An Innovative Method for Conventional Triaxial Tests of

Research ArticleAn Innovative Method for Conventional Triaxial Tests ofConcrete Applications of PVC Pipes as a Mould andSealing Membrane

Zhe Wang 1 Xiaoguang Zhou1 and Jili Feng2

1School of Civil Engineering Beijing Jiaotong University Beijing 100044 China2State Key Laboratory for Geomechanics and Deep Underground EngineeringChina University of Mining and Technology Beijing Beijing 100083 China

Correspondence should be addressed to Zhe Wang zhwangbjtueducn

Received 11 January 2020 Revised 24 April 2020 Accepted 2 May 2020 Published 25 August 2020

Academic Editor Yann Malecot

Copyright copy 2020 Zhe Wang et al )is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In this paper we propose an innovative method for conventional triaxial tests of concrete with a confining cell )e polyvinylchloride (PVC) pipe is used as a mould to cast concrete and also as a membrane to isolate the concrete specimen from oil underconfinements)is method is termed as PMM (ie PVC pipe is used as a mould andmembrane) However a heat-shrink sleeve isused as a membrane in the traditional test method (TMM) Specimens were made from mortar without coarse aggregates in thepresent experiment Under six confinements (0ndash70MPa) the conventional triaxial compression tests were performed on ul-trahigh-strength (150MPa) and high-strength (82MPa) mortar specimens by PMM and TMM)e results indicate the following(i) there is a characteristic confinement p0 when the confinement is lower than p0 the strength by PMM is higher than that byTMM on the contrary when the confinement is higher than p0 the strengths by both methods are almost identical In this workp0 is between 0 and 5MPa (ii) When the confinement is 5ndash70MPa the relationship between the peak stress of high-strengthmortar and confinement is characterized by a monotonically rising straight line however a monotonically rising upward convexcurve describes the peak stress of ultrahigh-strength mortar related to the confinement (iii) )e residual strength using PMM issignificantly higher than that using TMM at zero confinement or lower confinements but the residual strengths by these twomethods are approximately identical at higher confinements (iv) )e transverse cracks appear in the mortar specimen inside thePVC pipe after enduring a triaxial loading using PMM However there is no such phenomenon when TMM is applied

1 Introduction

Cylindrical specimens are usually used in conventional triaxialtests of concrete which can be prepared by drilling cores [1 2]or casting in concrete moulds [3 4] )e liquid is used as amedium in conventional triaxial testing machines to applyconfinement and membranes are employed to seal specimens)e membrane materials cover polymers and thin metals withgood deformability (such as copper [5]) )e commonly usedpolymermaterials include latex nitrile silicone neoprene andother flexible materials [6ndash10] Most testingmachines apply oilpressure to confine a specimen Generally the range of oilpressure is suitable for almost all confinements from high tolow Wang et al [8] sealed the specimen with a heat-shrink

sleeve Malecot et al [9] used a multilayer membrane com-posed of 8mm of latex and 2mm of neoprene under a veryhigh confinement of 650MPa For some tests with specialrequirements water is taken as a medium and the confine-ment is generally below 10MPa Chen et al [10] used a rubbermembrane of 2mm and another latex membrane of 04mm toseal the specimen together Bjerkeli et al [11] coated epoxy onthe specimen surface for sealing

)e experimental results have indicated that the mem-brane influences the uniaxial strength of a specimen Forexample Li and Ansari [12] examined the confining effect ofthe rubber membrane on axial stresses by comparing theuniaxial compressive strengths of jacketed and bare speci-mens It showed that the rubber membrane resulted in a 7

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 4125428 14 pageshttpsdoiorg10115520204125428

increase in axial strength However Sovjak et al [13]demonstrated that the membrane they used did not influ-ence the uniaxial compressive strength )erefore differentmembranes have different impacts on concrete strength

)e membrane is deformed under the action of con-finement [14ndash16] When a clip gauge was used to measurethe radial deformation of the specimen Candappa et al [14]passed ten metal studs through the membrane to avoiderroneously including the membrane deformation in mea-surement results One end of the stud was in direct contactwith the concrete surface and the other end was connectedthrough a piano wire to the two measuring arms of the clipgauge )e gap between the metal stud and the membranewas filled with a sealant to prevent the oil from penetratingLu and Hsu [15] used the same loading scheme to performtwo separate triaxial tests on a specimen-size solid steel rodwith and without the membrane respectively )e radialstrains under different confinements were measured and thedifference between them was the decrease in membranethickness under confinements In calculating the actualdeformation of the specimen the thickness change of themembrane should be subtracted from the total deformationWhen the gauge glued on the specimen surface was used tomeasure the deformation the specimen and the gaugeshould be sealed together by the membrane If there arepores on or near the specimen surface the flexible mem-brane is likely to crush the gauge or its wire on pores underthe action of the confinement Gabet et al [17] used a PVCshield which is locally set up on gauges as an additionalprotection)e PVC shield acts as a plane support surface tokeep gauges from being pressed into pores

PVC pipes have extensive applications in the constructionindustry [18] and their compression performances under axialloads [19] have been studied Concrete with the PVC pipe refersto a structural member where the PVC pipe and the concreteinside it bear loads together However there are few reports onits research Kurt [20] studied the effect of the slenderness ratioon the strength of concrete with the PVC pipe )e experi-mental results in [21] showed that both concrete strength andPVC pipe thickness have significant effects on the compressivestrength of concrete with the PVC pipe and a similar obser-vation was reported by Saadoon [22] )ese experiments showthat the concrete with the PVC pipe outperforms the concretewithout the PVC pipe in strength and ductility

)is paper proposed an innovative type of conventionaltriaxial test method (PMM) We use the PVC pipe as amould to cast concrete and as a membrane to isolate oilduring the testing Compared with the traditional testmethod (TMM) PMM has the following advantages

(1) In the process of concrete forming PVC pipes asdisposable moulds are suitable for casting a largenumber of concrete specimens at one time Cur-rently PVC pipes are priced relatively low and inample supply in various diameters )ey can be usedto form concrete specimens with various diametersand heights In addition PMM is free from cleaningassembling and disassembling moulds which is ahuge boost to test efficiency

(2) In the process of specimen processing PMM is moreconvenient for specimen cutting and grinding seeSection 22 for details

(3) In the process of triaxial loading the PVC pipe canalso be used to isolate the oil from the concretethereby simplifying the specimen sealing processbefore the triaxial test (refer to Section 23 fordetails)

If coarse aggregates are used in concrete it is worthnoting that PMM also has an edge effect like TMM

2 Materials and Experiments

21Materials and Specimens In the test the cement appliedwas PmiddotII525R type Portland cement according to the Chi-nese standard )e average diameter of the silica fumeranged from 01 to 03 μm )e average diameter of thequartz powder was 75 μm Two types of quartz sands in thediameter range 180ndash425 μm and 425ndash800 μm respectivelywere mixed by the mass proportion of 1 1 and they wereused as fine aggregates )e silica fume and the quartzpowder were used at the replacement percentages of 20and 27 for the cement to fill up voids that exist in ul-trahigh-strength mortar as well as to improve mechanicalproperties )e cellulose ether (CE) used in low-strengthmortar could prevent mortar from bleeding We propor-tionally used the polycarboxylate superplasticizer admixture(PSA) and the liquid defoamer (LD) )e PVC pipes have anominal pressure of at least 1MPa and are 50mm in di-ameter and 24mm in thickness )e mechanical propertiesof the PVC pipe are presented in Section 3 )e mix pro-portions are given in Table 1 Given the small size of thespecimen no coarse aggregate was used in the specimen

)e mixed mortar was poured into several PVC pipeseach of which is 135mm in height and is sealed at the lowerend by the tape )e specimens were then vibrated on ashaking table to remove the entrapped air bubbles Beforethe specimens were kept in the standard curing room forfour days they were covered with a plastic film )e spec-imens were then cured for six days in a high-temperaturecuring box at 90degC Afterward the specimens were taken outand cured atmospherically for 90 days regardless of the agingeffect on mortar strength Meanwhile three kinds of cubicmortar specimens with a side length of 707mm wereprepared and their average uniaxial compressive strengthsfor 100 days are listed in Table 1 )e standard deviation foraverage uniaxial compressive strength of each mortar is alsolisted in Table 1

22 SpecimenProcessing In the course of cutting the cornerof the mortar specimen surrounded by nothing is oftendamaged (see Figure 1(a)) due to the diagonal pulling effectof the cutter blade For the specimen surrounded by the PVCpipe however the radial restraint provided by the PVC pipecan weaken the diagonal tension generated by the cutterblade thus it can prevent damage on the mortar corner Ascan be seen from Figure 1(b) there is no damage when thespecimen is surrounded by the PVC pipe

