AnExperimentalInvestigationonDynamicCharacteristicsofSoft...

Research ArticleAnExperimental Investigation onDynamic Characteristics of SoftSoils Treated by Vibration-Drainage Method

Jie Yin , Yong Tang, Yong-hong Miao, and Ruo-yu Sheng

Department of Civil Engineering, Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China

Correspondence should be addressed to Jie Yin; [email protected]

Received 23 June 2020; Revised 9 August 2020; Accepted 14 August 2020; Published 29 August 2020

Academic Editor: Qiang Tang

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

(is paper presents an experimental investigation on the dynamic characteristics of soft soils that are treated by vibration-drainage method (VDM).(e representative dynamic axial strain at a given number of cycles was obtained.(e VDM-treated softsoil exhibited different dynamic deformation characteristics that are not only affected by the cyclic frequency but also influencedby the vibration frequency during the treatment process. Soil specimens at different cyclic frequencies show a similar variationtrend that the axial strain systematically grows with increasing number of cycles. (e rate of axial strain for all specimenssystematically linearly decreases with the increase of number of cycles in the log-log scale. Results showed that both axial strainand strain rate exhibit relatively lower values at a given number of cycles under the condition that the applied cyclic frequency isequal to vibration frequency. It is expected that the soil structure will be more stable if the applied cyclic frequency is close to thevibration frequency that is applied on VDM-treated soil. (erefore, the vibration frequency close to the possible dynamic loadingfrequency is recommended in the process of soft soil improvement via VDM in the related engineering applications.

1. Introduction

It has been well documented that the naturally deposited softsoil usually exhibits poor engineering properties such aspoor permeability, high compressibility, and low strength[1, 2]. (erefore, the infrastructures that are built upon softsoil foundations will result in some unfavorable problems ifthe soft soil is not treated well [3]. To solve these problems,some common methods dealing with soft soils have beendeveloped such as replacement method, compactiongrouting, deep soil mixing, vacuum preloading, micro- orminipiles, dynamic compaction, and dynamic-static drain-age consolidation [4–17].

Among these methods, the dynamic-static drainageconsolidation is a newly developed soil improvementtechnique widely used in China, which combines the tra-ditional dynamic compaction with the static consolidationmethod. (e limitations of both individual methods can beovercome, where the dynamic compaction is inapplicable tosoft clay and a long time is spent on the water drainageduring the static consolidation process. It should be noted

that the traditional dynamic compaction usually uses animpact load with hammer tamping that results in someunfavorable issues with soft soils such as excessive lateraldeformation, extrusion failure, and rubber soil [18–21]. Animproved method has been provided to address the aboveissues by applying a vibration load to replace the impact load[22, 23]. Additionally, a vertical drainage system was set toaccelerate the water drainage under the vibration load,named as the vibration-drainage method (VDM). (ismethod was inspired by the principle of vibration oil re-covery [24–26], which can accelerate solid and liquid sep-aration. Previous works have shown that the VDM-treatedsoils exhibit favorable mechanical properties which can beused in various engineering applications such as highwayengineering and costal engineering [27].

It should be noted that those treated soft soil foundationsmight still be subject to the effects of some dynamic loadssuch as highway traffic load, tidal water-level changes, andshore wave action. For further evaluating the dynamiccharacteristics of soft soils if treated by VDM, a series oflaboratory tests were conducted on VDM-treated soft soil

HindawiAdvances in Civil EngineeringVolume 2020, Article ID 8890562, 12 pageshttps://doi.org/10.1155/2020/8890562

mailto:[email protected]://orcid.org/0000-0001-9921-708Xhttps://creativecommons.org/licenses/by/4.0/https://doi.org/10.1155/2020/8890562

specimens considering the effect of the frequency applied onthe soft soil specimens prepared in and after the VDMtreatment process. Recommendations have been suggestedin the geotechnical applications on soft soils treated by thevibration-drainage method.

2. Materials and Methods

2.1. Materials. Soft soil samples used in this study wereacquired from an engineering site in Lianyungang city ofChina.(e in situ water content of the soil sample was 45.2%as per ASTM D2216 [28]. (e plastic limit (PL) and liquidlimit (LL) were 21 and 43 according to ASTM D4318 [29],respectively. (e corresponding plasticity index (PI� LL-PL) is 22.(e specific gravity (Gs) of the soil sample was 2.68measured following ASTM D854 [30]. According to theUnified Soil Classification System [31], the sample belongs tolean clay (CL).

