Dynamic strain softening of concrete in compression under rapid loading K. Fujikake*-, J. Mizuno*, A. Suzuki*, T. Ohno" & T.

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1 Transactins n the Built Envirnment vl 2, 1998 WIT Press, ISSN Dynamic strain sftening f cncrete in cmpressin under rapid lading K. Fujikake*-, J. Mizun*, A. Suzuki*, T. hn" & T. Nnaka' * Nuclear Department, Kajima Crpratin, Tky, 16 Japan * Disaster Preventin Research Institute Kyt University, Uji, 611 Japan Abstract This study is t investigate the strain sftening behavirs f cncrete material in cmpressin under rapid ladings. The length f specimen, the cnstraint f bth ends and the lading-rate are chsen as test parameters. Frm tests results, the effects f these parameters n the pre-peak behavirs, the stress sftening behavirs and the strain lcalizatin are examined. T measure precisely the strain in the sftening regin after the maximum stress, the strain measuring rd, called SMR, is prpsed in this study. 1 Intrductin There are a lt f prblems t be slved the behavirs and failure mechanism f cncrete structures subjected t impact lads. Thus it is imprtant t investigate quantitatively the dynamic prperties f cncrete materials under rapid lading. The results f cmpressive rapid lading tests and many studies related n the cmpressive prperties f cncrete have been reprted. Hwever, the assessment f the dynamic stress-strain relatin r the dynamic cnstitutive law f cncrete has nt

2 Transactins n the Built Envirnment vl 2, 1998 WIT Press, ISSN Structures Under Shck and Impact been established. Understanding the prcess f dynamic stress sftening under rapid lading is very imprtant t find the dynamic failure mechanism f cncrete. Cncrete is a hetergeneus material cmpsed f aggregate, sand and cement, thus micr-cracks exist riginally in cncrete even befre the applicatin f any lad. Upn lading, these micr-cracks prpagate and develp, and a zne f damage is frmed due t the calescence f micr-cracks. The strength f cncrete decreases after the peak stress as defrmatin increases. This phenmenn is called the stress sftening. Accrding t the past experimental studies n the cncrete subjected t uniaxial static cmpressive lading, the stress-strain curves in the pst-peak regin are much affected by the specimen length, the cnditin f end cnstraint and/r the measuring length f strain[2] ~[4]. Therefre the pst-peak prtin f these curves des nt reflect an intrinsic law f the behavir f cncrete material. 2 utline f Experiment 2.1 Cncept f Measuring verall Defrmatin and Lcal Strain in Cncrete Specimen In this study, hw t measure precisely the stress-strain relatin after the peak stress, that is; the pst-peak behavir, f cylindrical cncrete specimen under the uniaxial cmpressive rapid lading is fcused n. Generally, tests fr uniaxial cmpressive rapid lading, strain gauges which is t be attached t the surface f cncrete specimen have been cmmnly used t measure the strain. Frm the results f static uniaxial cmpressive tests, we have learned that the strain behavir, which is btained by averaging data frm strain gauges n the surface f specimen r verall defrmatin f specimen, quite differs after the peak stress[5]. This may be the reasn that the strain lcalizes t a certain part after the peak stress and thus the behavirs f strain at each pint f specimen shw the different features crrespndingly t their failure mdes. In the case f rapid lading tests, the methd f measuring verall defrmatin f specimen by means f displacement transducers has sme defects in their respnse, reslutin and fixing cnditins. Therefre, in this study, the ntched acrylic rd is prpsed t emply fr measuring verall defrmatin f specimen after the maximum strength under the uniaxial cmpressive rapid lading. This rd, attached 5 r 8 strain gauges with the gauge length f 2mm and called SMR; Strain