2 Advances in Civil Engineering

In the process of grinding we find that the mortarspecimens surrounded by the PVC pipe are easier to grindinto a plane meeting the flatness requirements than thosesurrounded by nothing )erefore it is recommended thatthe mortar specimen should be surrounded by the PVC pipeduring cutting and grinding

)e processed specimens are categorized into two typesie P Specimen (PS) which is the mortar specimen sur-rounded by the PVC pipe and T Specimen (TS) which is thePS removed from the PVC pipe )e outer and inner di-ameters of the PVC pipe are 50mm and 452mm respec-tively )e heights of PS and TS are 120plusmn 1mm and theangle between the normal direction of the specimen end faceand the axis of the specimen is not more than 025deg

23 Specimen Sealing )e specimen is placed between theupper and lower loading heads and is directly contacted withboth )e upper loading head is 50mm in diameter with aspherical joint the lower loading head is 53mm in diameterslightly larger than the diameter of the specimen

To the PS the PVC pipe on the outside of the mortarspecimen was used as a membrane thereby simplifying thespecimen sealing process As shown in Figure 2(a) a rubbersleeve was tightened on the outside of the PVC pipe and theloading head In the rubber sleeve the tangential tensioncomponent which points to the axis of the specimen madethe rubber sleeve tighten around the side of the PVC pipeand the loading head so as to prevent the oil from pene-trating into the end of the specimen

To the TS the heat-shrink sleeve which was longer thanthe mortar specimen acted as a membrane It wrappedaround the mortar specimen as well as both loading heads

Moreover both ends of the heat-shrink sleeve were coveredwith the rubber sleeve and the rubber sleeve was tightenedaround the heat-shrink sleeve and the loading head asshown in Figure 2(b) When the multilayer heat-shrinksleeve is used it is recommended that the outer heat-shrinksleeve should be longer and cover the both ends of the innerone

Before wrapping the heat-shrink sleeve we applied thequick-hardening cement to patch defects such as surfacepores to avoid the contact between oil and mortar caused bythe rupture of the heat-shrink sleeve around the mortarsurface Although the mortar surface of PS cannot bepatched the PVC pipe does not break easily even if it issqueezed into holes under the action of oil thanks to thePVC pipersquos suitable ductility and thickness In the presenttest the phenomenon of oil leakage was not found in themortar specimen sealed with the PVC pipe (PS)

24 Experimental Setup and Loading Procedure )e testswere conducted on an electrohydraulic servo-controlledtriaxial testing machine (XTR01) )e plunger of the con-fining cell is equipped with a self-balancing mechanism )eactual axial compressive stress of the specimen is σ1(=p+ q= p+ FA) where p is the confinement applied by oilq means the deviatoric stress applied by the plunger Findicates the axial loadmeasured by the load transducer andA represents the cross-sectional area of themortar specimenFigure 3(a) illustrates the mechanical model of a mortarspecimen Axial and radial extensometers were used tomeasure the deformation of the specimen as shown inFigure 3(b) Both ends of the axial extensometer were fixedon the loading heads and the measured deformation

Table 1 Mix proportions and cube compressive strength

Mortar type

Cementitiousmaterial (kgm3) Quartz powder

(kgm3)Quartz sand(kgm3)

Admixture (kgm3)Water(kgm3)

Strength(MPa)

Standarddeviation (MPa)

Cement Silicafume PSA LD CE

Low strength 6800 0 0 8840 0 0 1360 3536 17 05High strength 8320 0 0 10816 0 0 0 3162 82 26Ultrahighstrength 8370 1674 2260 8370 30132 3013 0 2009 150 51

Notes PSA polycarboxylate superplasticizer admixture LD liquid defoamer CE cellulose ether

Corner damage

(a) (b)

Figure 1 (a) Mortar surrounded by nothing (b) Mortar surrounded by the PVC pipe

Advances in Civil Engineering 3

covered two parts One is the deformation of the entirespecimen )e other is the deformation of the loading headsin the 45mm height range )e deformation of the loadingheads should be subtracted in data processing )e strains oftwo perpendicular directions in the middle of the specimenwere measured using the radial extensometer )e dynamicand static strain apparatus continuously collected load anddeformation data at the collecting frequency of 5Hz

)e loading processes of PS and TS include the followingsix steps (1) start collecting data and record zero points ofaxial load (F) and confinement (p) (2) the specimen isaxially precompressed and at the same time the end face ofthe upper loading head is automatically in parallel contactwith the end face of the plunger through the rotation of thespherical joint (3) p is applied at a rate of 01ndash02MPas untilthe designed value and then p remains constant until thedeformation tends to be stable )e viscoplastic deforma-tions of both the mortar and the heat-shrink sleeve (or thePVC pipe) are released (4) the axial displacement is appliedat a constant rate of 0002ndash0004mms (5) after the de-formation of the specimen reaches the critical value the axialdisplacement at a rate of 001mms is reduced until F is 0and then p at a rate of 01ndash02MPas is also reduced to 0 (6)the data collection is terminated

)e confinements of 0 5 10 20 40 and 70MPa areselected for the tests Each specimen corresponds to one ofthe confinements and two specimens of the same type aretested under each confinement It is required that under eachconfinement the difference between the peak deviatoricstresses of two identical specimens is less than 7 of theiraverage value In case oil leakage or any other reason in thetest distorts the experimental result and so it is necessary toincrease the number of the corresponding specimens

25 Two Test Methods We report two methods for con-ventional triaxial tests of mortar)e innovative method (so-called PMM) includes the following four steps (i) the mortaris cast by using a PVC pipe as a mould (ii) )e mortarspecimen is processed with the PVC pipe to meet the re-quirements for its size shape and precision )e specimenafter processing is called PS (iii) To seal the PS the PVC pipeon the outside of the mortar specimen acts as a sealingmembrane (iv) )e triaxial loading is performed on thespecimen It must be noted that as a membrane with certainshear strength and shear stiffness PVC pipersquos influence onthe mechanical behavior of mortar cannot be simply ignoredand need to be studied

σ1

σ3

σ3

σ2

σ1 = p + q

σ2 = σ3 = p

(a)

Ring with a conical half-angle

of 45 degrees

Radial extensometer

Cantilever beam Axial extensometer

Fixing ring of cantilever beam

Cantilever beamFixing ring of

cantilever beamStud for fixing the ring on loading head

Stud for transferring radial deformationof specimen to cantilever beam

Stud for fixing the ring on loading head

(b)

Figure 3 (a) Mechanical model of mortar (b) Placement of extensometers

PVC pipe

Rubber sleeve

Loading head

(a)

Heat-shrink sleeve

Rubber sleeve

Loading head

(b)

Figure 2 Sealing detail (a) PS (b) TS


)e traditional test method (so-called TMM) alsoconsists of the following four steps (i) the mortar is cast byusing a PVC pipe as a mould (ii) )e mortar specimen isprocessed with the PVC pipe to meet the requirements for itssize shape and precision )en the PVC pipe is removedand the processed specimen is called TS (iii) To seal the TSthe heat-shrink sleeve acts as a sealing membrane (iv) )etriaxial loading is performed on the specimen It is worthnoting that since the shear strength and the shear stiffness ofthe heat-shrink sleeve are very small its influence on themechanical behavior of mortar is negligible

Our present work includes three kinds of mortarspecimens namely the ultrahigh-strength mortar (UM) of150MPa the high-strength mortar (HM) of 82MPa and thelow-strength mortar (LM) of 17MPa To facilitate ourdiscussion in the subsequent sections we take P and T as apresymbol to represent PMM and TMM respectively Forexample P-HM indicates a high-strength mortar specimentested by PMM

3 Mechanical Property Tests of PVC Pipes

31 Conventional Triaxial Compression Tests of PVC PipesIn this work we regard compressive for stress or strain aspositive ε1 is the axial strain ε2 and ε3 are the two per-pendicular radial strains in the middle of the specimen εr isthe average value of radial strains εr (ε2 + ε3)2

)e conventional triaxial tests for the PVC pipe with aheight of 17plusmn 05mm were performed to understand itsmechanical properties To ensure that the oil pressure insideand outside the PVC pipe is equal the PVC pipersquos end facewas designed to contain grooves with a depth of less than04mm and a width of less than 03mm q-εr and q-ε1 curvesof the PVC pipes are shown in Figure 4 As the confinementrises the peak deviatoric stress of the PVC pipe increasesslightly )e stress-strain curves of the PVC pipe on thewhole coincide under different confinements before the peakpoint which indicates that the impact of the confinement ondeformation is practically negligible After the peak pointthe load decreases for PVC pipersquos instability and the radialand axial deformations increase rapidly One can find fromFigure 5 that the middle section of the damaged PVC pipeshows an obvious bulge Additionally the failure modes ofPVC pipes are basically identical under other confinements