2.2. Methods. A portable mechanical mixer was used toblend the soil sample obtained from the field by adding waterwith a target water content of approximately 64.5% (about1.5 times the liquid limit). After blending, the slurry-likemixture was poured into a cylindrical specimen mold (innerdiameter D� 61.8mm and height H� 130mm) to preparethe untreated soil specimen. Four geotextile filter strips (withlength� 15 cm and width� 1.5 cm) were evenly distributedalong the inner wall of the specimen mold as the verticaldrainage system.

A vibration loading system (Figure 1) developed in theprevious study [23] was used herein to prepare the VDM-treated soil specimen. Each untreated soil specimen wasisotropically consolidated under 100 kPa for 24 h, reflectingthe influence of surrounding pressure on the soil. Because ofthe low strength of the test soft soil, the direct application oflarge load or vibration load easily causes the failure of thetest. A target vertical static load of 0.2 kN was applied in-crementally three times onto the soil specimen (i.e., 0.067 kNfor each load increment). A sinusoidal harmonic vibrationloading was thereafter applied onto the soil specimen withdifferent vibration frequencies (fv) from 0Hz to 5Hz (i.e.,0Hz, 1Hz, 2Hz, and 5Hz). (e total loading process lastedfor 400min for each specimen under drained condition.After the static and dynamic loading process, specimenswere taken out of the chamber in Figure 1. Each specimenwas then carefully trimmed to prepare the VDM-treatedspecimen with a cylindrical size of D� 39.1mm andH� 80mm. (e VDM-treated specimens were used for thefollowing undrained dynamic triaxial loading tests in theDSZ-2 dynamic triaxial instrument, as shown in Figure 2.

Table 1 shows the detailed testing program for the un-treated and VDM-treated soil specimens. For untreated soilspecimens, the confining pressure (σ3′) applied to thespecimen is 100 kPa. (e static load of 0.2 kN was appliedincrementally onto the soil with three loading increments. Asinusoidal harmonic vibration load of 0.05 kN was thereafterapplied onto the soil specimen with different frequencies asmentioned above (i.e., 0Hz, 1Hz, 2Hz, and 5Hz). For the

VDM-treated soil specimen, the confining pressure (σ′3) wasset as 100 kPa and the dynamic stress of 40 kPa was appliedwith cyclic frequencies (fc) of 1Hz, 2Hz, and 5Hz, which areconsistent with the vibration frequencies.

3. Results

3.1. Vibration Drainage Behavior of Untreated Soils. Foruntreated soil specimens, the vibration load was applied withvarious values of frequency from 0Hz to 5Hz. Figures 3 and4 show the results obtained from vibration drainage tests.Figure 3 shows the variation of cumulative drainage volumewith time for specimens under different vibration fre-quencies. It can be seen that the vibration frequency (fv) has asignificant effect on the cumulative drainage volume duringthe treatment process. Cumulative drainage volume in-creases significantly at a relatively earlier time for allspecimens and tends to be stable when the time continues toincrease. Results show that the specimen under vibrationload exhibits higher drainage volume than that under staticload at a given time. (e possible reason is that cyclic shearstresses will result in the generation of excess pore pressuresdue to the low permeability of soft soils [32]. Besides, thespecimen at fv � 1Hz shows the largest cumulative drainagevolume compared with that at fv � 2 and 5Hz.(is is because

Displacement sensor

Control panelLoading piston

Pressure chamber

Air pump

Figure 1: Photograph of the cyclic loading system.

Electrical control system

Pressure controller

Pressure chamber

Drainage tubeLoading piston

Specimen

Figure 2: Photograph of the DSZ-2 dynamic triaxial instrument.

2 Advances in Civil Engineering

the applied vibration loads at fv � 1Hz are close to the soil’snatural frequency. (e resonant effect will drive the soilspecimen to oscillate with greater amplitude and enablemore water to drain out from the soil specimen [23]. Figure 4shows the total cumulative drainage volume with vibrationfrequency. It also shows the vibration frequency-dependentcharacteristics, and a maximum value of the volume of11.6mL can be observed when fv � 1Hz.