3 Transactins n the Built Envirnment vl 2, 1998 WIT Press, ISSN Structures Under Shck and Impact 48 acrylic defanned bar ( limn) (a) fr specimen length 2mm str ain gauge / ^L= =:2mm) ri/~i ^ T'^ r ] 1'i 1 1 J S (i si i-j i ml ii lie. defn N ne _ dbar i ^ j j ^^-- mn (b) fr specimen length 4mm Figure 1 : Strain measurement rd / Axial cmpressive strain Strain gauge Figure 2: Assumed strain prfile Measurement Rd as shwn in Figure L is placed in the center f cylindrical cncrete specimen. Since the elastic mdulus f acrylic resin is much smaller than that f cncrete, the defrmatin f cncrete may be nt cnstrained. The bnd between acrylic rd and cncrete is strengthen by making ntches in the rd. Then the lcalized strain in cncrete can be measured by each strain gauge. And then the verall defrmatin f cylindrical cncrete specimen is btained by integrating the measured strain alng the whle length f SMR. Fr example, the assumed strain prfile is btained frm measured strain at each pint n SMR as shwn in Figure 2 and then the verall defrmatin f specimen can be calculated by the fllwing equatin. (1) The interval f strain gauges(4-5mm), t be attached t SMR, determined by executing the preliminary tests. was

4 Transactins n the Built Envirnment vl 2, 1998 WIT Press, ISSN Structures Under Shck and Impact Test series H2-NP H2-NP-NR H2-TP H4 Length f specimen (mm) 2 4 Table 1 Test parameters Test parameters End cnditin Installatin f SMR NP TP Yes N Static Lading rate Lw Medium High N. f specimens w/c 6 W/P 4 W 18 C Table 2 Mix prprtin Unit weight (kg/rn^) LS 15 S 822 G 847 SP Px% 1.8 VA Wx%.25 Air (%) 4. Slump flw (cm) Nte ; P : Pwder(=C+LS), LS : Lime-stne pwder, SP : Superplasticizer, VA : Viscsity agent Experimental Parameters This study is t investigate experimentally the effects f the length f specimen and the setting cnditin f the bth ends f a specimen n the dynamic strain sftening characteristics f cncrete subjected t uniaxial cmpressive rapid lads. The length f cylindrical cncrete specimen, the setting cnditin f specimen and the lading speed were chsen as test parameters as given in Table 1. Tw kinds f cylindrical specimens, the diameter f 1mm and the different length f 2 and 4mm, were emplyed fr tests. Mix prprtin f cncrete fr the specimens is given in Table 2. There are tw types f setting cnditins in this test: 1) bth ends f a specimen were set up directry t the steel lading bar (NP-type) and 2) dubleply Tefln pad with Silicne greased were inserted between a specimen and the steel lading bar (TP-type). T examine the influence f SMR buried in the center f specimen n the stress-strain behavir f cn-

5 Transactins n the Built Envirnment vl 2, 1998 WIT Press, ISSN Structures Under Shck and Impact 485 crete, specimens withut SMR(H2-NP-NR) were als tested. Lads were applied t specimens by 4 srts f speed as static-, lw-, medium-, high-speed ladings. Their lading speeds may be rughly designated by the stress-rate as.2mpa/sec fr static, 2.4 X 1^(MPa/sec) fr lwspeed, 7.5 X 1^(MPa/sec) fr medium-speed and 2.4 X 1^MPa/sec) fr high-speed. Tests were dne times fr each lading speed. 2. Experimental Prcedures In tests, the serv-cntrlled cmpressive lading machine(maximum lad capacity f 98kN) was used fr the static uniaxial cmpressive test and the hydraulic rapid lading machine(maximum lad capacity f 49kN, Maximum lading speed f 4m/sec) was used fr the uniaxial rapid lading test as given in Figure. It has been pinted ut frm the past experimental studies that when the lading device with spherical platens is used, the rtatin f specimen affects seriusly the Figure : Rapid lading machine and test set-up stress-strain relatin after the maximum strength f cncrete [], [4]. Thus, bth ends f all specimens were restricted s as nt t rtate during test. When the lad acted n a cylindrical cncrete specimen is t measure, the lad cell shuld be pssibly placed n the nearest psitin t a specimen and the influence f inertia frce may be remved. Therefre, the shrtened lading bar, which is munted in the lad cell n the reactin flr, is emplyed fr this test. Anther lad cell t be used fr measuring the applied lad is als installed n the upper end f specimen. T examine the inertia frce caused by the defrmatin f specimen, an accelermeter is set n the lading beam f rapid lading machine. Axial cncrete strain n the surface f a specimen and the strain f SMR were measured.