)e elastic modulus E is defined by the approximatestraight line portion before the peak point As indicated inTable 2 the elastic modulus of the PVC pipe is slightlyenhanced at 5MPa confinement compared with zeroconfinement However under the confinements of5ndash70MPa the elastic modulus of the PVC pipe does notchange substantially

32 Hydrostatic Pressure Tests of PVC Pipes To furtherunderstand the deformation characteristics of PVC pipesunder hydrostatic pressure only the confinement was ap-plied during the test)e confinement change with time (t) isgiven in Figure 6(a) It is found from Figure 6(b) that theradial compression deformation (Dr) gradually increases

with the confinement enhancement According to thegeometric equation all of the parameters namely the innerdiameter the outer diameter and the thickness of the PVCpipe decrease under hydrostatic pressure When the con-finement is stable the variation range of the extensometer isless than 0003mm which is far less than the radial de-formation of the mortar specimen )erefore if the con-finement remains constant we can consider the thickness ofthe PVC pipe as an invariant factor

4 Conventional Triaxial Tests of Mortar

41 Failure Modes By TMM we can obtain the failuremodes of specimens under different confinements as shownin Figure 7 It is found that both the strength and theconfinement influence the failure modes of mortar speci-mens When the confinement is zero splitting failures ap-pear in T-UM and T-HM Numerous vertical cracks aredeveloped and divide the specimen into several crushedblocks Shear failures occur both in T-UM under the con-finements of 5ndash40MPa and in T-HM under the confine-ments of 5ndash20MPa Additionally a major inclined crackappears in these specimens When T-UM is under theconfinement of 70MPa and T-HM is under the confine-ments of 40ndash70MPa they swell in a certain height rangewith no strain localization

In PMM however we can also present the failure modesof specimens under different confinements as indicated inFigure 8 After the uniaxial compression in P-UM andP-HM vertical and nearly vertical cracks which appear inboth mortar specimens inside the PVC pipe (MIP) aresignificantly less than those of the same type specimenssubjected to the uniaxial compression in TMM After P-UMunder the confinements of 5ndash40MPa and P-HM under theconfinement of 5MPa a diagonal shear band separatelyappears in the corresponding PVC pipe Each MIP has amajor inclined crack in the same position Besides themortar blocks on both sides of the major inclined crack also

0MPa5MPa10MPa

20MPa40MPa70MPa

0

20

40

60

80

q (M

Pa)

ndash010 ndash005 000 005 010 015ndash015

Strainεr ε1

Figure 4 q-εr and q-ε1 curves of the PVC pipes


show approximate transverse cracks but none of thempasses through the major inclined cracks After the con-finement of 70MPa to P-UM and the confinements of10ndash70MPa to P-HM it is several approximate transversecracks rather than inclined cracks that appear in MIP

)e transverse cracks in MIP come as a result ofinteraction between the PVC pipe and MIP duringloading and unloading In the process of increasingconfinement alone or only applying axial displacementunder the constant confinement both PVC pipe and MIPare axially compressed Additionally the MIP also yieldsaxial compressive plastic deformation during the appli-cation of axial displacement In the process of reducingthe axial displacement to the load F approaching zerounder the constant confinement both PVC pipe and MIPare axially elongated but no transverse crack is gener-ated )is is because the confinement still exists Even atthe low confinement of 5MPa the axial load acting on thespecimen due to the confinement is still close to 10 kN sono transverse crack is formed In the process of reducing

the confinement to zero the PVC pipe and MIP stillundergo axial elongation Since the elastic elongation andthe deformability of the PVC pipe are greater than thoseof MIP the transverse cracks in MIP are caused bytension

One can find from Figure 9 that the end face of MIP islower than that of the PVC pipe after triaxial loading Butthey are in the same plane before loading which indicatesthat the rebound amount of the PVC pipe is larger than thatof MIP In Figure 8 after P-UM is subjected to triaxialloading under the confinements of 5ndash40MPa the approx-imate transverse cracks appearing in MIP do not passthrough the major inclined crack indicating that thetransverse cracks are formed after the major inclined crackIt coincides with the explanation that the transverse cracksare generated during unloading Also the surfaces of thetransverse cracks of MIP are relatively flat and there isalmost no powder generated by friction between the sur-faces)ese features are consistent with the characteristics ofthe tensile surfaces

(a) (b)

Figure 5 Failure modes of the PVC pipes (a) p 0MPa and (b) p 70MPa

Table 2 Elastic modulus of the PVC pipes

Confinement (MPa) 0 5 10 20 40 70E (GPa) 25 30 30 29 27 29

0

10

20

30

40

50

60

70

80

p (M

Pa)

500 10000 1500t (s)

(a)

000

004

008

012

016

020

Dr (

mm

)

500 10000 1500t (s)

(b)

Figure 6 )e relationships between (a) p and t and (b) Dr and t


)e axial compression of P-HM is relatively large underhigh confinements After loading termination MIP be-comes a cylinder extruded from powder particles and itstensile strength is almost zero )erefore in the process ofreducing the confinement the PVC pipe is more likely to crack

MIP leading to more transverse cracks If the compression ofP-UM is large enough dense transverse cracks will develop inMIP

Piotrowska et al [23] found that four kinds of concretecontaining coarse aggregates also formed multiple

Type p = 0MPa p = 5MPa p = 10MPa p = 20MPa p = 40MPa p = 70MPa

T-UM

T-HM

Figure 7 Failure modes of specimens tested by TMM under different confinements


P-UM

MIP

P-HM

MIP

Figure 8 Failure modes of specimens tested by PMM under different confinements Notes MIP mortar specimen inside the PVC pipe


transverse cracks after undergoing triaxial loading with650MPa confinement Similar phenomena also occurred inthe recycled aggregate concrete under high confinementsafter exposure to high temperatures [24] It was pointed outin [23] that the transverse cracks were generated in the laterstage of unloading but the reason for this was not given Wehypothesize that the cause of the transverse cracks in [23] isthe same as that in PMM which is also the result of thetensile deformation of the membrane on the concrete duringunloading Since the membrane of the cylinder specimen(Φ70times140mm) in [23] is composed of 8mm of latex and2mm of neoprene the concrete has basically lost its co-hesion in unloading and the tension generated by the re-bound of the membrane suffices to pull the concrete apart

42 Stress-Strain Relationships Figure 10 shows the q-εr andq-ε1 curves of the mortar specimens through TMM andPMM Some of the descendings are characterized by astraight line (as shown in Figure 10(a) with the confinementsof 0 5 10 and 20MPa respectively) which are caused by theinsufficient stiffness of the testing machine)e deformationcorresponding to this straight line is completed instantly)us only data at both ends of the straight line are collectedWhen the axial deformations of T-HM and P-HM increaseto a certain extent under the confinements of 40 and 70MPathe stress-strain relationships tend to be flat and then thereseems to be no deterioration phenomenon Xie et al [25]experimentally found that when the confinement exceeds50 of the uniaxial compressive strength of concrete thestress does not drop after the peak point which is similar tothe above situation Similar phenomena have been observedin rocks [26] Zingg et al [27] found that under very highconfinement the concrete behavior is influenced to a lesserextent by the matrix strength and is being essentially gov-erned by the granular stacking of the concrete Neverthelessit is worth noting that this conclusion is only valid for dryconcrete and the presence of water in capillary porosity willcertainly modify concrete behavior especially for concretewith low matrix strength under very high confinement[28 29]

43 Radial Interaction between PVC Pipe and MIP underUniaxial Compression Table 3 shows the uniaxial com-pressive strength of three strength mortar specimens byPMMand TMM As expected the uniaxial strength obtained

by PMM is higher than that by TMM )e explanations forthis are as follows

In PMM the PVC pipe can improve the mortar strengthnot only by applying radial pressure to MIP but also bybearing the axial load As can be seen fromTable 2 the elasticmodulus of the PVC pipe is 25GPa about 7 of UMAdditionally the cross-sectional area of the PVC pipe is lessthan 25 of the MIP cross-sectional area In uniaxialcompression tests the axial load borne by the PVC pipe atthe peak point is about 15 of MIP in P-UM 26 of MIPin P-HM and 88 ofMIP in P-LMWe therefore concludethat the axial load borne by the PVC pipe can be ignored

Under uniaxial compression the q-ε1 and ur-ε1 rela-tionships between themortar specimens with three strengthsand the PVC pipe are plotted in Figure 11 Here we regardthe expansion as negative In one case ur indicates thedeformation along the diameter direction for the mortarspecimen In the other case ur is the deformation along theinner diameter direction for the PVC pipe We assume thatthe PVC pipe is just in contact with the surface ofMIP beforethe axial strain (ε1) is applied but the radial pressure is zeroAt the beginning of loading ur of the PVC pipe is larger thanthat of the mortar As ε1 increases further ur of the mortarincreases rapidly When reaching a stress level before thepeak point the ur-ε1 curve of the mortar intersects the ur-ε1one of the PVC pipe and ε1 at the intersection is recorded asε1c After that ur of the mortar is larger than that of the PVCpipe For PMM in the process of applying ε1 on thespecimen when 0lt ε1lt ε1c the PVC pipe is separated fromMIP and the radial pressure between them approaches zeroWhen ε1gt ε1c the PVC pipe starts to contact with MIP andthen exerts radial pressure on MIP As can be seen fromFigure 11 ε1c of three mortar specimens is smaller than therespective axial strain at the peak point)is means that MIPis subjected to the radial pressure exerted by the PVC pipebefore the peak point so the uniaxial strength obtained byPMM is higher than that by TMM (as also referred inTable 3)