Figures 5 and 6 show the results of axial strain obtainedfrom vibration drainage tests. Figure 5 shows the variation ofaxial strain with time, and the trends are similar to that ofcumulative drainage volume with time, as shown in Figure 3.It can be observed that the axial strain grows remarkably at arelatively shorter time and tends to be stable as the timecontinues to increase. (e axial strain-time curves forspecimens under vibration load all lie above that for spec-imens under static load, which is consistent with the vari-ation of cumulative drainage volume with time. Specifically,the specimen under 1Hz shows the highest axial strain at acertain time, which is comparable with the largest cumu-lative drainage volume at fv � 1Hz, as shown in Figure 3. It isexpected that under the same confining pressure, the largerthe drainage volume is, the bigger the axial strain is. Figure 6shows the variation of total final axial strain with vibrationfrequency, and it can be observed that the final axial strainshows the maximum value of 6.8% when fv � 1Hz.

3.2. Results of Dynamic Triaxial Test. To further investigatethe dynamic characteristics of VDM-treated soils at differentvibration frequencies (fv), the dynamic triaxial tests underundrained conditions at different cyclic frequencies (fc) of1Hz, 2Hz, and 5Hz were conducted on VDM-treated soilspecimens. Following the testing program listed in Table 1,the axial strain as a function of the number of cycles can beobtained for VDM-treated specimens. For example, Figure 7shows the two sets of raw data of εa-N for VDM-treated soilspecimens at fc � 1Hz and fv � 0 and 1Hz in dynamic triaxialtests. Since some parts of the row data overlapped, they canbe simplified using some representative data points, asshown in Figure 8. (e εa-N curve in each cycle can beprocessed through the following equation to yield a value ofεaN:

εaN �εmaxN + εminN

2, (1)

Table 1: Testing program.

Untreated soil specimen (D� 61.8mm, H� 130mm) VDM-treated soil specimen (D� 39.1mm,H� 80mm)No. oftestsConfining

pressure, σ3′ (kPa)Value of staticload (kN)

Value ofvibration load

(kN)

Vibrationfrequency, fv (Hz)

Confiningpressure, σ3′ (kPa)

Dynamicstress (kPa)

Cyclicfrequency, fc

(Hz)

100 0.2 — 0 100 40 1, 2, 5 3100 0.2 0.05 1 100 40 1, 2, 5 3100 0.2 0.05 2 100 40 1, 2, 5 3100 0.2 0.05 5 100 40 1, 2, 5 3

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

0 40 80 120 160 200 240 280 320 360

Cum

ulat

ive d

rain

age v

olum

e, v

(mL)

Time, t (min)

σ′3 = 100kPa, fv = 5Hzσ′3 = 100kPa, fv = 2Hzσ′3 = 100kPa, fv = 1Hzσ′3 = 100kPa, fv = 0Hz

Figure 3: Variation of cumulative drainage volume with time.

8.0

9.0

10.0

11.0

12.0

0 1 2 3 4 5

Fina

l dra

inag

e vol

ume,

v (m

L)

Vibration frequency, fv (Hz)

Figure 4: Variation of final drainage volume with vibrationfrequency.

Advances in Civil Engineering 3

where εaN is the axial strain at the Nth cycle and εmaxN and

εminN are the maximum and minimum of axial strains at thecycles of N. By connecting the data point with respect to thevalue of εaN andN, a simplified representative red line can beobtained as shown in Figure 8. Similar simplificationmethods have also been reported in the existing literature[3, 33, 34].

3.2.1. Effect of Cyclic Frequency. In order to evaluate theeffect of cyclic frequency fc on dynamic deformation be-havior of VDM-treated soft soil, Figure 9 shows the variationof axial strain εa with the number of cycles N for soilspecimens at various fc (i.e., 1Hz, 2Hz, and 5Hz) at a givenfv. Figure 9(a) shows the scenario of fv � 0 as a reference

reflecting the soil specimens treated by static load comparedwith fv � 1Hz, 2Hz, and 5Hz in Figures 9(b)–9(d),respectively.

It can be seen in Figure 9(a) that soil specimens underdifferent fc show a similar variation trend in terms of εa andN, i.e., εa increases with increasing N. (e εa-N curve athigher fc lies below that at lower fc, indicating that fc has asignificant effect on εa for specimens treated under staticload (fv � 0). (is is because when the dynamic load (40 kPain this study) is less than the “safe load” (under which thestrain of soil specimen increases very slowly), the soilstructure will be more stable under the higher frequencydynamic load [34–36].

Figures 9(b) to 9(d) show the results of εa-N curves atvarious fc for VDM-treated soil specimens at different vi-bration frequencies. A similar increasing trend of εa with Ncan be seen compared with the static load results inFigure 9(a). In general, εa-N curve at higher fc lies below that

0 40 80 120 160 200 240 280 320 360Time, t (min)

σ′3 = 100kPa, fv = 5Hzσ′3 = 100kPa, fv = 2Hzσ′3 = 100kPa, fv = 1Hzσ′3 = 100kPa, fv = 0Hz

0.0

2.0

4.0

6.0

8.0A

xial

stra

in (%

)

Figure 5: Variation of axial strain with time.

