Research ArticleDesign Method and Verification of Electroosmosis-VacuumPreloading Method for Sand-Interlayered Soft Foundation

Yunliang Cui ,1 Jianbo Tu ,2 Xinquan Wang ,1 Hongguo Diao ,1 and Qianru Ge2

1Department of Civil Engineering, Zhejiang University City College, Hangzhou 310015, China2Zhejiang Provincial Institute of Communications Planning Design and Research. Co., Ltd., Hangzhou 310015, China

Correspondence should be addressed to Yunliang Cui; cuiyl@zucc.edu.cn

Received 3 September 2019; Revised 9 April 2020; Accepted 26 May 2020; Published 13 June 2020

Academic Editor: Melina Bosco

Copyright © 2020 Yunliang Cui et al. (is is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

(e design method of electroosmosis-vacuum preloading for soft foundation treatment is not systematic and complete, therebyrestricting the application of the technology in engineering. A designmethod for the electroosmosis-vacuum preloading treatmentof sand-interlayered soft foundation is therefore presented. A compressible electrical prefabricated vertical drain is developed, anda vacuum sealing and draining system is designed for the application of the electroosmosis-vacuum preloading in sand-interlayered soft foundation. Calculation formulas of site resistance considering the interlayer and interface resistivity of theelectrode are established to design the power supply and electrical circuit. A simple numerical simulation method is proposed topredict the ground settlement treated by electroosmosis-vacuum preloading. A field test of electroosmosis-vacuum preloading isdesigned using the suggested method, and comparison tests between the electroosmosis-vacuum preloading and the vacuumpreloading are performed to verify the proposed technique. (e test results show that the proposed design method is reasonablefor the design of electroosmosis-vacuum preloading in engineering.

1. Introduction

Many geotechnical researchers have studied electroosmosistechnology since it was introduced to soft ground im-provement engineering by Casagrande [1]. A large numberof laboratory tests have been conducted to study thecharacteristics and related laws of soft soil consolidation byelectroosmosis and the effectiveness of electroosmosis forsoft ground improvement [2–4].(e electroosmosis methodhas also been implemented in many field tests [5–7]. Testresults have shown that consolidation by electroosmosisonly is relatively less efficient, and the combined applicationof the electroosmosis method and other foundation treat-ment methods can achieve a better result. (e combinedapplications of electroosmosis and vacuum preloading [8, 9],electroosmosis and dynamic consolidation [10], electroos-mosis and pneumatic fracturing [11], and electroosmosisand chemical [12], among others, have been verified inlaboratory or field tests. Some theories have also beenestablished for the design of electroosmosis for soft soil

foundation. Zhuang and Wang [12] proposed the interfacevoltage drop hypothesis, based on which a simple interfaceresistance expression was given, to calculate the current andenergy consumption of consolidation by electroosmosis.Wang et al. [13] proposed the design, calculation steps, andestimation methods of relevant parameters for the treatmentof wet soil by electroosmosis. Zhuang [14] gave the mainprocedures and design contents of the electroosmoticdrainage consolidation design and developed a determina-tion method of water discharge, electroosmosis system,treatment time, etc. (e above studies provide a good ref-erence for calculating electroosmotic current and energyconsumption, but they did not consider the influence of sandlayer in ground. To simulate electroosmosis consolidationwith a numerical method, Yuan and Hicks [15, 16] proposeda numerical model for the numerical analysis of electro-osmosis consolidation and verified it with a case study.Chang and Sheen [17] used the excess pore water pressure ofthe three-dimensional consolidation behavior to deduce thethree-dimensional electroosmotic equation under solar

HindawiAdvances in Civil EngineeringVolume 2020, Article ID 1929842, 9 pageshttps://doi.org/10.1155/2020/1929842

mailto:cuiyl@zucc.edu.cnhttps://orcid.org/0000-0002-0965-2385https://orcid.org/0000-0002-1486-9757https://orcid.org/0000-0002-1518-8793https://orcid.org/0000-0001-9072-0754https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1155/2020/1929842

energy electroosmosis. Hu and Wu [18] proposed a math-ematical model of electroosmotic consolidation for softground improvement based on the finite element method.(e above method can be used to simulate the electroos-motic consolidation of simple cases, but its use for themodeling of complex projects is challenging and not ac-cessible for engineers to master.