44 Strength Characteristics We define the peak stress(σmax) of the mortar specimen as qmax + p where qmax is thepeak deviatoric stress and p is the confinement An averageof σmax of the same two types of specimens under theidentical confinement is denoted as σmax )e σmax minus p

curves drawn from the experimental data by two methodsare shown in Figure 12 in which abundant information can

(a) (b)

Figure 9 End faces of specimens after triaxial loading (a) P-UM (b) P-HM


be employed to analyze the mechanical properties of themortar

When the confinement ranges from 5 to 70MPa theσmax minus p curve of P-UM coincides with the correspondingone of T-UM and P-HM against T-HM has similar char-acteristics as well We naturally conclude that there is a

Table 3 Uniaxial compressive strengths of mortar specimens withthree strengths (MPa)

Type StrengthT-UM 1430T-HM 700T-LM 141P-UM 1680P-HM 850P-LM 203P-UM-end friction reduction 1645P-HM-end friction reduction 840Notes )e friction-reducing pad consists of three layers of polytetra-fluoroethylene (PTFE) with a thickness of 01mm

150

100

50

0

ndash001

ndash002

ndash003

ndash004

q (M

Pa)

u r (m

m)

Peak point

Peak point

UMHM

LMPVC

0001 0002 0003 00040000ε1

Figure 11 q-ε1 and ur-ε1 relationships between the mortarspecimens with three strengths and the PVC pipe

70MPa

40MPa

20MPa

10MPa

5MPa

0MPa

εr ε1

0

50

100

150

200

250

300

350q

(MPa

)

ndash002 ndash001 000 001 002 003 004ndash003

Strain

(a)

70MPa40MPa

20MPa

10MPa5MPa

0MPa

0

50

100

150

200

250

300

350

q (M

Pa)

εr ε1


Strain

(b)

70MPa40MPa

20MPa

10MPa

5MPa

0MPa

εr ε1

0

50

100

150

200

250

q (M

Pa)

ndash002 000 002 004 006 008ndash004

Strain

(c)

70MPa40MPa

20MPa

10MPa5MPa

0MPa

0

50

100

150

200

250

q (M

Pa)

εr ε1

ndash002 000 002 004 006 008ndash004

Strain

(d)

Figure 10 q-εr and q-ε1 curves of mortar specimens (a) T-UM (b) P-UM (c) T-HM (d) P-HM


characteristic confinement p0 When plt p0 the strengthobtained by PMM is greater than that by TMM whereaswhen pgt p0 the strengths by these two methods are almostidentical For the PVC pipes and the mortar used here0lt p0le 5MPa Additionally PMM can replace TMM toobtain the triaxial strength of mortar when pgt p0

For T-UM when 0le ple 70MPa the relationship be-tween σmax and p is a monotonically rising upward convexcurveWith the increase in p the slope of the curve graduallydecreases and finally approaches a constant To T-HM when5MPalt ple 70MPa σmax has a linear relationship with pWhen 0le ple 5MPa the σmax minus p curve has data only at bothends Based on the characteristics of the mortar material themissing data between both ends should be described by anonlinear curve Comparing the σmax minus p curves of mortarwith two different strengths we conclude that there shouldbe a strong correlation between the mortar strength and thenonlinear relationship of σmax versus p )e higher themortar strength the larger the confinement range corre-sponding to the nonlinear curve

For UM HM and LM the difference in uniaxialstrengths obtained by PMM and TMM is 250 150 and62MPa respectively Such strength difference is associatedwith themortar strength)e higher themortar strength thegreater the strength difference As can be seen from Fig-ure 12 when the confinement approaches zero the slope ofthe σmax minus p curve of P-UM is larger than that of P-HM If aconfinement increment starts from zero such incrementshould have a more significant influence on the compressivestrength for P-UM than that for P-HM As the MIP expandsradially the confining effect of the PVC pipe on MIP isequivalent to the confinement

It can be seen from Table 3 that the end friction has littleinfluence on the mortar strength when PMM is employedwhich is inconsistent with the generally accepted viewpoint)e reason is that the confinement weakens the influence ofthe tensile stress caused by the friction-reducing layer on themortar strength [30] and the confining effect of the PVC

pipe on the mortar is similar to the confinement which canalso weaken the effect of the friction-reducing layer

45 Residual Strength In Table 4 the residual strengths byPMM are significantly higher than those by TMM at zeroconfinement or lower confinements whereas there is basi-cally no difference at higher confinements Taking UM as anexample this phenomenon can be explained from theperspective of failure modes

(1) p 0)e damaged T-UM forms several crushed blocksand almost has no residual strength while the P-UMhas a great residual strength )e residual strengtharises from the radial pressure between the PVC pipeand the cracked MIP When the relative displace-ment occurs between the crushed blocks this gen-erates not only the friction (f1) between the crushedblocks but also the friction (f2) between surfaces ofthe crushed blocks and the inner wall of the PVCpipe )ese two kinds of frictions jointly contributeto the residual strength of MIP of P-UM Althoughthe axial load borne by the PVC pipe under zeroconfinement can also enhance the residual strengththis enhancement is limitedf2 is closely associated with not only the radialpressure and the friction coefficient between the MIPand the PVC pipe but also the shear stiffness andshear strength of the PVC pipe f2 can be ignoredsince the shear stiffness and shear strength of a heat-shrink sleeve are almost zero On the contrary f2must be taken into account because the PVC pipe hassome shear stiffness and shear strength

(2) p 5ndash40MPaWhether it is P-UMor T-UM the damagedmortar isdivided into two blocks by the major inclined crack)e residual strength of T-UM only depends on f1but the residual strength of MIP of P-UM is de-termined by f1 and f2)erefore even if the axial loaddirectly shared by the PVC pipe is not taken intoaccount the residual strength by PMM should alsobe higher than that by TMM

(3) p 70MPaRegardless of whether PMM or TMM is used for thetriaxial test of UM the damaged mortar shows noinclined crack )ere is no f2 since there is no dis-continuous displacement inside the mortar duringthe application of the axial displacement If the axialload shared by the PVC pipe is neglected the residualstrength of P-UM and T-UM should be approxi-mately equal in theory

46 Strain at the Peak Point Figure 13 shows the rela-tionships of confinement p versus ε1m (axial strain at thepeak point) and εrm (radial strain at the peak point) re-spectively Since the confinement hinders the generation andexpansion of mortar cracks the deformability of mortar is

T-UMP-UM

T-HMP-HM

50

100

150

200

250

300

350

400

σ_ max

(MPa

)

10 20 30 40 50 60 700p (MPa)

Figure 12 σmax minus p curves of mortar


improved As the confinement increases strain at the peakpoint of mortar increases linearly A similar phenomenonoccurs in concrete with different strengths and steel fiber-reinforced concrete [14 15 31 32] Under different con-finements strain at the peak point by PMM does not differgreatly from that by TMM

47 Failure Criterion Our test results show that theMohrndashCoulomb criterion can be used to describe the failurecharacteristics of mortar )is criterion is expressed as

σmax

fc 1 +

kσ3fc

(1)

where σmax is the triaxial compressive strength(σmax qmax + p) fc is the uniaxial compressive strengthσ3 is the confinement (σ3 p) and k is a parameter of theMohrndashCoulomb criterion related to materials )e valueof k ranges from 26 to 53 for mortar with diversifiedstrengths [32 33] and our fitting results are also withinthis range

As can be seen from Table 5 the fitting results of theMohrndashCoulomb criterion are in good agreement with theexperimental data of HM However for T-UM the relativecoefficient R2 is only 0772 16 and the fitting results are notideal Newman [34] proposed the following equation toreflect the nonlinear relationship between confinement andstrength

Aσ3fc

1113888 1113889

2

+ Bσ3fc

1113888 1113889 + 1

11139741113972

minusσmax

fc 0 (2)

where A and B are the Newman criterion parameters andother parameters are the same as those in equation (1)

Table 6 shows the fitting results of the Newman criterionin which R2 is higher than 099 indicating that the Newmancriterion accurately predicts mortar failure It can be foundfrom Figure 14(a) that the MohrndashCoulomb criterion issuitable for describing the change trend of compressivestrength of HM with confinement However it can onlyroughly reflect the change trend of compressive strength of

