applied sciences

Article The Seepage and Soil Plug Formation in Suction Caissons in Sand Using Visual Tests

Liquan Xie , Shili Ma * and Tiantian Lin College of , Tongji University, Shanghai 200092, China; [email protected] (L.X.); [email protected] (T.L.) * Correspondence: [email protected]; Tel.: +86-191-2176-3067

 Received: 4 December 2019; Accepted: 8 January 2020; Published: 13 January 2020 

Abstract: The rapid development of offshore wind energy in China is becoming increasingly relevant for movement toward green development. This paper presents the results of visual tests of a suction caisson used as for offshore wind turbines. The distribution of hydraulic gradients of sand at the mudline in the caisson was obtained to find out the relationship with the heights of soil plugs. The relationship equation was proposed and obtained by using quadratic regression, guiding project designs, and construction. It was found that there was no soil plug in the caisson when small suction was applied during the suction penetration. The relationship between the heights of the soil plugs and the hydraulic gradient of the soil was proposed and obtained by using quadratic regression to predict (roughly) the height of soil plugs in suction caissons in sand during suction penetration. The influence of settlement outside caissons on the soil plug was found to decrease as the buried depth rose.

Keywords: suction caisson; suction penetration; soil plug; hydraulic gradient; visual tests

1. Introduction In the past few decades, it has become increasingly important to rapidly develop the offshore wind industry, which provides practical sources of energy with a low carbon footprint [1,2]. Foundations play an important role in guaranteeing the safe operation of offshore wind turbines [3]. The suction caisson, being installed economically and efficiently into soil deposits, has been increasingly used as a competitive foundation for offshore wind turbines in deep water [4,5]. A suction caisson is a large cylindrical structure that is typically made of steel, open at the bottom and closed at the top [6]. To set up a perfect offshore wind turbine, two aspects need to be considered for the engineering design of this foundation: suction installation and in-service performance [7]. The capacity of suction caissons as the foundation for offshore wind turbines is enhanced by means of peripheral embedded thin walls, which confine the internal soil [8]. A caisson is installed by penetrating the under its own weight, and then by pumping water out of the caisson to create suction that forces the foundation into the seabed [9]. During suction penetration, the induced seepage flow through highly permeable sand into the caisson interior can create some negative effects. To investigate these effects, a number of studies have been completed, and they show that the seepage facilitates the installation process at the caisson tip and along the inner wall [10–13]. Erbrich and Tjelta [14] presented a series of finite element analyses and found that the suction forced water to migrate through the soil from outside to the inner caisson. Previous research [15,16] still has certain issues, in that the seepage around the suction was assumed to follow Darcy’s law, which requires that we carry on further discussion. Experimental investigations in sand have revealed that soil plugs are likely to occur during suction-assisted installation [15,17,18]. A series of centrifuge tests on the installation of suction caissons were carried out by Tran et al. [19,20],

Appl. Sci. 2020, 10, 566; doi:10.3390/app10020566 www.mdpi.com/journal/applsci Appl.Appl. Sci. Sci. 20202020, 10, 10, x, 566FOR PEER REVIEW 2 2of of 12 11 by Tran et al. [20,21], who found that the soil plugs heave up to 20% of the caisson penetration as who found that the soil plugs heave up to 20% of the caisson penetration as excessive suction, and they excessive suction, and they developed a void ratio–permeability relationship to check the sand heave developed a void ratio–permeability relationship to check the sand heave against the plugs. There is against the plugs. There is no previous study on the relationship between soil plugs and the seepage no previous study on the relationship between soil plugs and the seepage velocity of sand around velocity of sand around suction caissons. suction caissons. This paper presents the results of visual tests of a suction caisson used as a foundation for This paper presents the results of visual tests of a suction caisson used as a foundation for offshore wind turbines. The process of suction installation of the caisson foundations with wind turbines. The process of suction installation of the caisson foundations with axisymmetric axisymmetric geometry is simplified to a plane problem. In order to study their composition, the geometry is simplified to a plane problem. In order to study their composition, the heights of the final heights of the final soil plugs in the caisson were measured. The distribution of the hydraulic gradient soil plugs in the caisson were measured. The distribution of the hydraulic gradient of sand at the of sand at the mudline in the caisson was obtained to find out its relationship with the heights of the mudline in the caisson was obtained to find out its relationship with the heights of the soil plugs. The soil plugs. The relationship between the heights of soil plugs and the hydraulic gradient of soil was relationship between the heights of soil plugs and the hydraulic gradient of soil was proposed and proposed and obtained by using quadratic regression, guiding project designs, and construction. obtained by using quadratic regression, guiding project designs, and construction. 2. Experimental Program 2. Experimental Program The process of suction installation of the caisson foundations (shown in Figure 1a) with The process of suction installation of the caisson foundations (shown in Figure1a) with axisymmetric geometry is simplified to a plane problem in this paper. Due to the fact that the soil axisymmetric geometry is simplified to a plane problem in this paper. Due to the fact that the was replaced by the walls of the soil tank in tests, it is assumed that the forces of water adhesion to soil was replaced by the walls of the soil tank in tests, it is assumed that the forces of water adhesion to the walls are equal to that of the sand around the suction caissons. A soil tank (shown in Figure 1), as the walls are equal to that of the sand around the suction caissons. A soil tank (shown in Figure1), used in tests, has dimensions of 20 × 0.5 cm in its plan view, and a depth of 28 cm. Transparent as used in tests, has dimensions of 20 0.5 cm in its plan view, and a depth of 28 cm. Transparent fiberglass was used to make the soil tank×, with a thickness of 1.0 cm. The two pumping outlets in the fiberglass was used to make the soil tank, with a thickness of 1.0 cm. The two pumping outlets in the soil tank were connected to the suction loading system by a thin pipe and a drainpipe, respectively. soil tank were connected to the suction loading system by a thin pipe and a drainpipe, respectively. Figure 1b shows the diagram of the test device, with a constant suction S in the caisson caused by the Figure1b shows the diagram of the test device, with a constant suction S in the caisson caused by the suction loading system creating the different head H. The value of the applied constant suction can suction loading system creating the different head H. The value of the applied constant suction can be 3 be expressed as S = γwH, where γw is the unit weight of water (10 kN/m3 ). expressed as S = γwH, where γw is the unit weight of water (10 kN/m ).

