ANALYTICAL MODEL FOR PREDICTING STRESS-STRAIN BEHAVIOUR OF BACTERIAL CONCRETE

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1 Internatinal Jurnal f Civil Engineering and Technlgy (IJCIET) Vlume 9, Issue 11, Nvember 018, pp , Article ID: IJCIET_09_11_38 Available nline at ISSN Print: and ISSN Online: IAEME Publicatin Scpus Indexed ANALYTICAL MODEL FOR PREDICTING STRESS-STRAIN BEHAVIOUR OF BACTERIAL CONCRETE K Satya Sai Trimurty Naidu Research Schlar f Civil Engineering, JNTUH CEH, Hyderabad. M V Seshagiri Ra Ex-Prfessr, JNTUH CEH and Prfessr, CVR Cllege f Engineering, Hyderabad. V Srinivasa Reddy Prfessr, Department f Civil Engineering, GRIET, Hyderabad. ABSTRACT Bacillus subtilis, a mineral precipitating micrrganism, when intrduced int cncrete prduces calcium carbnate crystals which seals the micr cracks and pres in the cncrete. This prcess imparts high strength and durability t bacteria treated cncrete alng with enhancement in ther mechanical prperties. In rder t study ne such mechanical prperty, the stress-strain behavir f bacterial cncrete, apprpriate analytic stress-strain mdel is established that capture the real (bservable) behavir. In this paper, an attempt is made t develp a mathematical mdel fr predicting the stress-strain behaviur f bacteria induced high strength cncrete. Keywrds:-Bacterial cncrete, stress-strain curves, Saenz mdel, Bacillus subtilis, tughness. Cite this Article: K Satya Sai Trimurty Naidu, M V Seshagiri Ra and V Srinivasa Reddy, Analytical Mdel fr Predicting Stress- Behaviur f Bacterial Cncrete, Internatinal Jurnal f Civil Engineering and Technlgy, 9(11), 018, pp INTRODUCTION Fr decades, many researchers develped empirical and semi-empirical stress-strain relatinships t describe the behavir f cncrete in cmpressin. The better the stress-strain mdel, the mre reliable is the estimate f strength and defrmatin behavir f cncrete structural members. The cmpressive stress-strain behavir f cncrete is a significant issue in the flexural analysis f reinfrced cncrete beams and clumns. The stress-strain curve f cncrete is als useful fr investigating the ductility f cncrete. Mrever, the ttal area under editr@iaeme.cm

2 K Satya Sai Trimurty Naidu, M V Seshagiri Ra and V Srinivasa Reddy the stress-strain curve can represent the amunt f energy absrbed by the specimen under lading. A stress - strain curve is a graph btained by pltting the values f stresses and strains btained by testing cylinders f standard size made with cncrete under uni-axial cmpressin. It is bserved frm the stress-strain plts that, n prtin f the curves is in the frm f a straight line even thugh the stress strain relatin fr cement paste and aggregate when tested individually is practically linear. In cncrete the rate f increase f stress is less than that f increase in strain because f the frmatin f micr cracks, between the interfaces f the aggregate and the cement paste. Thus the stress strain curve is nt linear. In cntrlled cncrete, the value f stress is maximum crrespnding t a strain f abut 0.00 and further ges n decreasing with the increasing strain, giving a drpping curve till it terminates at ultimate crushing strain. After btaining the stress-strain behavir f cntrlled and bacterial cncrete mixes experimentally, an attempt is made by validating it against the analytical stress-strain curves fr cntrlled and bacterial cncrete mixes.. METHODOLOGY This paper mainly aims at utilizing the best attributes f earlier mdels and prpses a new stress-strain mdel that can well represent the verall stress-strain behavir f high strength bacterial cncrete mixes. After btaining the stress-strain behavir f cntrlled and bacterial cncrete experimentally, empirical equatins are develped t represent uni-axial stress-strain behavir f cntrlled and bacterial cncrete mixes. Frm these empirical equatins, theretical stresses fr cntrlled and bacterial cncrete are calculated and cmpared with experimental values. The prpsed equatins have shwn gd crrelatin with experimental values validating the mathematical mdel develped. The prpsed empirical equatins can be used as stress blck in analyzing the flexural behavir f cntrlled and bacterial cncrete. 3. EXPERIMENTAL INVESTIGATIONS In the present study, Stress- behavir f cntrlled and bacterial cncrete f high strength grades (M60 and M80) are studied. The test is carried ut n cylindrical specimens f diameter 150 mm and height 300 mm. Ttal 1 cylinders f standard size are cast with the specified cntrlled and bacterial cncrete mixes and tested in axial cmpressin under strain cntrl and stress-strain behavir is bserved by pltting stresses against strains. The capped cylindrical specimen is attached with setup having tw dial gauges and is placed n the mvable crss head f the testing machine and centered crrectly. The dial gauges having least cunt f 0.0mm is used. The specimen is placed in a cmputer cntrlled universal testing machine (UTM) f 3000 kn capacity. Fr satisfactry recrding f strain, the crss head mvement f 0.0 mm per secnd is suggested by the previus researchers. The specimens are tested under strain cntrl under uni-axial cmpressin as per IS : t get the stressstrain characteristics. 4. MATHEMATICAL MODELING FOR STRESS-STRAIN BEHAVIOUR 4.1. Mathematical Mdels available fr Stress- behaviur f Cncrete Many mdels were develped fr the Stress- behaviur predictin f cncrete by many researchers. Sme mdels are cnsidered belw editr@iaeme.cm