Table 4 Residual strengths of mortar specimens (MPa)

p (MPa)T-UM P-UM Residual

strengthdifference

T-HM P-HM Residualstrengthdifference

Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode

0 0 SPF 48 SPF 48 0 SPF 35 SPF 355 55 SHF 83 SHF 28 44 SHF 68 SHF 2410 82 SHF 103 SHF 21 73 SHF 95 SQF 2220 120 SHF 142 SHF 22 98 SHF 123 SQF 2540 211 SHF 235 SHF 24 165 SQF 170 SQF 570 305 SQF 310 SQF 5 240 SQF 238 SQF minus2Notes Splitting failure shear failure and squeeze flow are respectively expressed as SPF SHF and SQF

008

006

004

002

000

ndash002

ndash004

ε rmε 1

m

Fitting curve (T-UM)Fitting curve (P-UM)Fitting curve (T-HM)Fitting curve (P-HM)

T-UMP-UMT-HMP-HM

10 20 30 40 50 60 700p (MPa)

Figure 13 ε 1m-p and εrm-p curves of mortar


UM Figure 14(b) shows that the Newman criterion is morewidely applicable to mortar with different strengths than theMohrndashCoulomb criterion

5 Conclusions

We have performed a series of conventional triaxial tests onUM (82MPa) and HM (150MPa) by using PMM and TMMrespectively Based on the test results the following con-clusions can be drawn

(1) Compared with TMM PMM has the advantages ofavoiding cleaning assembling and disassemblingthe mould facilitating the specimen processing andsimplifying the specimen sealing before the triaxialtest PMM therefore greatly improves the testefficiency

(2) When the uniaxial compression test is conducted byPMM the radial expansion of the inner wall of thePVC pipe is larger than that of MIP at the beginningof loading When reaching a certain stress levelbefore the peak point the PVC pipe starts to contactwith MIP which leads to the radial pressure betweenthem With appearance of the radial pressure theuniaxial strength obtained by PMM is higher thanthat by TMM

(3) In triaxial compression tests there is a characteristicconfinement p0 When the confinement is higherthan p0 the strengths tested by PMM and TMM arealmost identical For the PVC pipes and the mortarused in the present work the range of p0 is 0ndash5MPa

(4) For UM and HM when the confinement ranges are0ndash40MPa and 0ndash20MPa respectively the residualstrength by PMM is higher than that by TMM


T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(a)


T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(b)

Figure 14 Comparison between fitting results and experimental data (a) MohrndashCoulomb criterion (b) Newman criterion

Table 5 Fitting results by using the MohrndashCoulomb criterion

Type k R2

T-UM 4109 0772 16P-UM 3612 0934 36T-HM 3483 0993 65P-HM 3192 0999 15

Table 6 Fitting results by using the Newman criterion

Type A B R2

T-UM minus14921 20667 0999 85P-UM minus3876 12865 0991 82T-HM 9449 9036 0997 62P-HM 10467 6207 0999 19


When the confinement ranges are 70MPa and40ndash70MPa respectively the residual strengths byboth methods are approximately identical )esebehaviors are closely associated with the failuremodes of mortar

(5) When PMM is used for the test the transverse cracksappearing in MIP after enduring a triaxial loadingare the result of interaction between the PVC pipeand MIP

Data Availability

)e data used to support this study are available within thearticle

Conflicts of Interest

)e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

)is research was supported by the National Natural ScienceFoundation of China (nos 51279003 and 51078024) and theNational Key RampD Program of China (no 2016YFC0600901)

References

[1] A Gholampour T Ozbakkaloglu and R Hassanli ldquoBehaviorof rubberized concrete under active confinementrdquo Con-struction and Building Materials vol 138 pp 372ndash382 2017

[2] I Imran and S J Pantazopoulou ldquoExperimental study of plainconcrete under triaxial stressrdquo ACI Materials Journal vol 93no 6 pp 589ndash601 1996

[3] S Sinaie A Heidarpour X L Zhao and J G SanjayanldquoEffect of size on the response of cylindrical concrete samplesunder cyclic loadingrdquo Construction and Building Materialsvol 84 pp 399ndash408 2015

[4] H Beshr A A Almusallam and M Maslehuddin ldquoEffect ofcoarse aggregate quality on the mechanical properties of highstrength concreterdquo Construction and Building Materialsvol 17 no 2 pp 97ndash103 2003

[5] M D Ingraham K A Issen and D J Holcomb ldquoResponse ofcastlegate sandstone to true triaxial states of stressrdquo Journal ofGeophysical Research Solid Earth vol 118 no 2 pp 536ndash5522013

[6] X H Vu Y Malecot and L Daudeville ldquoStrain measure-ments on porous concrete samples for triaxial compressionand extension tests under very high confinementrdquogte Journalof Strain Analysis for Engineering Design vol 44 no 8pp 633ndash657 2009

[7] A Cividini A Taliercio G S Landriani R BellottiG Ferrara and P Rossi ldquoAn apparatus for cyclic tests oncylindrical concrete specimensrdquo Materials and Structuresvol 25 no 8 pp 490ndash498 1992

[8] Z LWang H H Zhu J GWang and B Zhu ldquoExperimentalstudy on macroscopic mechanical behavior of SFRC undertriaxial compressionrdquo Mechanics of Advanced Materials andStructures vol 19 no 8 pp 653ndash662 2012

[9] Y Malecot L Daudeville F Dupray C Poinard andE Buzaud ldquoStrength and damage of concrete under high

triaxial loadingrdquo European Journal of Environmental and CivilEngineering vol 14 no 6-7 pp 777ndash803 2010

[10] Z Chen Y Hu Q Li M Sun P Lu and T Liu ldquoBehavior ofconcrete in water subjected to dynamic triaxial compressionrdquoJournal of Engineering Mechanics vol 136 no 3 pp 379ndash3892010

[11] L Bjerkeli J J Jensen and R Lenschow ldquoStrain developmentand static compressive strength of concrete exposed to waterpressure loadingrdquo ACI Structural Journal vol 90 no 3pp 310ndash315 1993

[12] Q Li and F Ansari ldquoMechanics of damage and constitutiverelationships for high-strength concrete in triaxial com-pressionrdquo Journal of Engineering Mechanics vol 125 no 1pp 1ndash10 1999

[13] R Sovjak F Vogel and B Beckmann ldquoTriaxial compressivestrength of ultra high performance concreterdquo Acta Poly-technica vol 53 no 6 pp 901ndash905 2013

[14] D C Candappa J G Sanjayan and S Setunge ldquoCompletetriaxial stress-strain curves of high-strength concreterdquo Journalof Materials in Civil Engineering vol 13 no 3 pp 209ndash2152001

[15] X Lu and C-T T Hsu ldquoBehavior of high strength concretewith and without steel fiber reinforcement in triaxial com-pressionrdquo Cement and Concrete Research vol 36 no 9pp 1679ndash1685 2006

[16] D A Mishra and I Janecek ldquoLaboratory triaxial testingmdashfrom historical outlooks to technical aspectsrdquo Procedia En-gineering vol 191 pp 342ndash351 2017

[17] T Gabet Y Malecot and L Daudeville ldquoTriaxial behaviour ofconcrete under high stresses influence of the loading path oncompaction and limit statesrdquo Cement and Concrete Researchvol 38 no 3 pp 403ndash412 2008

[18] G Akovali ldquoPlastic materials polyvinyl chloride (PVC)rdquoToxicity of Building Materials vol 5 no 3 pp 23ndash53 2012

[19] L M Alves and P A F Martins ldquoCold expansion and re-duction of thin-walled PVC tubes using a dierdquo Journal ofMaterials Processing Technology vol 209 no 9 pp 4229ndash4236 2009

[20] C E Kurt ldquoConcrete filled structural plastic columnsrdquoJournal of the Structural Division vol 104 no 1 pp 55ndash631978

[21] J-Y Wang and Q-B Yang ldquoInvestigation on compressivebehaviors of thermoplastic pipe confined concreterdquo Con-struction and Building Materials vol 35 pp 578ndash585 2012

[22] A S Saadoon ldquoExperimental and theoretical investigation ofpvc-concrete composite columnsrdquo University of BasrahBasra Iraq Doctoral Dissertation 2002

[23] E Piotrowska Y Malecot and Y Ke ldquoExperimental inves-tigation of the effect of coarse aggregate shape and compo-sition on concrete triaxial behaviorrdquo Mechanics of Materialsvol 79 pp 45ndash57 2014

[24] E Meng Y Yu J Yuan K Qiao and Y Su ldquoTriaxialcompressive strength experiment study of recycled aggregateconcrete after high temperaturesrdquo Construction and BuildingMaterials vol 155 pp 542ndash549 2017

[25] J Xie A E Elwi and J G Macgregor ldquoMechanical propertiesof three high-strength concretes containing silica fumerdquo ACIMaterials Journal vol 92 no 2 pp 135ndash143 1995