(a) Suction caisson. (b) Diagram of test devices.

FigureFigure 1. 1. TestTest devices devices..

TheThe suction suction caisson withwithan an external external diameter diameterD ofD 12of cm12 had cm a ha heightd a height of 17.5 of cm 17.5L and cm a L thickness and a thicknessT of 0.5 cm. T of In 0.5 order cm. toIn createorder anto enclosedcreate an compartmentenclosed compartment between the between soil tank, the the soil suction tank, the caisson, suction and caissonthe soil,, and UV the glue soil, was UV used glue to stickwas used the soil to tankstick andthe soil the suctiontank and caisson the suction together. caisson The suctiontogether. caisson The suctionmodel caisson was located model at wa a distances located 7.5 atcm a distance from the 7.5 bottom cm from of the the soil bottom tank. of the soil tank. TheThe siliceous siliceous sand sand shown shown in in Figure Figure 22 waswas used used in in tests tests because because it it is is commercially commercially available available and and showsshows aa deep deep contrast contrast with with the the carmine carmine stain stain.. The void ratioratio ee ofof thethe soilsoil waswas determined determined according according to tothe the standard standard soil soil testing testing methods, methods and, and can can be written be written as e =asρ ew =G ρs/wρGd-1,s/ρd where-1, whereρd is ρ thed is drythe densitydry density of the ofsand the andsandG sandis the Gs specificis the specific gravity gravity of the sand. of the Table sand.1 shows Table the 1 shows properties the ofproperties the siliceous of the sand siliceous in tests. sandThe siliceous in tests. sand The siliceousparticles had sand an particle averages radiushad an of average 0.748 mm, radius and theyof 0.748 obeyed mm uniform, and they distribution, obeyed uniform distribution, with a ratio of maximum to minimum radii of 2.0. The pluviation method and Appl. Sci. 2020, 10, 566 3 of 11 withAppl. Sci. a ratio 2020,of 10, maximum x FOR PEERto REVIEW minimum radii of 2.0. The pluviation method and the compaction method3 of 12 were used to prepare uniform sand specimens in layers in the soil tank. The permeability coefficient the compaction method were used to prepare uniform sand specimens in layers2 2 in the soil tank. The of the siliceous sand was obtained by using an empirical equation, k = 2d10 e [21], where d10 is the permeability coefficient of the siliceous sand was obtained by using an empirical equation, k = 2d102e2 effective size of the sand. Due to the uniform particle size of the sand, it is suggested that d10 is equal [22], where d10 is the effective size of the sand. Due to the uniform particle size of the sand, it is to the average particle size (0.718 mm). Before carrying out every test, the sand specimen was left to suggested that d10 is equal to the average particle size (0.718 mm). Before carrying out every test, the stand for 24 h. sand specimen was left to stand for 24 h.