3 Analytical Mdel fr Predicting Stress- Behaviur f Bacterial Cncrete Desayi s and Krishnan s Mdel (1964) This mdel is a derivatin frm Saenz s riginal equatin. Fr nrmal strength cncrete, stressstrain relatinship is given by Ax f = 1 + Bx Where f = The Nrmalized stress (f / f ) ; x = Nrmalized strain ( / ) and A, B are the cnstants and they can be fund ut by using bundary cnditins. This mdel is valid nly t ascending prtin f stress-strain curve Mdified Saenz Mdel (1964) Cnsidering the limitatin f analytical equatin prpsed by Desayi et al, Saenz prpsed a mdel by taking int accunt bth the ascending and descending prtins f the stress-strain Ax curve. This mdel is in the frm f y = Where y = σ / σ 1+ Bx + Cx u and x = / u Hgnestad Mdel (1955) Fr Nrmal strength cncrete up t ascending prtin: The stress-strain mdel is ' fc = fc { ( / ) ( / ) } where fc = cmpressive strength ; = strain at peak stress = ( fc' ) ¼ Wang et al, Mdel (1978) The mdel used by Wang et al. is in the frm f f A( / ) + B( / ) = ' c fc 1+ C( / ) + D( / ) Hwever instead f using ne set f the cefficients A, B, C, and D t generate the cmplete curve, Wang et al, used tw sets f cefficients ne fr the ascending branch and the ther t the descending branch. The respective cefficients being btained frm the relevant bundary cnditins assigned t each part f the curve Carriera and Chu Mdel (1985) This mdel is in the frm f ' β ( / ) ' fc = fc In which β = 1 ( f ) β 1 + ( / ) β c / Eit where fc = cylinder ultimate cmpressive strength and = strain at ultimate stress; Eit = Initial tangent mdulus 4.. Prpsed Mdel fr Stress- behavir f bacterial cncrete Of all the abve stress-strain mdels, simplified and the mdified single variable plynmial equatins based n mdified Saenz s mdel that fits with develped nrmalized stress-strain curves seems t be valid fr bth ascending and descending prtins f the curve. The develped equatins fr ascending and descending prtins f analytical stress-strain curve are in the frm f Ax y 1 Bx Cx Dx y = 1+ Ex + Fx = And editr@iaeme.cm