In summary, the above design theories are not completeand sufficient for the engineering design of electroosmosis-vacuum preloading and the prediction of foundation set-tlement. Although there is research on the design method ofelectroosmosis, the design of the combined method ofvacuum preloading and electroosmosis has not been fullystudied. No systematic and complete design method can beused to design the electroosmosis-vacuummethod. Notably,the deep soft soil foundation in coastal areas often has acertain thickness of sand interlayers. (ese interlayers arerich in water and have a significant permeability coefficient.(is will quickly lead to electrode corrosion, line overloadfrom the excessive current, and air leak of the vacuumsealing system in the electroosmosis-vacuum preloadingtreatment. Proper and accurate designs are needed for theelectrode, vacuum sealing system, and circuit system. In thisstudy, a relatively complete design method for electroos-mosis-vacuum preloading was developed and verified by afield test.

2. Design Methods

2.1. Electrode Design. (e electrode in the soft soil foun-dation improvement system in the electroosmosis-vacuumpreloading method should be electrically conductive anddrainable. (e electrode should be flexible or compressibleso that it does not pierce the vacuum geomembrane coveringon the foundation surface during the settlement of thefoundation. For a soft soil foundation with a sand layer, thewater flow in the sand layer may easily lead to a short circuit,resulting in an excessive current in the circuit of the elec-troosmosis system; thus, the electrode should be insulated inthe sand layer. (e electrical prefabricated vertical drain(ePVD) is proposed in this work to meet the requirementsabove. (e ePVD is made of a galvanized steel pipe withholes drilled all over.(e pipe is wrapped in a geotextile filtercloth. A spring hose and a copper core wire are connected atthe top. (e copper core wire is connected to the galvanizedsteel pipe with a steel ring, and the joint of the cable and thesteel pipe is wrapped in rubber tape for corrosion protection.A diagram of the proposed ePVD can be seen in Figure 1.(e spring hose can be compressed during the foundationsettlement to avoid piercing the vacuum geomembrane, andthe spring hose can be directly connected to the horizontaldrainage pipe to improve the vacuum transfer effect. Inpractice, a hole is drilled into the foundation with a high-pressure water gun, and the ePVD is inserted into the hole.In this manner, the geotextile filter on the ePVD can remainin place/intact during construction. For a soft soil foun-dation with a sand layer, the ePVD is enwound with a rubbertape on the galvanized steel pipe in the sand layer so that this

part of the steel pipe is insulated from the surroundingaquifer.

In electroosmosis consolidation engineering, the spacingof the drainage electrodes has a great influence on theelectroosmotic effect. At the same voltage, the smaller theelectrode spacing, the larger the voltage gradient applied onthe soil between the electrodes and the more obvious theelectroosmotic effect. Because an excessively small electrodespacing will result in a high electrode material cost, theelectrode spacing in electroosmosis engineering can refer tothe electrical prefabricated vertical drain (PVD) spacing inthe conventional vacuum preloading. (e spacing is usually1.0–1.5m, and the electrode is always arranged in a square ora quincunx. In soft ground improvement by the electro-osmosis-vacuum preloading method, the electrode spacingcan be appropriately increased to reduce the material cost,and the ePVD can be alternatively arranged with the con-ventional PVD. (at is, the drainage electrode spacing istwice the PVD spacing; the drainage electrode and the PVDcomplement each other. (e length of the electrode is de-termined according to the depth of the soft soil layer to betreated. For deeper soft soil layers, a short electrode and along PVD can be combined. However, the length of theelectrode should meet the treatment depth of the soft soillayer.