Figure 2. The siliceous sand in tests.tests. Table 1. Properties of siliceous sand. Table 1. Properties of siliceous sand. Specific Void Saturated Permeability Angle of Internal Specific Void Saturated Permeability Cohesion Angle of Internal Property Gravity Ratio Weight Coefficient Cohesion Friction Property Gravity Ratio Weight 3 Coefficient c (kPa) Friction Gs e γsat (kN/m ) k (cm/s) c (kPa) ϕ (◦) Gs e γsat (kN/m3) k (cm/s) φ (°) Value 2.66 0.75 19.5 0.28 0 31 Value 2.66 0.75 19.5 0.28 0 31

The seepageseepage field field around the suction caisson model wa wass visualized by the tracer tracer titration titration system system,, which consisted of an infusion system and carmine stain. The infusion system waswas made of a medical syringe withwith aa thinthin pipe pipe (radius (radius of of 2 mm),2 mm shown), shown in Figurein Figure1b. Three1b. Three holes holes were were drilled drilled in the in soil the tank soil attank points at points A, B, A, and B, C,and connecting C, connecting to the to infusionthe infusion system system with with the the thin thin pipes. pipe Ats. At points points A, A, B, andB, and C, theC, the carmine carmine stain stain was was released released with with pinpoint pinpoint accuracy accuracy by by the the infusion infusion system. system. To To reduce reduce the the eff ecteffect of turbulence,of turbulence the, the carmine carmine stain stain was wa injecteds injected into into the the soil soil used used in testsin tests as slowlyas slow asly possible.as possible. The suction caisson model had a buried depth h (5, 10,10, and 15 cm) before each test,test, toto simulatesimulate the process ofof suctionsuction installation.installation. The The influence influence of of the temperature temperaturess of the environment and the water were not considered inin thethe tests. A video camera was used to collect images of the experimental phenomenaphenomena of seepage and the soil plug in the suctionsuction caisson. At the end of the trial,trial, the height of the soil plug did not seem to change. The testing program programss are listed in Table2 2 in in tests. tests. TheThe pre-testpre-test results show that seepage failure took place in the sand when the suction in thethe caissoncaisson with buried depthsdepths of 5, 10,10, and 15 cm were greatergreater thanthan 2.0,2.0, 3.5,3.5, andand 4.04.0 kPa,kPa, respectively.respectively.

Table 2. List of visual tests on suction caissons. Table 2. List of visual tests on suction caissons.

BuriedBuried Depth Depthh (cm) h (cm) SuctionSuctionS (kPa) S (kPa) 55 0.50.5 1.0 1.0 1.51.5 ------1010 0.50.5 1.0 1.0 1.51.5 2.02.0 2.52.5 3.03.0 - - 15 0.5 1.0 1.5 2.0 2.5 3.0 3.5 15 0.5 1.0 1.5 2.0 2.5 3.0 3.5

3. Test Results and Discussion

3.1. Visual Seepage Paths The seepage field can be visualized where the carmine stain flows along streamlines in the soil around the suction caisson. Figure 3 shows the visualization of the seepage flow at point B as h = 15 cm and S = 0.5 kPa. It was observed that the visual tests achieved good results to study the seepage Appl. Sci. 2020, 10, 566 4 of 11

3. Test Results and Discussion

3.1. Visual Seepage Paths The seepage field can be visualized where the carmine stain flows along streamlines in the soil around the suction caisson. Figure3 shows the visualization of the seepage flow at point B as h = 15 cm and S = 0.5 kPa. It was observed that the visual tests achieved good results to study the seepage of Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 12 sand around a suction caisson during suction penetration. It took 500 s for the carmine stain to move fromof point sand Baround to the a mudline, suction caisson and the during length suction of the penetration. seepage pathIt took was 500 3.21s for cm.the carmine Tests revealed stain to that the seepagemove from paths point of B soil to withthe mudline different, andS inthe suction length of caissons the seepage had path the samewas 3.21 motion cm. Tests path. revealed The results indicatedthat the that seepage the seepage paths pathof soil of with soil isdifferent unrelated S in to suction the S appliedcaissons inhad the the caisson same motion and is apath.ffected The by the penetrationresults indicate depth duringd that the the seepage installation path of ofthe soil foundation. is unrelated The to the seepage S applied paths in ofthe the caisson carmine and stainis in sandaffected are plotted by the with penetration a plane depth coordinate during system,the installation shown of inthe Figure foundation.4. It can The be seepage seen thatpaths there of the is an carmine stain in sand are plotted with a plane coordinate system, shown in Figure 4. It can be seen obvious trend: the streamline dyed by carmine stain moves toward the wall of the caisson model. that there is an obvious trend: the streamline dyed by carmine stain moves toward the wall of the Additionally, the larger the penetration depth, the more obvious was the streamline–adherent trend. caisson model. Additionally, the larger the penetration depth, the more obvious was the streamline– It wasadherent observed trend. that It the was seepage observed path that lengths the seepage were 1.95 path and lengths 1.34 h werewhen 1.95 the and penetration 1.34 h when depths the were equalpenetration to 5 and 15 depths cm, respectively.were equal to 5 The and distance 15 cm, respectively. between the The carmine distance stainbetween in the carmine mudline stain and the innerin wall the ofmudline the caisson and the model inner waswall 0.375of the timescaisson the model diameter was 0.375 of the times suction the diameter caisson, of for theh suction= 0.42, 0.83, and 1.25caissonL, respectively., for h = 0.42, 0.83, and 1.25 L, respectively.