4 K Satya Sai Trimurty Naidu, M V Seshagiri Ra and V Srinivasa Reddy where y is the stress at any level ; x is the crrespnding strain at that level; A, B, C are the cnstants fr ascending prtin and D, E, F are the cnstants fr descending prtin f analytical stress-strain curve. Similarly, the equatins fr ascending and descending prtins f nn-dimensinal stress-strain curve are in the frm f f / f = A 1 ( / ) /(1+ B 1 ( / ) + C 1 ( / ) ) and f / f = D 1 ( / ) + /(1+ E 1 ( / ) + F 1 ( / ) ) A 1, B 1, C 1 are the cnstants fr ascending prtin and D 1, E 1, F 1 are the cnstants fr descending prtin f nn-dimensinal stress-strain curve. f / f is nrmalized stress(stress rati) and / is the nrmalized strain (strain rati).cnstants are evaluated based n the bundary cnditins f nrmalized stress-strain curves fr bth cntrlled and bacterial cncrete. Bundary cnditins fr ascending and descending prtins f stress-strain curves are, (1) At the rigin the rati f stresses and strains are zer i.e. at ( / )= 0,(f / f ) = 0 () The strain rati ( / ) and stress rati at the peak f the nn-dimensinal stress-strain curve is unity. i.e at ( / )= 1, (f / f ) = 1 (3) The slpe f nn-dimensinal stress-strain curve at the peak is zer i.e at ( / )=1.0, d(f / f ) / d( / )= 0 (4) At 85% stress rati, the crrespnding values f strain rati is recrded i.e at (f / f ) = 0.85, ( / )=strain rati crrespnding t 0.85 stress rati where f - peak stress and - strain at peak stress ; f and crrespnds t stress and strain values at any ther pint. Bundary cnditins (1), () and (3) are fr determining the cnstants A 1, B 1, C 1 in the ascending prtin f the nrmalized stress-strain curve and (), (3) and (4) are fr determining the cnstants D 1, E 1, F 1 in the descending prtin f the curve.. Crrespnding A, B, C cnstants fr ascending prtin and D, E, F cnstants fr descending prtin f analytical stress-strain curve are then evaluated using equatins A= A 1 (f / ), B= B 1 ( 1/ ) and C= C 1 (1/ ) D= D 1 (f / ), E= E 1 ( 1/ ) and F= F 1 (1/ ) Ultimately analytical equatins giving the cmplete stress-strain behavir are develped fr high strength grades f cntrlled and bacterial cncretes Develpment f Analytical equatins The fllwing tables present cnstants and Analytical equatin fr ascending and descending prtins f nn-dimensinal stress-strain curve. Table 1 Cnstants fr ascending and descending prtins f nn-dimensinal stress-strain curve Grade f Cncrete Cntrlled Cncrete Bacterial Cncrete Ascending prtin Cnstants Descending prtin cnstants Ascending prtin Cnstants Descending prtin cnstants A 1 B 1 C 1 D 1 E 1 F 1 A 1 B 1 C 1 D 1 E 1 F 1 M M editr@iaeme.cm

5 Analytical Mdel fr Predicting Stress- Behaviur f Bacterial Cncrete Grade f Cncrete Table Peak stress values and their crrespnding strains Cntrlled Cncrete Crrespnding strain Peak Stress at peak stress f Bacterial Cncrete Crrespnding strain Peak Stress at peak stress M M Table 3 Cnstants fr ascending and descending prtins f theretical stress-strain curve Cntrlled Cncrete Grade f Ascending prtin Cnstants Descending prtin cnstants Cncrete A B C D E F M M Bacterial Cncrete M M Calculatin f Theretical Stresses using prpsed Analytical Equatins Theretical stresses have been calculated using prpsed empirical equatins fr cntrlled and bacterial cncrete which are derived frm mdified Saenz s mdel in the frm f Ax y 1 Bx Cx = And + + f Dx y = 1+ Ex + Fx Where y is the stress at any level; x is the crrespnding strain at that level After develping empirical equatins fr stress-strain curves f cntrlled and bacterial cncrete, theretical values f stresses are calculated at different values f strains in cncrete based n the develped empirical equatins. These theretical stress-strain curves are cmpared with experimental stress-strain curves and fund that, theretical stress-strain curves have shwn gd crrelatin with experimental stress-strain curves fr all grades f cntrlled and bacterial cncrete mixes. 5. TEST RESULTS The test results f the experimental investigatins are presented belw editr@iaeme.cm