2.2. Power Supply and Circuit Design. DC power supply isthe main equipment for foundation improvement engi-neering by the electroosmosis-vacuum preloading method.(e power used in construction sites is usually 380V three-phase AC, which needs to be converted to DC by aDC powersupply. (e commonly used DC power supplies are mainlyclassified as unidirectional pulse or unidirectional constantDC power supplies. (e current waveform output by theformer is a high-frequency unidirectional square wave, and

Copper core wire

Spring horse

Steel ring

Drain holeFilter cloth

Steel pipe

Figure 1: Diagram of the proposed ePVD.

2 Advances in Civil Engineering

the current waveform output by the latter is a unidirectionalconstant direct current. According to an experimental studyof the authors, pulse DC power supplies have high elec-troosmotic efficiency and are recommended over constantDC power supplies.(e drainage electrodes inserted into thefoundation are converged to the lead wire through branchwires and connected to the anode and the cathode of the DCpower supply. (e copper core wire or aluminum core cablecan be optional for the circuit. Compared with copper corewires, aluminum core cables have poorer current-carryingcapacity. Nevertheless, they are easy to heat and cheaperthan copper core wires. In cases with low current, aluminumcore cables can be used. In actual engineering, due to thehigh water content and low resistance of soil, there is aconsiderable demand for the current-carrying capacity ofsuch wires and power from DC power supplies, which arealso the limiting factors for electroosmotic treatment.(erefore, it is important to calculate the wire current andthe power of the power supply. In the engineering design, thebranch wire’s current should be calculated according to thenumber of electrodes connected in series with each branchwire and then summarized to obtain the lead wire’s current,thus separately determining the sectional area of the branchwire and that of the lead wire. Finally, the power required iscalculated according to the lead wire’s current and the designvoltage. (e higher the power, the heavier the power supplyand the higher the price. In engineering, the large-area siteshould be divided into small-area electroosmotic blocks,each of which is controlled by a DC power supply.

(e power of the power supply can be obtained byP � UI, in whichU is the output voltage of the power supply.Wu et al. [19] used a voltage of 40V in their study, andWanget al. [13] used an average voltage of 40V. (e voltages usedin Bjerrum et al. [5] and Lo et al. [6] were less than 70V and120V, respectively. (e higher the voltage, the better theconsolidation that can be achieved but the higher the cost. Avoltage of 36V was used in the present study for safeconstruction. I is the total output current of the powersupply, and the current is the sum of the current I′ of eachanode (or cathode) branch wire. (e current of each anodebranch wire is I’�U/ΣR′, where ΣR′ is the total resistance ofthe area controlled by each anode branch wire. (e elec-troosmotic circuit system is shown in Figure 2.

(e total resistance ΣR′ of the area controlled by eachanode branch wire can be described by the apparent re-sistance of each anode-cathode pair. Each such pair and thesoil between them are divided into a soil strip, as shown inFigure 2. (e apparent resistance Ra of the anode-cathodepair can be expressed by the following:

Ra � Rw + Re + Ri + Rs, (1)

where Rw is the resistance generated at the wire and the wireconnection, Re is the resistance of the material of thedrainage electrode, Ri is the interface resistance of theelectrodes and the surrounding soil, and Rs is the resistanceof the soil between the anode and the cathode. Rw � 0 isassumed in the engineering cost estimate. When a metalelectrode is used, Re � 0 can be assumed. Zhuang and Wang[12] gave formulas for calculating the interface resistance Ri

and soil resistance Rs. (e expressions of Ri and Rs proposedby Zhuang and Wang [12] can be rewritten as follows toconsider the influence of the sand layer in the ground:

Ri �1

d hi−

1b hi

kj, (2)

Rs �ρsl

hib, (3)

where kj is the interface resistivity (Ω·m− 2); d is the anode or

cathode diameter,m; and hi is the thickness of the soil layer iin the electrode treatment range, m. (e sand and soil layerthicknesses at the electrode top’s spring hose are excludedfor the case of using the ePVD to treat a foundation with asand layer; b is the anode spacing or cathode spacing,m. ρs isthe average resistivity of the soil between the anode and thecathode. (e resistivity of each soil layer is weighted andaveraged according to the thickness of the soil layer. (eresistivities of the sand and soil layers at the electrode top’sspring hose section are excluded for the case of using theePVD to treat a foundation with a sand layer; l is the distancebetween the anode and the cathode, m.