(a) t1 = 0 s. (b) t2 = 100 s. (c) t3 = 200 s.

(d) t4 = 300 s. (e) t5 = 400 s. (f) t6 = 500 s.

FigureFigure 3. The 3. The visualization visualization of of seepage seepage flowflow at point B B with with h h= =1515 cm cm and and S = S0.5= kPa0.5. kPa. Appl. Sci. 2020, 10, 566 5 of 11 Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 12

(a) h = 5 cm. (b) h = 10 cm. (c) h = 15 cm.

FigureFigure 4. TheThe seepage seepage path path of of the the carmine carmine stain stain in in sand sand..

3.2.3.2. Hydraulic Hydraulic Gradient Gradient Analysis Analysis InIn this this paper paper,, the the test test results results prove prove that that Darcy’s Darcy’s law law is is not applicable applicable,, and th thisis phenomenon phenomenon was was alsoalso observed from from the large test pressure difference difference found in thethe literatureliterature [[23]22].. F Foror t thehe seepage velocity v,, it it was assumed that that the the streamlines streamlines around around the the caissons caissons were were stable stable and and not not affected affected by by eacheach other. other. The The path path lengths lengths of of the the carmine stain were measured from test images. All All results results are are presented in terms of dimensionless form forms.s. The The seepage seepage velocity velocity vv ofof the the sand sand was was assumed to to be affectedaffected by x/D and S/γ’hγ’h. The The hydraulic hydraulic gradient gradient v//k of the the sand sand in in tests tests at at the the mudline mudline was was proposed proposed byby using using the regression function function,, and can be expressed as follows:follows:

" #0.76 v 0.94DS 0.76 v = 0.163 0.94DS  (1) k 0.163  (0.5D x)γ h  , (1) k (0.5D −x）0 'h where x is the abscissa value in Figure1 and γ’ is the effective unit weight of soil. whereThe x is comparison the abscissa of value actual in valuesFigure and1 and calculated γ’ is the effective values is unit shown weight in Figure of soil.5. It can be seen that the fitted values agree with the actual values. Compared with v/k obtained from tests, the fitted valuesThe have comparison a residual of sum actual of squaresvalues and of about calculated 1.467. values is shown in Figure 5. It can be seen that the fitted values agree well with the actual values. Compared with v/k obtained from tests, the fitted values have a residual sum of squares of about 1.467. Appl. Sci. Sci. 20202020,, 1010,, x 566 FOR PEER REVIEW 66 of of 12 11 Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 12

