supplement. The negative pore water pressure generated cannot be directly treated as effective stress in the condition without the water supplement.

Therefore， the influence of water boundary conditions on electroosmosis treatment is important and cannot be ignored. It is necessary to consider this factor in the application of electroosmosis and in related research.