(e apparent resistance of each anode-cathode pair con-nected to a branch wire is in a parallel connection. (erefore,the total resistance of the area controlled by each branchwire isΣR’�Ra/n, where n is the number of anode-cathode pairs.Since one anode branch wire and two adjacent cathode branchwires form a loop, n is twice the number of anodes connectedto one branch wire. (e current of each branch wire can beobtained by I’�U/ΣR’. According to the calculated current, theappropriate branch wire type can be selected according to thecurrent-carrying capacity of the wire’s sectional area. (e totalcurrent of each power supply is I�ΣI’.(e sectional area of thelead wire can be determined based on the total current to selectthe appropriate lead wire type.

2.3. Vacuum Seal and Drainage System Design. For the ap-plication of the electroosmosis-vacuum preloading methodfor sand-interlayered soft foundation, a vacuum seal anddrainage system are proposed, as seen in Figure 3. For

Cathode

d

Anode l

b

Rai Rai+l

I′i I′i+l

Lead wire I = ∑I′i

Powersupply

P = UI

Bran

ch w

ire

+–

Figure 2: Schematic view of electroosmotic circuit.

Advances in Civil Engineering 3

foundation with sand layers, air leakage can easily occur atthe site during the vacuuming process, and the vacuumdegree cannot meet the design requirements. (erefore, it isnecessary to provide a sealing wall around the site to blockthe permeable layer. (e mud mixing wall can be used as thesealing wall, and mud made of clay is poured into thefoundation through a cement-mixing pile machine to form aclay sealing wall. (e clay in the mud adopted by the claysealing wall should be not less than 20%, the clay graincontent of the clay should be more than 20%, the muddensity should be 1.2–1.3, and the permeability coefficientshould be k

pressure consolidation to approximately simulate the elec-troosmotic consolidation may satisfy the engineering needsunder the same discharge of the unit soil.

According to Mitchell [20], the excess pore pressure atthe cathode induced by electroosmosis can be determined bythe following:

u � −ke

kh cwϕ, (4)

where ke is the electroosmosis coefficient, kh is the horizontalosmotic coefficient, and ϕ is the electrical potential at thecathode.

(e unit seepage flow generated by the potential ϕ isequal to that generated by the negative excess pore pressureu � − (kecwϕ/kh). In the finite element simulation of elec-troosmosis consolidation, we propose that the negativeexcess pore pressure drainage method be used to approxi-mately simulate the electroosmotic drainage. In the pro-posed method, the anode is set to an excess pore pressureboundary, and the excess pore pressure can be calculated byformula (4). During electroosmosis, water flows from theanode to the cathode and then is discharged from thecathode. (e excess pore pressure at the cathode is kept at 0,where no water is discharged at the anode and the pore waterat the anode is discharged to the cathode. (en, a negativeexcess pore pressure is formed gradually at the anode, andthe soil at the anode is first consolidated, resulting in a moresignificant settlement compared with that of the soil at thecathode. (is is consistent with the law of consolidationsettlement of the soil in the actual electroosmosis process.However, in the finite element simulation of electroosmosisusing the proposed simplified method, the negative excesspore pressure applied at the anode will generate seepagefrom the cathode to the anode, which is inconsistent with theactual electroosmotic seepage direction; hence, this methodis merely a simplified approximation method. Nevertheless,while ensuring equal displacement of the soil, this methodcan reflect the law that the soil at the anode is consolidatedand settled earlier than that at the cathode. In soft groundimprovement, settlement and displacement are the mostcrucial factors. (e direction of seepage is not as important.(erefore, this method can be applied in soft soil foundationimprovement engineering.