1.4 Regression equation 1.4 1.2 Regression equation 1.2 1.0 1.0 0.8 0.8 0.6 Fitted values Fitted 0.6

Fitted values Fitted 0.4 0.4 0.2 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.0 0.2 0.4 Actual0.6 0.8values1.0 1.2 1.4 Actual values Figure 5. The comparison of actual values and fitted values for v/k. v k. FigureFigure 5. 5. TheThe comparison comparison of of actual actual values values and and fitted fitted values values for for v/k./ FFigureigure 66 showsshows thethe hydraulichydraulic gradientgradient of sand around a suction caisson with different di fferent x/Dx/D when Figure 6 shows the hydraulic gradient of sand around a suction caisson with different x/D when thethe suction in in the caisson is equal to 1.5 kPa. It It can be seen that the hydraulic gradient v/k increases the suction in the caisson is equal to 1.5 kPa. It can be seen that the hydraulic gradient v/k increases with the increas increasee of x/D. The results indicated that the seepage velocity velocity is is larger larger as as the streamline with the increase of x/D. The results indicated that the seepage velocity is larger as the streamline moves toward toward the the wall wall of of the the suction suction caissons. caissons. The The hydraulic hydraulic gradient gradient v/k,v with/k, with x/Dx =/D 0.2675= 0.2675 and andh/D moves toward the wall of the suction caissons. The hydraulic gradient v/k, with x/D = 0.2675 and h/D =h /1.25D =, 1.25,is shown is shown in Figure in Figure 7. It 7can. It be can ob beserved observed that thatthe v/k the increasesv/k increases with withthe increase the increase of S/γ’h of S and/γ’h = 1.25, is shown in Figure 7. It can be observed that the v/k increases with the increase of S/γ’h and theand fitted the fitted values values of the of thev/k vagree/k agree well well with with the the test test results. results. The The v/kv/ kwhenwhen SS/γ’h/γ’h == 2.4512.451 is is 5.85 5.85 times times the fitted values of the v/k agree well with the test results. The v/k when S/γ’h = 2.451 is 5.85 times greater than when S/γ’hγ’h = 0.3510.351 in in tests. tests. The The minimum minimum relative relative error error is is 5.05% 5.05% for for Eq Equationuation (1) when greater than when S/γ’h = 0.351 in tests. The minimum relative error is 5.05% for Equation (1) when S/γγ’h’h = 5.478. When h//DD == 0.42,0.42, thethe streamlinestreamline around around the the suction suction becomes becomes disordered disordered as aas result a result of the of S/γ’h = 5.478. When h/D = 0.42, the streamline around the suction becomes disordered as a result of thelarger larger applied applied suction suction (S =(S1.5 = 1.5 kPa). kPa). Due Due to to the the assumption assumption that that thethe streamlinesstreamlines areare stable and not the larger applied suction (S = 1.5 kPa). Due to the assumption that the streamlines are stable and not affectedaffected by each other, the seepage velocity obtained is smaller than the actual situation situation,, leading to affected by each other, the seepage velocity obtained is smaller than the actual situation, leading to largelarge deviation deviationss as compared with EquationEquation (1). large deviations as compared with Equation (1). 1.3 1.3 h/D=0.42 1.2 h/DFitting=0.42 function (h/D = 0.42) 1.2 h/D=0.83 1.1 Fitting function (h/D = 0.42) h/DFitting=0.83 function (h/D = 0.83) 1.1 1.0 Fittingh/D=1.25 function (h/D = 0.83) 1.0 h/DFitting=1.25 function (h/D = 1.25) 0.9 Fitting function (h/D = 1.25) 0.9

k / 0.8

v

k / 0.8 v 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.30.10 0.15 0.20 0.25 0.30 0.10 0.15 0.20 0.25 0.30 x/D x/D Figure 6. The hydraulic gradient with S = 1.5kPa. Figure 6. The hydraulic gradient with S = 1.5 kPa. Figure 6. The hydraulic gradient with S = 1.5 kPa. Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 12 Appl. Sci. 2020, 10, 566 7 of 11 Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 12 1.1 1.11.0 x/D=0.2675 Fitting function 1.00.9 x/D=0.2675 Fitting function 0.90.8 0.80.7

k / 0.70.6

v

k / 0.6

v 0.5 0.50.4 0.40.3 0.30.2 0.20.1 0.0 0.5 1.0 1.5 2.0 2.5 0.1 0.0 0.5 1.0 1.5 2.0 2.5 S/'h S/'h Figure 7. The hydraulic gradient with x/D = 0.2675 and h/D = 1.25. Figure 7. The hydraulic gradient with x/D = 0.2675 and h/D = 1.25. Figure 7. The hydraulic gradient with x/D = 0.2675 and h/D = 1.25. 3.3. Soil Plug and Settlement Formation 3.3. Soil Plug and Settlement Formation During suction penetration, a part of the soil in thethe caissonscaissons getsgets intointo thethe open-endedopen-ended hollow caissonDuring cavity, suction formingforming penetration, aa soilsoil plugplug a [ [24]23part].. TheTheof the finalfinal soil soilsoil in plugsplugsthe caissons inin the caisson gets into at thethethe buriedopen-ended depth hollow of 5 cm caisson(caused(caused cavity, byby thethe forming caisson)caisson) a are soil shownshown plug [24] in FigureFigure. The final8 8.. TheThe soil testtest plugs resultsresults in the showshow caisson thatthat at therethere the buried isis nono soilsoil depth plug plug of in in5 the cmthe (caissonscaused by withwith the small smallcaisson suctionsuction) are appliedshown applied in during during Figure suction suction8. The penetration. testpenetration. results show The The maximum thatmaximum there heights is heights no soil of of soilplug soil plugs inplug the ins caissonsthein the suction suction with caisson smallcaisson modelssuction model withapplieds with buried buried during depths depth suction ofs 5, of 10,penetration. 5, 10 and, and 15 cm15 The cm are maximumare 0.169, 0.169, 0.085, 0.085 heights and, and 0.087 of 0.087 soil times plug times thes iburiedthen the buried suction depths, depths, caisson respectively. respectively. models Itwith was It was buried observed observed depth that sthat of the 5,the 10 suction suction, and 15 caused cause cm ared settlement settlement 0.169, 0.085 of of, the theand surroundingsurrounding 0.087 times thesoils buried outsideoutside depths, thethe caisson. caisson. respectively. The The maximum maximum It was observed soil soil settlement settlem that theent appeared suction appeared cause a certain a dcertain settlement distance distance of from the from thesurrounding outer the out waller soilsofwall a suction outsideof a suction caisson the caisson.caisson due to dueThe caisson–soil tomaximum caisson friction.– soilsoil friction. settlem ent appeared a certain distance from the outer wall of a suction caisson due to caisson–soil friction.