6 K Satya Sai Trimurty Naidu, M V Seshagiri Ra and V Srinivasa Reddy Table 4 Experimental Stress - values f High strength grade cncrete (M60) Cntrlled Cncrete Bacterial Cncrete Stress, Stress, MPa MPa Table 5 Experimental Stress - values f High strength grade cncrete (M80) Cntrlled Cncrete Bacterial Cncrete Stress, Stress, MPa MPa editr@iaeme.cm

7 Analytical Mdel fr Predicting Stress- Behaviur f Bacterial Cncrete Table 6 Experimental and Theretical Stress - values f High strength grade cncrete (M60) Cntrlled Cncrete Bacterial Cncrete Experimental Theretical Experimental Theretical Stress, MPa Stress, MPa Stress, MPa Stress, MPa Table 7 Experimental and Theretical Stress - values f High strength grade cncrete (M80) Cntrlled Cncrete Bacterial Cncrete Experimental Theretical Experimental Theretical Stress, MPa Stress, MPa Stress, MPa Stress, MPa editr@iaeme.cm

8 K Satya Sai Trimurty Naidu, M V Seshagiri Ra and V Srinivasa Reddy M60 Cntrlled Cncrete M60 Bacterial Cncrete M80 Cntrlled Cncrete M80 Bacterial Cncrete Stress (MPa) Figure 1 Stress- Curves editr@iaeme.cm

9 Analytical Mdel fr Predicting Stress- Behaviur f Bacterial Cncrete Figure Graph shwing Experimental and Theretical stress strain values f cntrlled and bacterial cncrete (M60 Grade) Figure 3 Graph shwing Experimental and Theretical stress strain values f cntrlled and bacterial (M80 Grade) editr@iaeme.cm

10 K Satya Sai Trimurty Naidu, M V Seshagiri Ra and V Srinivasa Reddy 6. DISCUSSIONS Frm experimental nn- dimensinal stress-strain data, the theretical nn-dimensinal stress strain data is generated. There is a gd agreement in experimental and theretical values which cnfirms the validatin f prpsed mdel adpted t study the stress-strain behaviur f cntrlled and bacterial cncrete f high strength grades (M60 and M80). Frm the values f stresses and strains, stress-strain curve fr each mix is pltted, taking the average values f the results f the three cylinders. Frm the stress-strain values f cntrlled and bacterial cncrete mixes the crrespnding nrmalized stress-strain values are calculated by dividing each stress value by the peak stress and dividing each strain value by strain at peak strain. Frm the nrmalized stress-strain values f cntrlled and bacterial cncrete mixes, the average nrmalized stress-strain curves are pltted fr cntrlled and bacterial cncrete separately and empirical equatins are prpsed in the frm f y= Ax/(1+Bx+Cx ) fr ascending and descending prtins f cntrlled and bacterial cncrete mixes fr high strength grades f cncrete. Theretical stresses are evaluated and cmpared with experimental stress values t fund that there is very little variatin which validates the prpsed mathematical mdel. Frm the bservatins made frm stress-strain curves f all the cntrlled and bacterial cncrete mixes, the stress-strain behaviur is bserved t be almst similar. The nly difference is that bacterial cncrete mixes have shwn imprved stress values fr the same strain levels cmpared t that f cntrlled cncrete mixes. It can be bserved frm stress-strain curves that fr high strength cncrete, the shape f the ascending part f the stress-strain curve is mre linear and steeper, that results in the increase f elastic mdulus. The strain at peak stress is slightly higher, and the slpe f the descending part is steeper as cmpared t nrmal strength cncrete. That was due t the decrease in the extent f internal micr cracking in higher strength cncrete. In the uniaxial cmpressin f cncrete cylinders, the results shw that the strain at peak stress f nrmal strength cncrete is usually less than that f high perfrmance cncrete, mdulus f elasticity f high perfrmance cncrete is higher than that f nrmal strength cncrete behavir f cntrlled and bacterial cncrete sectins. Fr all different grades f cntrlled and bacterial cncrete, the prpsed equatins have shwn gd crrelatin with experimental values. Frm the literature it appears that mdified secnd degree plynmial as suggested by L.P. Saenz seems t be better fit with apprpriate cnstants suitable fr present curves 7. CONCLUSIONS Frm the experimental results btained thrughut the curse f this study, the fllwing cnclusins can be drawn as fllws: 1. The Bacterial cncrete mixes have shwn imprved stress values fr the same strain levels cmpared t that f cntrlled cncrete mixes in all high strength grades. Average values f strain at peak stress fr cntrlled and bacterial cncrete are very clse t the value f strain at peak stress fr cntrlled cncrete in axial cmpressin which is 0.00 as per IS The analytical equatins fr the stress-strain respnse f cntrlled and bacterial cncrete mixes have been prpsed in the frm f y = Ax / (1+Bx+Cx ), bth fr ascending and descending prtins f the curves with different set f values fr cnstants. The prpsed equatins have shwn gd crrelatin with experimental values. 4. The prpsed empirical equatins can be used as stress blck in analyzing the flexural behaviur f sectins f cntrlled and bacterial cncrete editr@iaeme.cm