Although this method cannot reflect the mechanism ofelectroosmosis consolidation in essence, it can predict thesettlement of the soil and be used for the settlement pre-diction of soft soil foundation treated by electroosmosis-vacuum preloading. Accurately predicting the foundationsettlement by the finite element simulation can help designthe treatment process reasonably.

3. Verification of the Design Methods

3.1. Overview of the Test Area. (e test was conducted on adredged fill site. (e dredged fill was consolidated by vac-uum preloading. Roads needed to be built on the site, but thebearing capacity of the site could not meet the design re-quirements, so further treatment was needed. (e upperlayer of the site was the dredged fill consolidated by vacuum

preloading. (e lower layer of the soil was mainly muckysilty clay, between which a sand interlayer about 1.5m thickwas sandwiched. (e groundwater level was 0.5m below theground. A static bearing test showed that the average bearingcapacity of the soft soil foundation was about 55 kPa.(e soilparameters in the test area are shown in Table 1.

(e total test area was 1200m2, and it was divided intofour small subareas each sized 20m× 15m. (e four sub-areas were named A1, A2, A3, and B zones. (e A1, A2, andA3 zones were subjected to the electroosmosis-vacuumpreloading test, and the B zone to the conventional vacuumpreloading test.

3.2. Design of Field Test. EPVDs (outer diameter: 0.024m;inner diameter: 0.02m) were inserted in the ground up to adepth of 7.5m. (e upper 1.5m was a spring hose, and thelower 6m depth acted as an electrode. (ere was a sandinterlayer in the foundation, so the electrodes were insulatedin the depth range of the sand interlayer. (e electrodespacing was 2m, and the electrodes were arranged in asquare. (e PVDs were installed between the ePVDs to addmore drainage channels, and the PVD spacing was 1m. (ePVD (0.1m× 0.004m) was used in the conventional vacuumpreloading test area. In this area, the PVD spacing was 1m.(ey were arranged in a square, and the depth of insertioninto the foundation was 15m. Because the foundation had asand interlayer ranging from 3.5m to 5m deep, a self-settingmortar wall measuring 1m thick and 8m deep was used toseal the site. (e branch wires were arranged in the directionof the side of the test area with a length of 15m, includingfive anode branch wires and six cathode branch wires. Eightelectrodes were connected in series on each branch wire.(earrangement of the branch wires, lead wires, and electrodescan be seen in Figure 3.

(e proposed design method in this study was used todesign the circuit, power supply, and settlement in theexperiment. First, the soil resistivity of the site samples wasdetermined by a Miller Soil Box. (e average resistivity ofthe site was ρ± � 3Ω·m. According to formula (3), the soilresistance between an anode-cathode pair can be calculatedby Rs � (3 × 2/2 × (5 + 1.5 + 2.5)) � 0.67Ω.

To determine the interface resistivity kj, we inserted twoePVDs into the foundation as the cathode and the anodewith a spacing of 2m, and then, a 36V DC supply wasconnected. (e measured initial current was about 8.5 A,and the resistance of the circuit was 4.24Ω. (erefore, theinterface resistivity was kj � 0.3897Ω·m2. According toformula (2), the interface resistance of an anode-cathodepair was Ri � ((1/(0.024 × 4.5)) − (1/(2 × 4.5))) × 0.3897 �3.57Ω. Assuming that the resistance of the circuit and themetal electrode was negligible and the initial interface re-sistance of the cathode and the anode was the same, Ra �0 + 0 + 0.67 + 3.57 × 2 � 7.81Ω Ω was obtained accordingto formula (1). (us, the total resistance of the area con-trolled by each branch wire was ΣR′� 7.81/(8× 2)� 0.49Ω.(e adopted input voltage was 36V for safe construction.(e current of each anode branch wire was I’� 36/0.49� 73.8A, and five anode branch wires were arranged ineach test area, so the total current of the lead wire was

Advances in Civil Engineering 5

I� 73.8× 5� 369A. With reference to the current-carryingcapacity of aluminum core insulated wires and consideringthe safety factor, two aluminum core insulated wires with anominal cross-section of 70mm2 were combined as one leadwire with a current-carrying capacity of 420A. Aluminumcore insulated wires with a nominal cross-section of 16mm2

were used as the branch wire with a current-carrying ca-pacity of 90A. (e output power of the power supply couldbe calculated by P� 369× 36�13284W. (erefore, given acertain safety factor, we selected a high-frequency switchingDC power supply with a stable voltage and a steady currentoutput, with an output voltage of 40V, output current of500A, and output power of 20000W. (e input voltage wasthree-phase AC 380V, and the output was a high-stability25 kHz high-frequency wave.