(a) S = 0.5 kPa. (b) S = 1.0 kPa. (c) S = 1.5 kPa. (a) S = 0.5 kPa. FigureFigure 8.8. The( b soil) S plug = 1.0 in kPa the. caisson.caisson. (c) S = 1.5 kPa. Figure 8. The soil plug in the caisson. Figure9 shows the curves of the heights of soil plug h and of soil settlement h outside Figure 9 shows the curves of the heights of soil plug sphsp and of soil settlementsettlement hsettlement outside the caisson. Other test conditions not drawn in Figure9 did not have the obvious soil plug and soil the caisson.Figure 9 O showsther test the conditions curves of notthe drawnheights in of Figure soil plug 9 did hsp not and have of soil the settlement obvious soil hsettlement plug andoutside soil settlement around the suction caisson model. There is no obvious soil settlement outside the suction thesettlement caisson. around Other test the conditionssuction caisson not drawn model. in There Figure is no9 did obvious not have soil thesettlement obvious outside soil plug the and suction soil caisson with a buried depth of 15 cm. The height of soil plug h increases with the increase of x settlementcaisson with around a buried the suctiondepth of caisson 15 cm. model.The height There of issoil no plug obvious hsp increases spsoil settlement with the outside increas thee ofsuction x as a as a result of the distribution of seepage velocity, which is greater as it moves toward the wall of caissonresult of with the adistribution buried depth of seepageof 15 cm. velocity The height, which of soilis greater plug h assp increasesit moves towardwith the the increas wall eof of suction x as a suction caissons. resultcaissons. of the distribution of seepage velocity, which is greater as it moves toward the wall of suction caissons. Appl. Sci. 2020, 10, 566 8 of 11 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 12

x/cm

Soil heave plug 1.2 h=5cm, S=1.0 kPa

h=5cm, S=1.5 kPa soil settlement 0.9 h=10cm, S=2.5 kPa h=10cm, S=3.0 kPa 0.6 h=15cm, S=3.5 kPa

(cm) h=15cm, S=4.0 kPa

sp 0.3

h

h 0.0 settlement 0 1 2 3 4 5 6 7 8 9 10 -0.3

(cm)

-0.6

Soil heave plug Soil Sand -0.9 Settlement

-1.2 Suction caisson FigureFigure 9. The 9. The height height of of soil soil plug plug andand soil settlement settlement outside outside the the caisson. caisson.

The volumeThe volume of soil of soil plug plugVsp Vandsp and that that of of soil soil settlement settlement Vsettlementsettlement werewere measured measured by using by using the the volumevolume formula formula after obtaining after obtaining the size the of size the soilof the plug soil and plug settlement and settlement from the from images. the images. The comparison The comparison between the volume of soil plug Vsp and that of soil settlement Vsettlement in tests is shown between the volume of soil plug Vsp and that of soil settlement Vsettlement in tests is shown in Table3. in Table 3. The soil plug consists of the soil heaved by seepage force into the caisson, and the soil from The soil plug consists of the soil heaved by seepage force into the caisson, and the soil from outside outside into the caisson, leading to soil settlement around the foundation. It can be seen that the into theinfluence caisson, of settlement leading to outside soil settlement the caisson around on the soil the plug foundation. decreases Itas can the beburied seen depth that rises. the influence The of settlementsoil plug outsideis mainly the influenced caisson by on the the soil soil from plug outside decreases into the as c theaisson buried, and depthVsettlement rises./Vsp = 1.581 The soildue plug is mainlyto the influenced decrease in the by thevoid soil ratio from of soil outside around intothe caisson the caisson, caused andby theVsettlement seepage /forceVsp =during1.581 suction due to the decreasepenetration in the when void h ratio = 5 cm of and soil S around= 1.0 kPa. the The caisson influence caused of the soil by heaved the seepage by the soil force plug during increase suctions penetrationwith the when increash =e of5 cmh. The and volumeS = 1.0 of kPa. soil heaved The influence begins to of rise the as soil the heaved velocity by of the seepage soil plug reache increasess a with thecertain increase value. of h. The volume of soil heaved begins to rise as the velocity of seepage reaches a certain value. Table 3. The volume of soil plug and soil settlement in tests.