[26] S-Q Yang Y Ju F Gao and Y-L Gui ldquoStrengthdeformability and X-ray micro-CT observations of deeplyburied marble under different confining pressuresrdquo RockMechanics and Rock Engineering vol 49 no 11 pp 4227ndash4244 2016


[27] L Zingg M Briffaut J Baroth and Y Malecot ldquoInfluence ofcement matrix porosity on the triaxial behaviour of concreterdquoCement and Concrete Research vol 80 pp 52ndash59 2016

[28] Y Malecot L Zingg M Briffaut and J Baroth ldquoInfluence offree water on concrete triaxial behavior the effect of porosityrdquoCement and Concrete Research vol 120 pp 207ndash216 2019

[29] X-D Vu M Briffaut Y Malecot L Daudeville and B CireeldquoInfluence of the saturation ratio on concrete behavior undertriaxial compressive loadingrdquo Science and Technology ofNuclear Installations vol 2015 Article ID 976387 10 pages2015

[30] Z Wang and L C Wu ldquoTriaxial test study of reactive powderconcrete with different sizes under different friction reducingconditionsrdquo Journal of Zhejiang University (Engineering Sci-ence) vol 53 no 1 pp 40ndash50 2019 in Chinese

[31] F Ansari and Q B Li ldquoHigh-strength concrete subjected totriaxial compressionrdquo ACI Materials Joumal vol 95 no 6pp 747ndash755 1998

[32] G M Ren H Wu Q Fang J Z Liu and Z M GongldquoTriaxial compressive behavior of UHPCC and applications inthe projectile impact analysesrdquo Construction and BuildingMaterials vol 113 pp 1ndash14 2016

[33] Y Farnam M Moosavi M Shekarchi S K Babanajad andA Bagherzadeh ldquoBehaviour of slurry infiltrated fibre concrete(SIFCON) under triaxial compressionrdquo Cement and ConcreteResearch vol 40 no 11 pp 1571ndash1581 2010

[34] J B Newman ldquoConcrete under complex stressrdquo Developmentin Concrete Technology vol 1 pp 151ndash219 1979


increase in axial strength However Sovjak et al [13]demonstrated that the membrane they used did not influ-ence the uniaxial compressive strength )erefore differentmembranes have different impacts on concrete strength

)e membrane is deformed under the action of con-finement [14ndash16] When a clip gauge was used to measurethe radial deformation of the specimen Candappa et al [14]passed ten metal studs through the membrane to avoiderroneously including the membrane deformation in mea-surement results One end of the stud was in direct contactwith the concrete surface and the other end was connectedthrough a piano wire to the two measuring arms of the clipgauge )e gap between the metal stud and the membranewas filled with a sealant to prevent the oil from penetratingLu and Hsu [15] used the same loading scheme to performtwo separate triaxial tests on a specimen-size solid steel rodwith and without the membrane respectively )e radialstrains under different confinements were measured and thedifference between them was the decrease in membranethickness under confinements In calculating the actualdeformation of the specimen the thickness change of themembrane should be subtracted from the total deformationWhen the gauge glued on the specimen surface was used tomeasure the deformation the specimen and the gaugeshould be sealed together by the membrane If there arepores on or near the specimen surface the flexible mem-brane is likely to crush the gauge or its wire on pores underthe action of the confinement Gabet et al [17] used a PVCshield which is locally set up on gauges as an additionalprotection)e PVC shield acts as a plane support surface tokeep gauges from being pressed into pores

PVC pipes have extensive applications in the constructionindustry [18] and their compression performances under axialloads [19] have been studied Concrete with the PVC pipe refersto a structural member where the PVC pipe and the concreteinside it bear loads together However there are few reports onits research Kurt [20] studied the effect of the slenderness ratioon the strength of concrete with the PVC pipe )e experi-mental results in [21] showed that both concrete strength andPVC pipe thickness have significant effects on the compressivestrength of concrete with the PVC pipe and a similar obser-vation was reported by Saadoon [22] )ese experiments showthat the concrete with the PVC pipe outperforms the concretewithout the PVC pipe in strength and ductility

)is paper proposed an innovative type of conventionaltriaxial test method (PMM) We use the PVC pipe as amould to cast concrete and as a membrane to isolate oilduring the testing Compared with the traditional testmethod (TMM) PMM has the following advantages

(1) In the process of concrete forming PVC pipes asdisposable moulds are suitable for casting a largenumber of concrete specimens at one time Cur-rently PVC pipes are priced relatively low and inample supply in various diameters )ey can be usedto form concrete specimens with various diametersand heights In addition PMM is free from cleaningassembling and disassembling moulds which is ahuge boost to test efficiency

(2) In the process of specimen processing PMM is moreconvenient for specimen cutting and grinding seeSection 22 for details

(3) In the process of triaxial loading the PVC pipe canalso be used to isolate the oil from the concretethereby simplifying the specimen sealing processbefore the triaxial test (refer to Section 23 fordetails)

If coarse aggregates are used in concrete it is worthnoting that PMM also has an edge effect like TMM

2 Materials and Experiments

21Materials and Specimens In the test the cement appliedwas PmiddotII525R type Portland cement according to the Chi-nese standard )e average diameter of the silica fumeranged from 01 to 03 μm )e average diameter of thequartz powder was 75 μm Two types of quartz sands in thediameter range 180ndash425 μm and 425ndash800 μm respectivelywere mixed by the mass proportion of 1 1 and they wereused as fine aggregates )e silica fume and the quartzpowder were used at the replacement percentages of 20and 27 for the cement to fill up voids that exist in ul-trahigh-strength mortar as well as to improve mechanicalproperties )e cellulose ether (CE) used in low-strengthmortar could prevent mortar from bleeding We propor-tionally used the polycarboxylate superplasticizer admixture(PSA) and the liquid defoamer (LD) )e PVC pipes have anominal pressure of at least 1MPa and are 50mm in di-ameter and 24mm in thickness )e mechanical propertiesof the PVC pipe are presented in Section 3 )e mix pro-portions are given in Table 1 Given the small size of thespecimen no coarse aggregate was used in the specimen

)e mixed mortar was poured into several PVC pipeseach of which is 135mm in height and is sealed at the lowerend by the tape )e specimens were then vibrated on ashaking table to remove the entrapped air bubbles Beforethe specimens were kept in the standard curing room forfour days they were covered with a plastic film )e spec-imens were then cured for six days in a high-temperaturecuring box at 90degC Afterward the specimens were taken outand cured atmospherically for 90 days regardless of the agingeffect on mortar strength Meanwhile three kinds of cubicmortar specimens with a side length of 707mm wereprepared and their average uniaxial compressive strengthsfor 100 days are listed in Table 1 )e standard deviation foraverage uniaxial compressive strength of each mortar is alsolisted in Table 1

22 SpecimenProcessing In the course of cutting the cornerof the mortar specimen surrounded by nothing is oftendamaged (see Figure 1(a)) due to the diagonal pulling effectof the cutter blade For the specimen surrounded by the PVCpipe however the radial restraint provided by the PVC pipecan weaken the diagonal tension generated by the cutterblade thus it can prevent damage on the mortar corner Ascan be seen from Figure 1(b) there is no damage when thespecimen is surrounded by the PVC pipe











Mortar type




Strength(MPa)





Corner damage

(a) (b)







σ1

σ3

σ3

σ2

σ1 = p + q

σ2 = σ3 = p

(a)


of 45 degrees

Radial extensometer







(b)


PVC pipe

Rubber sleeve

Loading head

(a)

Heat-shrink sleeve

Rubber sleeve

Loading head

(b)














0MPa5MPa10MPa

20MPa40MPa70MPa

0

20

40

60

80

q (M

Pa)


Strainεr ε1







(a) (b)




0

10

20

30

40

50

60

70

80

p (M

Pa)

500 10000 1500t (s)

(a)

000

004

008

012

016

020

Dr (

mm

)

500 10000 1500t (s)

(b)







T-UM

T-HM



P-UM

MIP

P-HM

MIP











(a) (b)







150

100

50

0

ndash001

ndash002

ndash003

ndash004

q (M

Pa)

u r (m

m)

Peak point

Peak point

UMHM

LMPVC

0001 0002 0003 00040000ε1


70MPa

40MPa

20MPa

10MPa

5MPa

0MPa

εr ε1

0

50

100

150

200

250

300

350q

(MPa

)


Strain

(a)

70MPa40MPa

20MPa

10MPa5MPa

0MPa

0

50

100

150

200

250

300

350

q (M

Pa)

εr ε1


Strain

(b)

70MPa40MPa

20MPa

10MPa

5MPa

0MPa

εr ε1

0

50

100

150

200

250

q (M

Pa)

ndash002 000 002 004 006 008ndash004

Strain

(c)