0 1 2 3 4 5Vibration frequency, fv (Hz)

4.0

5.0

6.0

7.0

8.0

Fina

l axi

al st

rain

(%)

Figure 6: Variation of final axial strain with vibration frequency.

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00 2000 4000

Number of cycles, N

Axi

al st

rain

, εa (

%)

6000 8000 1000

fv = 0Hzfv = 1Hz

Figure 7: Variation of axial strain with the number of cycles forVDM-treated soil specimens at fc � 1Hz.

Axi

al st

rain

, εa (

%)

Number of cycles, N

Figure 8: (e simplified treatment schematic.


at lower fc except for a case.(e difference is that when fv � fc,the εa-N curve is lying on the bottom indicating the soilstructure is more stable. It means that the vibration fre-quency fv during the VDM-treated process can affect thedeformation behavior of VDM-treated soil at different fc.

For further investigating the effect of fc on axial strainrate _εa, test data in Figure 9 were used to determine _εa at agiven number of cyclesN for VDM-treated soil specimens atvarious fc (i.e., 1Hz, 2Hz, and 5Hz), and the results areshown in Figure 10. Figure 10(a) depicts the variation of_εawith N for specimens treated under static load (fv � 0). It

can be seen that _εa-N curves for specimens treated at dif-ferent fc show a consistent linearly decreasing trend in thelog-log scale. Moreover, the _εa-N curve of the specimen athigher fc lies above that of the specimen at lower fc. (ereason is that the specimen at a higher fc will take less time toreach the same cycles. It can be seen in Figure 11 that axialstrain at a higher fc takes less time to increase, resulting in ahigher value of _εa.

In contrast, Figures 10(b) to 10(d) show the axial strainrate _εa as a function of the number of cycles N for specimenstreated at the vibration loading frequency fv � 1Hz, 2Hz,

0.0

0.5

1.0

0 2000 4000 6000 8000 10000

Axi

al st

rain

, εa (

%)

Number of cycles, N

fc = 1Hzfc = 2Hzfc = 5Hz

(a)

Axi

al st

rain

, εa (

%)

Number of cycles, N


0.0

0.5

1.0

0 2000 4000 6000 8000 10000

(b)

Axi

al st

rain

, εa (

%)


0 2000 4000 6000 8000 10000Number of cycles, N

0.0

0.5

1.0

(c)

Axi

al st

rain

, εa (

%)


Number of cycles, N0 2000 4000 6000 8000 10000

0.0

0.5

1.0

(d)

Figure 9: Variation of εa with N on VDM-treated specimens at fv of (a) 0Hz, (b) 1Hz, (c) 2Hz, and (d) 5Hz.


and 5Hz, respectively. A similar variation trend of _εa with Ncan be observed as _εa linearly decreases with increasing Ncompared with the results in Figure 10(a). (e same featurecan also be observed in Figure 10(d) that, at a given fv, thehigher the fc, the greater the value of _εa at a certain N exceptfor fc � 5Hz. It can be found that the _εa-N curve for thespecimen at fc � 5Hz lies below the curve for the specimen atfc � 2Hz. According to Figure 11(d), the significantly loweraxial strain at fc � 5Hz caused the phenomenon. (is ispossibly caused by the fact that the soil structure had

undergone the vibration loading treatment at fv � 5Hz, sothat the soil structure can maintain a relatively stable stateunder this frequency of vibration. When the dynamic cyclicloading frequency fc is equal to fv, the specimen would bemore difficult to deform. Moreover, it can be found that thevalue of ε̇a is different at the same N and fc but different fv.(is indicates that the effect of fv cannot be ignored, whichwill be further discussed in the next section.

In order to further evaluate the effect of fc on the axialstrain εa and axial strain rate ε̇a, the values of εa and ε̇a at

Axi

al st

rain

rate

, ε̇a (

%/m

in)


0.001

0.01

0.1

1

10

1 10 100 1000 10000Number of cycles, N

(a)

Axi

al st

rain

rate

, ε̇a (

%/m

in)


Number of cycles, N

0.001

0.01

0.1

1

1 10 100 1000 10000

(b)

Axi

al st

rain

rate

, ε̇a (

%/m

in)



0.001

0.01

0.1

1

(c)

Axi

al st

rain

rate

, ε̇a (

%/m

in)


Number of cycles, N1 10 100 1000 10000

0.001

0.01

0.1

1

(d)

Figure 10: Variation of _εa with N at fv of (a) 0Hz, (b) 1Hz, (c) 2Hz, and (d) 5Hz.