Tableh 3. = The5 cm volume of soil plug andh = soil10 cm settlement in tests. h = 15 cm

S = 0.1 kPa S = 1.5 kPa S = 2.5 kPa S = 3.0 kPa S = 3.5 kPa S = 4.0 kPa h = 5 cm h = 10 cm h = 15 cm Vsettlement (cm3) 0.544 0.970 0.020 0.473 0.000 0.000 S = 0.1 kPa S = 1.5 kPa S = 2.5 kPa S = 3.0 kPa S = 3.5 kPa S = 4.0 kPa Vsp (cm3) 0.344 1.520 0.519 1.954 0.849 2.827 3 VVsettlementsettlement/V(cmsp ) 1.5810.544 0.638 0.970 0.039 0.020 0.242 0.473 0.000 0.000 0.000 0.000 3 Vsp (cm ) 0.344 1.520 0.519 1.954 0.849 2.827 3.4.Vsettlement Prediction/Vsp of Soil Plug1.581 Height 0.638 0.039 0.242 0.000 0.000

The relationship between the height of the soil plug hsp and the hydraulic gradient v/k was 3.4. Predictionproposed ofby Soil using Plug quadratic Height regression, and can be expressed as follows:

2 The relationship between the height of the soil plug hsp and2 the hydraulic gradient v/k was hsp S  S  v  v  Sv proposed by using quadratic regression,A  B  andC can be  expressedD  E as follows: F , (2) h  'h   'h  k  k   'hk !2 hsp S S v v2 Sv where A–F are constant coefficients= A + B (given+ C in Table+ 4)D. Figure+ E 10 shows+ F the ,comparison of actual (2) values and fitted valuesh for the dimensionlessγ h γ soilh plug khsp/h. Fittedk valuesγ hk are evenly distributed 0 0 0 around the actual values. Compared with the actual values, the fitted values have an average relative whereerrorA–F ofare about constant 28.74%. coe fficients (given in Table4). Figure 10 shows the comparison of actual values and fitted values for the dimensionless soil plug hsp/h. Fitted values are evenly distributed around the actual values. Compared withTable the 4. Optimal actual values,value of constant the fitted coefficients values for have hsp/h. an average relative error of about 28.74%.A B C D E F 0.57495 −0.49370 0.09759 0.05075 −0.02168 0.02252 Table 4. Optimal value of constant coefficients for hsp/h.

ABCDEF 0.57495 0.49370 0.09759 0.05075 0.02168 0.02252 − − Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 12 Appl.Appl. Sci. Sci. 20202020,, 1010,, x 566 FOR PEER REVIEW 99 of of 12 11

0.180.18 0.160.16 QuadraticQuadratic regressionregression

0.140.14

h

h

/

/

sp

sp

h 0.12

h 0.12

0.100.10

0.080.08

0.060.06

Fitted values of values Fitted Fitted values of values Fitted 0.040.04

0.020.02

0.000.00 0.000.00 0.020.02 0.040.04 0.060.06 0.080.08 0.100.10 0.120.12 0.140.14 0.160.16 0.180.18 ActualActual valuesvalues ofof hh //hh spsp

FigureFigure 10. 10. TheThe comparisoncomparison ofof actualactual valuesvalues andand fitted fittedfitted values values for for the the dimensionless dimensionless soil soil plug plug hhspsp///hhh...

Figure 11 shows the relationship between hsp/h and v/k when h = 15 cm. It is shown that the FigureFigure 1111 showsshows thethe relationshiprelationship betweenbetween hhspsp//hh andand v/kv/k whenwhen hh == 1515 cm.cm. ItIt isis shownshown thatthat thethe dimensionless soil plug hsp/h first increases and then decreases with the increase of v/k. The reason dimensionlessdimensionless soilsoil plugplug hhspsp//hh firstfirst increaseincreasess andand thenthen decreasedecreasess withwith thethe increaseincrease ofof v/kv/k.. TheThe reasonreason behindbehind thethe decreaseddecreased trend trend is is that that thethe soilsoil plugplug isis subjectedsubjected toto downdown downwardwardward frictionfriction appliedapplied byby thethe innerinner wallwall of of the the suction suction caisson. caisson. TheThe combincombin combinationationation ofof EqEq Equationsuationsuations (1)(1) (1) andand (2)(2) isis usedused toto predict predict roughly roughly thethe heightheight ofof soilsoil plug plugsplugss in in suction suction caissons caissons inin sandsand duringduring suctionsuction penetration,penetration, guidingguiding projectproject project designsdesigns designs,,, andand construction.construction. 0.120.12 SS=3.5=3.5 kPakPa FittingFitting functionfunction ((SS == 3.53.5 kPa)kPa) 0.100.10 SS=4.0=4.0 kPakPa FittingFitting functionfunction ((SS == 4.04.0 kPa)kPa)