3.3.TestMethod. (eA1,A2, andA3 zones were powered bya DC power supply and received the vacuum electroosmosis-surcharge preloading under the same voltage. (e con-ventional vacuum-surcharge preloading test was performedin the B zone. (e A and B zones were covered with acomplete vacuum geomembrane, and the vacuum degreeunder the geomembrane reached 85–90 kPa in 10 daysbecause of the vacuuming with the vacuum pump. A sur-charge load of 20 kPa was applied after 15 days by pouringwater on the vacuum geomembrane. (en, the electroos-mosis-vacuum and surcharge preloading kept acting for 30days.(e vacuum and surcharge loads are shown in Figure 4.

After 20 days of electroosmotic operation, current tran-sition was performed every five days. (at is, the anode waschanged to be the cathode, and the cathode was changed to bethe anode. Current transition could prevent the formation oflarge interface resistances at the anode, which reduce theefficiency of electroosmosis after long-term application.

4. Field Test Results Analysis

(ree electroosmotic power supplies were set at 36V con-stant voltage output mode to verify the rationality of the wire

and power supply selection. At the initial stage of electro-osmosis, the lead wire currents monitored at the A1, A2, andA3 zones were about 390A, 384A, and 380A, respectively.(erefore, the current-carrying capacity of the wire and theoutput power of the power supply selected could meet therequirements. Compared with the monitoring results, thecalculated results had some errors, but the calculation ac-curacy could meet engineering needs.

(e voltage difference was measured every 0.1m alongthe direction to the anode with the cathode as the center, andthe normalized voltage distribution is shown in Figure 5.(evoltage distributions reported in references [6, 7] werecompared in Figure 5 with that in this study. (e figureshows that the voltage loss at the cathode and the anodeaccounted for a large proportion of the total voltage.According to this study, 14%–17% of the voltage loss was atthe cathode; 33%–49% was at the anode; and 37%–50% ofthe voltage remained in the soil. (e voltage consumption atthe cathode and the anode was mainly caused by the

Table 1: Statistics of physical and mechanical characteristics of soil.

Soil layer(ickness

(h)

Naturaldensity(c)

Moisturecontent(W)

Voidratio(e)

Compressionmodulus (Es)

Cohesion(C)

Internalfrictionangle (Φ)

Horizontalpermeabilitycoefficient (kh)

Verticalpermeabilitycoefficient (kv)

m kN/m3 % MPa kPa o 10− 9m/s 10− 9m/s①Dredgedfill 2.0 17.8 48.8 1.32 2.42 12.9 10.3 6.6 3.8

②-1Mucky siltyclay

1.5 18.0 42.1 1.42 2.83 13.3 11.6 8.6 5.4

③ Sandinterlayer 1.5 19.5 39.4 1.25 3.25 7.5 24.1 84.7 71.5

②-2Mucky siltyclay

4.0 18.2 44.8 1.43 2.86 14.5 11.1 8.2 4.6

④ Siltyclay withsand

20.0 18.9 43.4 1.34 2.94 9.5 12.7 9.8 4.5

Vacuum loadSurcharge load

10 403020 500Time (day)

0

20

40

60

80

100

120

Load

(kPa

)

Figure 4: Vacuum degree under geomembrane and surcharge load.