6 Transactins n the Built Envirnment vl 2, 1998 WIT Press, ISSN Structures Under Shck and Impact J C )... c/> 1.4 m -S 1.2 D A H2-NP H2-NP-NR H2-TP H4 Eq.(2).8 1 ^ 1 1^ 1^ 1^ 1^ 1^ Stress Rate (MPa/sec) Figure 4: Relatin between dynamic increase factr and stress-rate Results and Cnsideratins Examining the data f applied lads measured by bth upper and lwer lad cells, it was fund that the difference between tw lad values is equivalent t the inertia frce f lading bar and specimen. Then, the applied lad t a specimen is designated as the measured data frm a lwer lad cell. The stress-rate, designated in this study as a index f lading speed, is the average value f the maximum stress and the initial stress..1 Relatin between Increasing Rate f Cmpressive Strength and Stress-rate Figure 4 shws the btained relatin between the dynamic increase factr (D. I. F.) f cncrete strength in cmpressin and the stress-rate. D.I.F. f cmpressive strength is given by the rati f the dynamic strength t the static ne. The average static cmpressive strengths f cncrete were 45.98MPa fr H2-NP series, 45.4MPa fr H2-NP- NR series, 44.75MPa fr H2-TP series and 45.4MPa fr H4 series, respectively. The static cmpressive strength shws almst the same value regardless f the length f specimen and the setting cnditin. And, thus the influence f SMR can be negligible. D.I.F. f cmpressive strength btained frm this test increases with the increase f the stressrate and this value may be cmparable fr each lading speed. D.I.F. f

7 Transactins n the Built Envirnment vl 2, 1998 WIT Press, ISSN Structures Under Shck and Impact 487 cmpressive strength increases with the increase f the stress-rate in the same as that ne reprted by the past studies. Each value f D.I.F. given by the results frm all tests is cmparable t the value at each stress-rate. Cnsequently, D.I.F. f the cmpressive strength depends nly n the stress-rate. The relatin between D.I.F. and the stress-rate btained frm this test can be expressed by the equatin as: Ai^AI L '^^ (2) /;, "l*j in which d,, is the stress rate fr static lading (.2MPa/sec), /^ is the static cmpressive strength f cncrete (MPa), d is stress rate fr rapid ladings (MPa/sec), /^ is the cmpressive strength f cncrete laded by any stress rate d (MPa), a,( are experimental cnstants (a =.585,=1.585)..2 Strain Lcalizatin The failure mdes f specimens in each test series can be categrized as fllws. In the case f H2-NP and H4 series, either the hur-glass type failure mde r the slant shear failure mde were bserved. In the case f H2-TP series, the mixed failure mdes accmpanied with the prminent splitting failure mde and the shear failure mde were bserved. The failure mdes are nt affected nticeably by the difference f the stress-rates. Typical examples f axial strain prfiles in the sftening regin after the peak stress fr bth static and high rate ladings are shwn in Figures 5-7. Each line f axial strain prfile crrespnds t the peak stress and the stress at each 1% interval f the peak stress in the descending prtin. In the ascending prtin befre the peak stress, the strain in a certain zne where damage is lcalized after the peak stress, have the tendency f a little increase after apprximately 9% f the peak stress cmparing t the strain in the ther area. Even then, the strains at each pint n SMR never decrease befre the peak stress. In the sftening regin after the peak stress, it may be recgnized that the existence f tw different regins: that is, the regin where the strain increases and where the strain decreases. Therefre, it may be cncluded that, fr the rapid lading, the strain lcalizatin will be happened at the peak stress regardless f the specimen length, the end cnstraint and the stress-rate. This is the same result as the static experimental result f