11 Analytical Mdel fr Predicting Stress- Behaviur f Bacterial Cncrete 5. The stress-strain curves btained in the experiment fr different grades f cntrlled and bacterial cncrete exhibit a similar trend when cmpared t the empirical equatins f mdified Saenz mdel. S Saenz mathematical mdel is successfully evaluated and validated fr bacterial cncrete. REFERENCES [1] ACI Cmmittee 363, "State-f-the-Art Reprt n High Strength Cncrete," ACI Jurnal, vl. 81, n. 4, pp , July-August, [] Attard, M. M. & Setunge, S Stress-strain relatin-ship f cnfined and uncnfined cncrete. ACI Mate-rials Jurnal 93(5): [3] Carreira D, Chu K-H. Stress-strain relatinship fr plain cncrete in cmpressin, ACI Jurnal, N. 6, 8(1985) [4] Hsu L S, Hsu C T T 1994 Cmplete stress strain behaviur f high strength cncrete under cmpressin. Mag. Cncr. Res. 46: [5] K. K. B. Dahl, "Uniaxial Stress- Curves fr Nrmal and High Strength Cncrete," ABK Reprt n. R8, Department f Structural Engineering, Technical University f Denmark, 199. [6] M. M. Attard and S. Setunge, "Stress- Relatinship f Cnfined and Uncnfined Cncrete," ACI Materials Jurnal, vl. 93, n. 5, pp , September-Octber, [7] Madhu Karthik Murugesan Reddiar (009) Stress- Mdel Of Uncnfined And Cnfined Cncrete And Stress-Blck Parameters, A Ms Thesis, Texas A&M University [8] P. T. Wang, S. P. Shah, and A. E. Naaman, "Stress- Curves f Nrmal and Lightweight Cncrete in Cmpressin," ACI Materials Jurnal, vl. 75, n. 11, pp , Nvember-December, [9] Ppvics, S. (1973). "A numerical apprach t the cmplete stress-strain curves f cncrete." Cement and Cncrete Research, 3(5), [10] Saenz LP. Discussin f Paper By Desai P, Krishnan S. Equatin fr stress-strain curve f cncrete, Jurnal f ACI, Prc., N. 9, 61(1964) [11] Threnfeldt, E., Tmaszewicz, A., and Jensen, J.J. (1987). "Mechanical prperties f highstrength cncrete and applicatin in design." Prc. f the Sympsium n Utilizatin f High-Strength Cncrete, Tapir, Trndheim, Nrway, [1] Tsai, W.T. (1988). "Uniaxial cmpressin stress-strain relatin f cncrete." J. Struct. Eng., 114(9), editr@iaeme.cm