6 Advances in Civil Engineering

interface resistance, so it was necessary to consider theinterface resistance in calculating the overall resistance of thesite in the electroosmosis design. Because the soil moisturecontents around the cathode and the anode are different andthe contact of the electrode with the soil changes rapidlyafter the electroosmosis begins, different interface resistiv-ities should be adopted at the cathode and the anode.Moreover, interface resistivity varies greatly with soil layers;therefore, the interface resistance should be computed byusing the average resistivity of the soil layer that is in contactwith the electrode.

Settling plates were set in the test zones to monitor thesurface settlement of the foundation. All settling plates wereplaced in the middle of the adjacent vertical drainagechannels. (e surface settlements of the sites are shown inFigure 6.

As shown in Figure 6, in stage 1 (before surchargeloading), the A1, A2, and A3 zones were subjected to thecombined action of vacuum preloading and electroosmosis,whereas the B zone underwent only vacuum preloading. Inthe second stage, from the 15th day after the start of the test,the surcharge load was applied in all the zones. In Figure 6,Vstands for vacuum preloading, E for electroosmosis, and Sfor surcharge load. (e morphology of the settlement curvein Figure 6 shows that the settlement increased sharply afterthe surcharge loading. A comparison of the settlements ofthe A and B zones reveals that the settlement of the elec-troosmosis-vacuum preloading test area was 20% higherthan that of the vacuum-surcharge preloading test area.(erefore, the electroosmosis-vacuum preloading testdesigned by the proposed method can promote a faster andlarger consolidation settlement of soft soil foundation withsand interlayers.

We used the finite element software ABAQUS to nu-merically simulate the electroosmosis-vacuum preloadingtest and verify the rationality of the proposed numericalsimulation method. According to the proposed method,

excess pore pressure was applied on the PVDs and ePVDs inthe simulation. As shown in Table 1, the average horizontalosmotic coefficient of the soil within the effective electrodedepth range was calculated as kh � 8.2×10− 9m/s. Mitchell[20] stated that the value of the electroosmotic coefficient keshould be between 1× 10− 9 and 1× 10− 8m2/V/s. Accordingto the common values in previous studies, the electroos-motic coefficient of the soil taken in the calculation waske � 2×10

− 9m2/V/s. In the field test, the power outputvoltage was ϕ� 36V. (e study result of the voltage dis-tribution between the electrodes showed that only 37%–50%of the voltage remained in the soil, and the average value of44% was used in the calculation. (us, the actual appliedvoltage in the soil was 16V, and the excess pore waterpressure applied to the vertical drainage body in the sim-ulation was − 39 kPa, according to formula (4). (e con-verted excess pore pressure and the actually applied vacuumdegree were superposed and applied to the anode in thenumerical simulation. A two-dimensional finite elementmodel was established with ABAQUS for the electroos-mosis-vacuum preloading test simulation, and theMohr–Coulomb model was used for the soil constitutivemodel. (e soil parameters are shown in Table 1. (e set-tlement curve of the central point on the foundation surfacein the electroosmosis-vacuum preloading area obtained bythe numerical simulation settlement curve is shown inFigure 6. (e foundation settlement contour is shown inFigure 7. (e average measured settlement of A zone at theend of stage 1 is 406.1mm, and the simulated settlement is427.8mm. Compared with the measured data, the error ofthe simulation results is only 5.3%. (e average measuredsettlement of A zone at the end of stage 2 is 601.5mm, andthe simulated settlement is 631.1mm. Compared with themeasured data, the error of the simulation results at the endof stage 2 is only 4.9%. (e simulation errors of the twostages are acceptable in engineering. By comparing thesimulation curve with the measured curves in Figure 6, it canbe found that the finite element simulation curve agrees well

Bjerrum et al. (1967) day 8Bjerrum et al. (1967) day 80Lo et al. (1991) day 1Lo et al. (1991) day 12

Cathode

Anode

This study day 1This study day 3Linear extrapolation

0.0

0.2

0.4

0.6

0.8

1.0

Nor

mal

ized

elec

tric

al v

olta

ge

0.2 0.80.60.4 1.00.0Normalized distance from the test point to the cathode

Figure 5: Distribution of voltage between anode and cathode.