70MPa40MPa

20MPa

10MPa5MPa

0MPa

0

50

100

150

200

250

q (M

Pa)

εr ε1

ndash002 000 002 004 006 008ndash004

Strain

(d)













T-UMP-UM

T-HMP-HM

50

100

150

200

250

300

350

400

σ_ max

(MPa

)

10 20 30 40 50 60 700p (MPa)





σmax

fc 1 +

kσ3fc

(1)



Aσ3fc

1113888 1113889

2

+ Bσ3fc

1113888 1113889 + 1

11139741113972

minusσmax

fc 0 (2)





strengthdifference


Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode


008

006

004

002

000

ndash002

ndash004

ε rmε 1

m


T-UMP-UMT-HMP-HM

10 20 30 40 50 60 700p (MPa)




5 Conclusions







T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(a)


T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(b)



Type k R2

T-UM 4109 0772 16P-UM 3612 0934 36T-HM 3483 0993 65P-HM 3192 0999 15


Type A B R2





Data Availability




Acknowledgments


References















































Mortar type




Strength(MPa)





Corner damage

(a) (b)







σ1

σ3

σ3

σ2

σ1 = p + q

σ2 = σ3 = p

(a)


of 45 degrees

Radial extensometer







(b)


PVC pipe

Rubber sleeve

Loading head

(a)

Heat-shrink sleeve

Rubber sleeve

Loading head

(b)














0MPa5MPa10MPa

20MPa40MPa70MPa

0

20

40

60

80

q (M

Pa)


Strainεr ε1







(a) (b)




0

10

20

30

40

50

60

70

80

p (M

Pa)

500 10000 1500t (s)

(a)

000

004

008

012

016

020

Dr (

mm

)

500 10000 1500t (s)

(b)







T-UM

T-HM



P-UM

MIP

P-HM

MIP











(a) (b)







150

100

50

0

ndash001

ndash002

ndash003

ndash004

q (M

Pa)

u r (m

m)

Peak point

Peak point

UMHM

LMPVC

0001 0002 0003 00040000ε1


70MPa

40MPa

20MPa

10MPa

5MPa

0MPa

εr ε1

0

50

100

150

200

250

300

350q

(MPa

)


Strain

(a)

70MPa40MPa

20MPa

10MPa5MPa

0MPa

0

50

100

150

200

250

300

350

q (M

Pa)

εr ε1


Strain

(b)

70MPa40MPa

20MPa

10MPa

5MPa

0MPa

εr ε1

0

50

100

150

200

250

q (M

Pa)

ndash002 000 002 004 006 008ndash004

Strain

(c)

70MPa40MPa

20MPa

10MPa5MPa

0MPa

0

50

100

150

200

250

q (M

Pa)

εr ε1

ndash002 000 002 004 006 008ndash004

Strain

(d)













T-UMP-UM

T-HMP-HM

50

100

150

200

250

300

350

400

σ_ max

(MPa

)

10 20 30 40 50 60 700p (MPa)





σmax

fc 1 +

kσ3fc

(1)



Aσ3fc

1113888 1113889

2

+ Bσ3fc

1113888 1113889 + 1

11139741113972

minusσmax

fc 0 (2)





strengthdifference


Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode


008

006

004

002

000

ndash002

ndash004

ε rmε 1

m


T-UMP-UMT-HMP-HM

10 20 30 40 50 60 700p (MPa)




5 Conclusions







T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(a)


T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(b)



Type k R2

T-UM 4109 0772 16P-UM 3612 0934 36T-HM 3483 0993 65P-HM 3192 0999 15


Type A B R2





Data Availability




Acknowledgments


References










































σ1

σ3

σ3

σ2

σ1 = p + q

σ2 = σ3 = p

(a)


of 45 degrees

Radial extensometer







(b)


PVC pipe

Rubber sleeve

Loading head

(a)

Heat-shrink sleeve

Rubber sleeve

Loading head

(b)














0MPa5MPa10MPa

20MPa40MPa70MPa

0

20

40

60

80

q (M

Pa)


Strainεr ε1







(a) (b)




0

10

20

30

40

50

60

70

80

p (M

Pa)

500 10000 1500t (s)

(a)

000

004

008

012

016

020

Dr (

mm

)

500 10000 1500t (s)

(b)







T-UM

T-HM



P-UM

MIP

P-HM

MIP











(a) (b)







150

100

50

0

ndash001

ndash002

ndash003

ndash004

q (M

Pa)

u r (m

m)

Peak point

Peak point

UMHM

LMPVC

0001 0002 0003 00040000ε1


70MPa

40MPa

20MPa

10MPa

5MPa

0MPa

εr ε1

0

50

100

150

200

250

300

350q

(MPa

)


Strain

(a)

70MPa40MPa

20MPa

10MPa5MPa

0MPa

0

50

100

150

200

250

300

350

q (M

Pa)

εr ε1


Strain

(b)

70MPa40MPa

20MPa

10MPa

5MPa

0MPa

εr ε1

0

50

100

150

200

250

q (M

Pa)

ndash002 000 002 004 006 008ndash004

Strain

(c)

70MPa40MPa

20MPa

10MPa5MPa

0MPa

0

50

100

150

200

250

q (M

Pa)

εr ε1

ndash002 000 002 004 006 008ndash004

Strain

(d)













T-UMP-UM

T-HMP-HM

50

100

150

200

250

300

350

400

σ_ max

(MPa

)

10 20 30 40 50 60 700p (MPa)





σmax

fc 1 +

kσ3fc

(1)



Aσ3fc

1113888 1113889

2

+ Bσ3fc

1113888 1113889 + 1

11139741113972

minusσmax

fc 0 (2)





strengthdifference


Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode


008

006

004

002

000

ndash002

ndash004

ε rmε 1

m


T-UMP-UMT-HMP-HM

10 20 30 40 50 60 700p (MPa)




5 Conclusions







T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(a)


T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(b)



Type k R2

T-UM 4109 0772 16P-UM 3612 0934 36T-HM 3483 0993 65P-HM 3192 0999 15


Type A B R2





Data Availability




Acknowledgments


References

















































0MPa5MPa10MPa

20MPa40MPa70MPa

0

20

40

60

80

q (M

Pa)


Strainεr ε1







(a) (b)




0

10

20

30

40

50

60

70

80

p (M

Pa)

500 10000 1500t (s)

(a)

000

004

008

012

016

020

Dr (

mm

)

500 10000 1500t (s)

(b)







T-UM

T-HM



P-UM

MIP

P-HM

MIP











(a) (b)







150

100

50

0

ndash001

ndash002

ndash003

ndash004

q (M

Pa)

u r (m

m)

Peak point

Peak point

UMHM

LMPVC

0001 0002 0003 00040000ε1


70MPa

40MPa

20MPa

10MPa

5MPa

0MPa

εr ε1

0

50

100

150

200

250

300

350q

(MPa

)


Strain

(a)

70MPa40MPa

20MPa

10MPa5MPa

0MPa

0

50

100

150

200

250

300

350

q (M

Pa)

εr ε1


Strain

(b)

70MPa40MPa

20MPa

10MPa

5MPa

0MPa

εr ε1

0

50

100

150

200

250

q (M

Pa)

ndash002 000 002 004 006 008ndash004

Strain

(c)

70MPa40MPa

20MPa

10MPa5MPa

0MPa

0

50

100

150

200

250

q (M

Pa)

εr ε1

ndash002 000 002 004 006 008ndash004

Strain

(d)













T-UMP-UM

T-HMP-HM

50

100

150

200

250

300

350

400

σ_ max

(MPa

)

10 20 30 40 50 60 700p (MPa)





σmax

fc 1 +

kσ3fc

(1)



Aσ3fc

1113888 1113889

2

+ Bσ3fc

1113888 1113889 + 1

11139741113972

minusσmax

fc 0 (2)





strengthdifference


Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode


008

006

004

002

000

ndash002

ndash004

ε rmε 1

m


T-UMP-UMT-HMP-HM

10 20 30 40 50 60 700p (MPa)




5 Conclusions







T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(a)


T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(b)



Type k R2

T-UM 4109 0772 16P-UM 3612 0934 36T-HM 3483 0993 65P-HM 3192 0999 15


Type A B R2





Data Availability




Acknowledgments


References










































(a) (b)




0

10

20

30

40

50

60

70

80

p (M

Pa)

500 10000 1500t (s)

(a)

000

004

008

012

016

020

Dr (

mm

)

500 10000 1500t (s)

(b)







T-UM

T-HM



P-UM

MIP

P-HM

MIP











(a) (b)







150

100

50

0

ndash001

ndash002

ndash003

ndash004

q (M

Pa)

u r (m

m)

Peak point

Peak point

UMHM

LMPVC

0001 0002 0003 00040000ε1


70MPa

40MPa

20MPa

10MPa

5MPa

0MPa

εr ε1

0

50

100

150

200

250

300

350q

(MPa

)