0.080.08

h

h 0.06 / 0.06

/

sp

sp

h

h 0.040.04

0.020.02

0.000.00

0.00.0 0.50.5 1.01.0 1.51.5 2.02.0 2.52.5 3.03.0 3.53.5 4.04.0 vv//kk

Figure 11. The relationship between hsp/h and v/k when h = 15 cm. FigureFigure 11.11. TheThe relationshiprelationship betweenbetween hhspsp//hh andand v/kv/k whenwhen hh == 1515 cmcm.. 4. Conclusions 4.4. ConclusionsConclusions A series of model tests were conducted in this study to investigate the visualization of suction caissonAA seriesseries penetration ofof modelmodel in sand. teststests werewere The following conductedconducted conclusions inin thisthis studystudy can toto be investigateinvestigate drawn: thethe visualizationvisualization ofof suctionsuction caissoncaisson penetrationpenetration inin sand.sand. TheThe followingfollowing conclusionsconclusions cancan bebe drawn:drawn: (1) The seepage field can be visualized while the carmine stain flows along a streamline in the soil (1)(1) TheThearound seepageseepage the fieldfield suction cancan caisson. bebe visualizedvisualized The seepage whilewhile thethe velocity carminecarmine is larger stainstain flow asflow thess along streamlinealong aa streamlinestreamline moves toward inin thethe soilsoil the aroundaroundwall of the the suction suction caissons.caisson.caisson. TheThe The seepageseepage pre-test velocityvelocity results show isis largerlarger that asas the thethe seepage streamlinestreamline failure movesmoves took placetowardtoward in thethe wallwallsand ofof when thethe suctionsuction the suction caissons.caissons. in the TheThe caisson prepre--test withtest resultsresults buried showshow depths thatthat of the 5,the 10, seepageseepage and 15 failurefailure cm was tooktook greater placeplace than inin thethe 2.0, sandsand3.5, and whenwhen 4.0 thethe kPa, suctionsuction respectively. inin thethe caissoncaisson The results withwith buried indicatedburied depthdepth thatss oftheof 5,5, seepage 1010,, andand path1515 cmcm of waswas the greatergreater soil is unrelated thanthan 2.0,2.0, 3.53.5,, andand 4.04.0 kPa,kPa, respectively.respectively. TheThe resultresultss indicateindicatedd thatthat thethe seepageseepage pathpath ofof thethe soilsoil iiss unrelatedunrelated Appl. Sci. 2020, 10, 566 10 of 11

to S applied in the caisson and is affected by the penetration depth during the installation of the foundation. (2) The hydraulic gradient v/k of the sand in tests at the mudline was proposed by using the regression function. It can be seen that the fitted values agree well with the actual values. Darcy’s law is not applicable, and the hydraulic gradient v/k increases with the increase of x/D. The results indicated that the seepage velocity is larger as the streamline moves toward the wall of the suction caissons. The v/k when S/γ’h = 2.451 is 5.85 times greater than when S/γ’h = 0.351 in tests. The minimum relative error is 5.05% for Equation (1) when S/γ’h = 5.478. (3) There is no soil plug in the caissons with small suction applied during suction penetration. The maximum heights of the soil plugs in the suction caisson models with buried depths of 5, 10, and 15 cm are 0.169, 0.085, and 0.087 times the buried depths, respectively. The height of soil plug hsp increases with the increase of x as a result of the distribution of seepage velocity, which is greater as it moves toward the wall of suction caissons. The influence of the soil heaved by the soil plug increases with the increase of h. The volume of the soil heaved begins to rise as the velocity of the seepage reaches a certain value. The dimensionless soil plug hsp/h first increases and then decreases with the increase of v/k.

Author Contributions: Conceptualization, S.M. and L.X.; methodology, L.X. and S.M.; validation, T.L.; formal analysis, T.L. and S.M.; investigation, T.L. and S.M.; resources, data curation, T.L. and S.M.; writing original draft preparation, T.L. and S.M.; visualization, T.L. and S.M; supervision L.X.; project administration, L.X.; funding acquisition, L.X. All authors have read and agreed to the published version of the manuscript. Funding: This work was financially supported by the Chinese National Natural Science Foundation (No. 51479137). Conflicts of Interest: The authors declare no conflict of interest.

Notation

S Applied suction in the caisson H Water head 3 γw Unit weight of water (10 kN/m ) D External diameter of the suction caisson L Height of the suction caisson T Thickness of the wall of the suction caisson ρd Dry density of the sand Gs Specific gravity of the sand d10 Effective size of the sand e Void ratio of the sand γsat Saturated weight of the sand k Permeability coefficient h Buried depth of the suction caisson x Abscissa value in Figure1 γ’Effective unit weight of soil c Cohesion of soil ϕ Angle of internal friction hsp Height of soil plug hsettlement Soil settlement outside the caisson

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