N� 10,000 obtained from Figures (9) and (10) were re-plotted as a function of cyclic frequency fc in Figures 12(a)and 12(b), respectively. It can be seen from Figure 12(a) thatthe value of εa at N� 10,000 almost decreases with the in-crease of fc except for a little increase in εa from fc � 1 to 2Hzat fv � 1Hz and from fc � 2 to 5Hz at fv � 2Hz. Specifically, ata given fv, a minimum value of εa can be found when theapplied fc is equal to fv for specimens treated by vibrationloading. In detail, a minimum value of εa � 0.48% whenfc � fv � 1Hz, a minimum value of εa � 0.37% when

fc � fv � 2Hz, and a minimum value of εa � 0.29% whenfc � fv � 5Hz were observed. (ese phenomena further in-dicated that the soil structure of VDM-treated soil speci-mens is more stable when fc � fv. Figure 12(b) depicts thevariation of _εa at N� 10,000 with fc at different values of fv. Itcan be seen that the value of _εa at N� 10,000 significantlyincreases with increasing fc for specimens at a given fv exceptfor a little increase in εa from fc � 1 to 2Hz at fv � 2Hz andfrom fc � 2 to 5Hz at fv � 5Hz. A similar phenomenon can befound in Figure 12(b) that a minimum value of _εa at

Axi

al st

rain

, εa (

%)


0.0

0.5

1.0

0 60 120 180Time, t (min)

(a)

Axi

al st

rain

, εa (

%)


Time, t (min)

0.0

0.5

1.0

0 60 120 180

(b)

Axi

al st

rain

, εa (

%)


0 60 120 180Time, t (min)

0.0

0.5

1.0

(c)

Axi

al st

rain

, εa (

%)


Time, t (min)0 60 120 180

0.0

0.5

1.0

(d)

Figure 11: Variation of εa with t on VDM-treated specimens at fv of (a) 0Hz, (b) 1Hz, (c) 2Hz, and (d) 5Hz.


0.0

0.5

1.0

1 2 3 4 5Cyclic frequency, fc (Hz)

fv = 0Hzfv = 1Hz

fv = 2Hzfv = 5Hz

Axi

al st

rain

, εa,

at 1

0000

th cy

cle (%

)

(a)

Cyclic frequency, fc (Hz)

fv = 0Hzfv = 1Hz

fv = 2Hzfv = 5Hz

0.0

0.0

0.0

0.0

0.0

1 2 3 4 5

Axi

al st

rain

rate

, εa,

at 1

0000

th cy

cle (%

/min

)(b)

Figure 12: Variation of (a) εa and (b) _εa with fc at 10,000th cycle.

Number of cycles, N

fv = 1Hzfv = 2Hzfv = 5Hz

0.0

0.5

1.0

0 2000 4000 6000 8000 10000

Axi

al st

rain

, εa (

%)

(a)

Number of cycles, N


0.0

0.5

1.0

0 2000 4000 6000 8000 10000

Axi

al st

rain

, εa (

%)

(b)

Figure 13: Continued.



Number of cycles, N0 2000 4000 6000 8000 10000

0.0

0.5

1.0

Axi

al st

rain

, εa (

%)

(c)

Figure 13: Variation of εa with N at fc of (a) 1Hz, (b) 2Hz, and (c) 5Hz.

0.001

0.01

0.1

1



Axi

al st

rain

rate

, ε̇a (

%/m

in)

(a)

Number of cycles, N


0.001

0.01

0.1

1

1 10 100 1000 10000

Axi

al st

rain

rate

, ε̇a (

%/m

in)

(b)

Figure 14: Continued.


N� 10,000 is obtained at a given fc when fc � fv. In detail, i.e.,a minimum value of _εa � 0.0029%/min at fc � fv � 1Hzcompared with fc � 1Hz and fv � 0Hz, 2Hz, and 5Hz, aminimum value of _εa� 0.0044%/min at fc � fv � 2Hz, and aminimum value of _εa � 0.0086%/min at fc � fv � 5Hz wereobserved. (is also demonstrates that the soil structure forVDM-treated soil specimens is more stable when fc � fv.