Strain

(a)

70MPa40MPa

20MPa

10MPa5MPa

0MPa

0

50

100

150

200

250

300

350

q (M

Pa)

εr ε1


Strain

(b)

70MPa40MPa

20MPa

10MPa

5MPa

0MPa

εr ε1

0

50

100

150

200

250

q (M

Pa)

ndash002 000 002 004 006 008ndash004

Strain

(c)

70MPa40MPa

20MPa

10MPa5MPa

0MPa

0

50

100

150

200

250

q (M

Pa)

εr ε1

ndash002 000 002 004 006 008ndash004

Strain

(d)













T-UMP-UM

T-HMP-HM

50

100

150

200

250

300

350

400

σ_ max

(MPa

)

10 20 30 40 50 60 700p (MPa)





σmax

fc 1 +

kσ3fc

(1)



Aσ3fc

1113888 1113889

2

+ Bσ3fc

1113888 1113889 + 1

11139741113972

minusσmax

fc 0 (2)





strengthdifference


Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode


008

006

004

002

000

ndash002

ndash004

ε rmε 1

m


T-UMP-UMT-HMP-HM

10 20 30 40 50 60 700p (MPa)




5 Conclusions







T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(a)


T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(b)



Type k R2

T-UM 4109 0772 16P-UM 3612 0934 36T-HM 3483 0993 65P-HM 3192 0999 15


Type A B R2





Data Availability




Acknowledgments


References










































T-UM

T-HM



P-UM

MIP

P-HM

MIP











(a) (b)







150

100

50

0

ndash001

ndash002

ndash003

ndash004

q (M

Pa)

u r (m

m)

Peak point

Peak point

UMHM

LMPVC

0001 0002 0003 00040000ε1


70MPa

40MPa

20MPa

10MPa

5MPa

0MPa

εr ε1

0

50

100

150

200

250

300

350q

(MPa

)


Strain

(a)

70MPa40MPa

20MPa

10MPa5MPa

0MPa

0

50

100

150

200

250

300

350

q (M

Pa)

εr ε1


Strain

(b)

70MPa40MPa

20MPa

10MPa

5MPa

0MPa

εr ε1

0

50

100

150

200

250

q (M

Pa)

ndash002 000 002 004 006 008ndash004

Strain

(c)

70MPa40MPa

20MPa

10MPa5MPa

0MPa

0

50

100

150

200

250

q (M

Pa)

εr ε1

ndash002 000 002 004 006 008ndash004

Strain

(d)













T-UMP-UM

T-HMP-HM

50

100

150

200

250

300

350

400

σ_ max

(MPa

)

10 20 30 40 50 60 700p (MPa)





σmax

fc 1 +

kσ3fc

(1)



Aσ3fc

1113888 1113889

2

+ Bσ3fc

1113888 1113889 + 1

11139741113972

minusσmax

fc 0 (2)





strengthdifference


Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode


008

006

004

002

000

ndash002

ndash004

ε rmε 1

m


T-UMP-UMT-HMP-HM

10 20 30 40 50 60 700p (MPa)




5 Conclusions







T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(a)


T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(b)



Type k R2

T-UM 4109 0772 16P-UM 3612 0934 36T-HM 3483 0993 65P-HM 3192 0999 15


Type A B R2





Data Availability




Acknowledgments


References














































(a) (b)







150

100

50

0

ndash001

ndash002

ndash003

ndash004

q (M

Pa)

u r (m

m)

Peak point

Peak point

UMHM

LMPVC

0001 0002 0003 00040000ε1


70MPa

40MPa

20MPa

10MPa

5MPa

0MPa

εr ε1

0

50

100

150

200

250

300

350q

(MPa

)


Strain

(a)

70MPa40MPa

20MPa

10MPa5MPa

0MPa

0

50

100

150

200

250

300

350

q (M

Pa)

εr ε1


Strain

(b)

70MPa40MPa

20MPa

10MPa

5MPa

0MPa

εr ε1

0

50

100

150

200

250

q (M

Pa)

ndash002 000 002 004 006 008ndash004

Strain

(c)

70MPa40MPa

20MPa

10MPa5MPa

0MPa

0

50

100

150

200

250

q (M

Pa)

εr ε1

ndash002 000 002 004 006 008ndash004

Strain

(d)













T-UMP-UM

T-HMP-HM

50

100

150

200

250

300

350

400

σ_ max

(MPa

)

10 20 30 40 50 60 700p (MPa)





σmax

fc 1 +

kσ3fc

(1)



Aσ3fc

1113888 1113889

2

+ Bσ3fc

1113888 1113889 + 1

11139741113972

minusσmax

fc 0 (2)





strengthdifference


Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode


008

006

004

002

000

ndash002

ndash004

ε rmε 1

m


T-UMP-UMT-HMP-HM

10 20 30 40 50 60 700p (MPa)




5 Conclusions







T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(a)


T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(b)



Type k R2

T-UM 4109 0772 16P-UM 3612 0934 36T-HM 3483 0993 65P-HM 3192 0999 15


Type A B R2





Data Availability




Acknowledgments


References










































150

100

50

0

ndash001

ndash002

ndash003

ndash004

q (M

Pa)

u r (m

m)

Peak point

Peak point

UMHM

LMPVC

0001 0002 0003 00040000ε1


70MPa

40MPa

20MPa

10MPa

5MPa

0MPa

εr ε1

0

50

100

150

200

250

300

350q

(MPa

)


Strain

(a)

70MPa40MPa

20MPa

10MPa5MPa

0MPa

0

50

100

150

200

250

300

350

q (M

Pa)

εr ε1


Strain

(b)

70MPa40MPa

20MPa

10MPa

5MPa

0MPa

εr ε1

0

50

100

150

200

250

q (M

Pa)

ndash002 000 002 004 006 008ndash004

Strain

(c)

70MPa40MPa

20MPa

10MPa5MPa

0MPa

0

50

100

150

200

250

q (M

Pa)

εr ε1

ndash002 000 002 004 006 008ndash004

Strain

(d)













T-UMP-UM

T-HMP-HM

50

100

150

200

250

300

350

400

σ_ max

(MPa

)

10 20 30 40 50 60 700p (MPa)





σmax

fc 1 +

kσ3fc

(1)



Aσ3fc

1113888 1113889

2

+ Bσ3fc

1113888 1113889 + 1

11139741113972

minusσmax

fc 0 (2)





strengthdifference


Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode


008

006

004

002

000

ndash002

ndash004

ε rmε 1

m


T-UMP-UMT-HMP-HM

10 20 30 40 50 60 700p (MPa)




5 Conclusions







T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(a)


T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(b)



Type k R2

T-UM 4109 0772 16P-UM 3612 0934 36T-HM 3483 0993 65P-HM 3192 0999 15


Type A B R2





Data Availability




Acknowledgments


References
















































T-UMP-UM

T-HMP-HM

50

100

150

200

250

300

350

400

σ_ max

(MPa

)

10 20 30 40 50 60 700p (MPa)





σmax

fc 1 +

kσ3fc

(1)



Aσ3fc

1113888 1113889

2

+ Bσ3fc

1113888 1113889 + 1

11139741113972

minusσmax

fc 0 (2)





strengthdifference


Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode


008

006

004

002

000

ndash002

ndash004

ε rmε 1

m


T-UMP-UMT-HMP-HM

10 20 30 40 50 60 700p (MPa)




5 Conclusions







T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(a)


T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(b)



Type k R2

T-UM 4109 0772 16P-UM 3612 0934 36T-HM 3483 0993 65P-HM 3192 0999 15


Type A B R2





Data Availability




Acknowledgments


References








































σmax

fc 1 +

kσ3fc

(1)



Aσ3fc

1113888 1113889

2

+ Bσ3fc

1113888 1113889 + 1

11139741113972

minusσmax

fc 0 (2)





strengthdifference


Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode

Residualstrength

Failuremode


008

006

004

002

000

ndash002

ndash004

ε rmε 1

m


T-UMP-UMT-HMP-HM

10 20 30 40 50 60 700p (MPa)




5 Conclusions







T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(a)


T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(b)



Type k R2

T-UM 4109 0772 16P-UM 3612 0934 36T-HM 3483 0993 65P-HM 3192 0999 15


Type A B R2





Data Availability




Acknowledgments


References







































5 Conclusions







T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(a)


T-UMP-UMT-HMP-HM

10

15

20

25

30

35

40

45

σ max

f c

02 04 06 08 1000σ3fc

(b)



Type k R2

T-UM 4109 0772 16P-UM 3612 0934 36T-HM 3483 0993 65P-HM 3192 0999 15


Type A B R2





Data Availability




Acknowledgments


References








































Data Availability




Acknowledgments


References















































Documents

An Innovative Method for Conventional Triaxial Tests of