B zone : V + SB zone : VA zone : V + E + SA zone : V + E

Stage 1

A1 zone (V + E + S)A2 zone (V + E + S)A3 zone (V + E + S)B zone (V + S)

PredictionV : VacuumE : EletroosmosisS : Surcharge

Stage 2

Surcharge

40 503010 200Time of duration (d)

700650600550500450400350300250200150100

500

–50

Settl

emen

t (m

m)

Figure 6: Surface settlements of test zones.

Advances in Civil Engineering 7

with the settlement data of the electroosmosis-vacuumpreloading test area. It indicates that the numerical simu-lation has a high precision. (is proves that the proposedsimulation method is feasible for predicting the foundationsettlement of electroosmosis-vacuum preloading, and itscalculation accuracy can meet engineering needs.

5. Conclusions

Aiming at the treatment design of soft soil foundation withsand interlayers by the electroosmosis-vacuum preloadingmethod, a design method that includes the ePVD design,power supply and conducting circuit design, vacuum sealand drainage system design, and settlement prediction wasdeveloped and verified with a field test. (e following resultsare concluded through the study:

(1) (e developed compressible ePVD has the functionsof both conductivity and drainage and can isolate thesand interlayer without puncturing the vacuumgeomembrane. (erefore, it is suitable for thetreatment of sand-interlayered soft soil foundationwith the electroosmosis-vacuum preloading method.

(2) Reasonable circuit and supply power design is thekey to electroosmosis treatment engineering. (einfluence of interface resistance and the sand in-terlayer should be considered to accurately calculatethe site resistance. (e proposed calculation methodcan be used to reasonably calculate the wire sectionalarea and the power of the power supply.

(3) (e sealing effect of the site should be guaranteed forsoft soil foundation with sand interlayers. A self-setting mortar wall is recommended for vacuumsealing. (e mixing ratio of the self-setting mortarobtained in this work can be used for soft soilfoundation with sand interlayers.

(4) A simplified finite simulation method for electro-osmosis consolidation is proposed. Under an equalseepage flow of the unit soil, the voltage can beconverted into the excess pore pressure and applied

to the drainage boundary. (e simulation methodcan be used to predict the settlement of a site byelectroosmosis-vacuum preloading.

Notation

PVD: Prefabricated vertical drainRs: Resistance of the soil between electrodesePVD: Electrical PVDkj: Interface resistivityAC,DC:

Alternating current and direct current

hi: Soil thickness of the layer i in the electrodetreatment range

P, U: Output power and voltageB: Anode spacing or cathode spacingI, I′: Total current and the current of each branch wireρs: Average resistivity of the soil between the anode

and the cathodeΣR′: Total resistance of the area controlled by each

branch wirel: Distance between the anode and the cathodeRa: Apparent resistance of a pair of electrodeske: Electroosmosis coefficientRw: Resistance generated at the wire and the wire

connectionkh: Horizontal osmotic coefficientRe: Resistance of the material of the drainage electrodeϕ: Electrical potential at the cathodeRi: Interface resistance between the electrode and the

surrounding soilu: Excess pore pressure at the cathode.

Data Availability

(e data used to support the findings of this study areavailable from the corresponding author upon request.

Conflicts of Interest

(e authors declare no conflicts of interest.

U, U2

–6.867e – 01

–6.289e – 01

–5.710e – 01

–5.131e – 01

–4.553e – 01

–3.974e – 01

–3.395e – 01

–2.817e – 01

–2.238e – 01

–1.659e – 01

–1.080e – 01

–5.017e – 02

+7.696e – 03

Figure 7: Settlement contour by finite element simulation.

8 Advances in Civil Engineering

Acknowledgments

(is work was financially supported by the Zhejiang Pro-vincial Natural Science Foundation of China (Grant no.LGF20E080007), National Natural Science Foundation ofChina (Grant nos. 51508507 and 51808493), and ScientificResearch Project of Zhejiang Provincial CommunicationsDepartment (Grant no. 2017004).

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