3.2.2. Effect of Vibration Frequency. (e above analysisindicated that VDM-treated soft soil exhibited differentdynamic deformation characteristics not only affected by thecyclic frequency fc but also influenced by the vibrationfrequency during the treatment process of VDM. For in-vestigating the effect of fv on dynamic deformation behaviorof VDM-treated soft soil, Figure 13 depicts the variation ofaxial strain εa with the number of cyclesN for soil specimensat various fv (i.e., 1Hz, 2Hz, and 5Hz) at a certain fc. It canbe observed in Figure 13 that εa consistently grows with theincrease of N for specimens treated with different values offv. A significant increase in εa can be seen at a relatively lowermagnitude of N (about 3000) and followed by a stable trendas N continues increasing. At a given N, the higher the valueof fv is, the higher the value of εa is, as shown in Figure 13(a).However, Figures 13(b) and 13(c) show different results. Itcan be found that the εa-N curve at fv � 2Hz lies at thebottom in Figure 13(b) yet the εa-N curve at fv � 5Hz lies atthe bottom in Figure 13(c). (e reason why the εa-N curve atdifferent values of fv did not follow the same trend is mainlydue to the differences in the applied fc. A similar result is thatthe εa-N curve always lies at the bottom when fv � fc. (is

result also demonstrates that the soil structure for VDM-treated soil specimens is more stable when fv � fc.

Figure 14 shows the variation of axial strain rate ε ȧ withthe number of cycles N at different values of fv in the log-logscale. It can be found that ε̇a for all specimens systematicallylinearly decreases with the increase of N. Specifically, the ε̇a-N curve for specimens with applied fv equal to fc lies at thebottom resulting from the same reason as mentioned above.(erefore, it is expected that the soil structure will be morestable if the applied cyclic frequency is close to the vibrationfrequency using VDM treatment.

4. Conclusions

In this study, a series of laboratory tests were performed onVDM-treated soft soil specimens to investigate the dynamiccharacteristics of treated soils. Effects of the vibration fre-quency fv applied in the treatment process and the cyclicfrequency fc applied on the treated soil specimens wereevaluated, and the main conclusions are summarized below:

(1) Vibration frequency (fv) has a significant effect onthe cumulative drainage volume during the treat-ment process. Cumulative drainage volume increasessignificantly at a relatively earlier time for all spec-imens and tends to be stable when the time continuesto increase. (e specimen at fv � 1Hz shows thelargest cumulative drainage volume.

(2) Soil specimens at different values of cyclic frequency(fc) show a similar variation trend that the axial strainεa grows with increasing number of cycles. A



0.001

0.01

0.1

1

Axi

al st

rain

rate

, ε̇a (

%/m

in)

(c)

Figure 14: Variation of εȧ with N at fc of (a) 1Hz, (b) 2Hz, and (c) 5Hz.


significant increase in εawas seen at a relatively lowerN of about 3000 followed by a stable trend as Ncontinues to increase. (e axial strain rate (_εa) for allspecimens systematically linearly decreases with theincrease of N in the log-log scale.

(3) (e influence of vibration frequency fv cannot beignored in the discussion of dynamic behavior ofVDM-treated soil under cyclic load. At a givennumber of cycles N, both εa and _εa show relativelylower values under the condition that the applied fc isequal to fv. It is expected that the soil structure will beless likely to settle and deform if the applied fc is closeto fv.

Results from this study are based on Lianyungang softsoil from one source in China. However, a general trend isexpected to be similar if specimens of soft soils from differentsources are adopted. (e VDM-treated soft soil exhibiteddifferent dynamic deformation characteristics not only af-fected by the cyclic frequency fc but also influenced by thevibration frequency fv during the treatment process. Resultsshowed that soil structure will be more stable if the cyclicfrequency of dynamic loads possibly applied to the foun-dation soil is equal to the vibration frequency used to treatthe soft soil using the vibration-drainage method (VDM).(erefore, the vibration frequency should be carefully se-lected during the treatment process considering the possiblevalue of cyclic frequency of dynamic load that may be en-countered during the operation period. Vibration frequencyclose to the possible dynamic loading frequency is recom-mended in the process of soft soil improvement via VDM inrelated engineering applications.

Data Availability

Data are available from the corresponding author uponrequest.

Disclosure

(e opinions, findings, conclusions, or recommendationsexpressed herein are those of the authors and do not nec-essarily represent the views of the sponsors.

Conflicts of Interest

(e authors declare that they have no conflicts of interest.

Acknowledgments

(e authors gratefully acknowledge the financial supportfrom the National Natural Science Foundation of China(Grant no. 51978315).

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