8 Transactins n the Built Envirnment vl 2, 1998 WIT Press, ISSN Structures Under Shck and Impact Trrenti etal.[4]. There is a big difference between tw strain prfiles fr H2-NP series and H2-TP series in bth static and high rate ladings as shwn in Figures 5 and 6. This may be resulted by the difference f the end cnditins. When the frictin at bth ends f a specimen becmes large. the axial strain near the end decreases and the strain near the central part remarkably increases. That is, the strain lcalizes t a certain regin f the middle part f a specimen regardless f the stress-rate. When the frictinal end cnstraint becmes small, the strain at either ends remarkably increases. In spite f the existence f Tefln pads at bth ends t remve frictinal resistance, the axial strain distributin is nt unifrm alng the specimen length. That is, the axial strain lcalizes t either end f a specimen. In the case f H4 series, the strain at near the middle f either upper r lwer half f a specimen remarkably increases. The axial strain prfiles in the zne f strain lcalizatin are similar t thse f H2-NP series. The length f the zne where strain lcalizes were apprximately 15cm in H2-NP series, 1cm in H2-TP series and 2cm in H4 series, regardless f the stress-rate. Frm test results, it can be cncluded that the length f the strain lcalizatin is nt affected nticeably by the difference f stress-rates.. Effects f Experimental Parameters n Strain Sftening Behavirs Figure 8 shws the stress-average strain relatins btained frm each test. The average strain is the average f measurements by 5-8 strain gauges n SMR. By emplying SMR, presented in this study, the stressstrain behavirs f cncrete after the peak stress can be well measured. In the case f rapid lading t a cncrete specimen, increasing the stress-rate, the cmpressive strength and the tangent mdulus f cncrete increases and the sftening slpe after the peak stress in the stressstrain relatin shws a sharp descent. When cncrete specimens are in the same stress-rate, the sftening behavir will be greatly influenced by the specimen length and the end cnditin f a specimen. In all tests, the strain at the maximum strength becmes minimum fr the lw speed lading and it will increase with the increase f lading speed. The envelpe line f the maximum stress is given in Figure 8(a). It can be recgnized frm this line that the stress-rate which minimizes the strain at the maximum stress may be existed between static and lw speed ladings.

9 Transactins n the Built Envirnment vl 2, 1998 WIT Press, ISSN Structures Under Shck and Impact IE % % 1 ^ Cmpressive strain (LI) (a) Static lading Cmpressive strain (LI) (*>) High rate lading Figure 5: Strain prfiles (H2-NP series) 2 15 % 1 : ^ IE Z Cmpressive strain (LI) (a) Static lading Cmpressive strain (LI) (b) High rate lading Figure 6: Strain prfiles (H2-TP series) 4 5 " 25 % 2 # 15 ^ Cmpressive strain (LI) (a) Static lading Figure 7: Strain prfiles (H4 series) Cmpressive strain (LI) (b) High rate lading

10 Transactins n the Built Envirnment vl 2, 1998 WIT Press, ISSN Structures Under Shck and Impact E Ave. Axial Cmpressive Strain (\i) (a) H2-NP series -15 E Ave. Axial Cmpressive Strain (b) H2-TP series -5-1 Ave. Axial Cmpressive Strain (c) H4 series Figure 8: Stress - average axial Cmpressive strain curves

11 Transactins n the Built Envirnment vl 2, 1998 WIT Press, ISSN Structures Under Shck and Impact Cncluding Remarks The fllwing cncluding remarks are btained frm this study. 1. By emplying SMR prpsed in this study, it is pssible t measure reliably the lcal strains and the verall defrmatin f specimens under the rapid ladings. 2. In the case f the uniaxial cmpressive rapid lading, the lcalizatin f strain will be happened at the maximum stress and in a certain regin. The end cnditin f a specimen makes a great difference in the strain distributin f the lcalized regin.. The sftening behavirs f cncrete after the peak stress will be greatly influenced by the difference f the stress-rates, the lengths and end cnditins f specimens. Acknwledgement This study is partly supprted by the research fund f Disaster Preventin Research Institute Kyt University (N.8P-l). The authrs wuld like t express their gratitude t Prf. Sidney Mindess, University f British Clumbia, fr his valuable cmments t this study. References [1] Bischff, P. H & Perry, S. H, Cmpressive behaviur f cncrete at high strain rates. Mat. and Struct., 24, pp , [2] Jansen, D. C. & Shah, S. P., Effect f length n cmpressive strain sftening f cncrete, J. fengrg. Mech., pp.25-5, Jan., [] Chi, S., Thienel, K. -C, & Shah, S. P., Strain sftening f cncrete in cmpressin under different end cnstraints, Mag. f Cnr. K&y., 48, N.175, ppi-115, June, [4] Trrenti, J. M, Benaija, E. H & Bulay, C, Influence f bundary cnditins n strain sftening in cncrete cmpressin test, J f Engrg. Mech., Vl.119, N.12, pp , Dec., 199. [5] Van Mier, J. G. M., Fracture Prcesses f Cncrete, CRC Press, pp , 1997.

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