Simplified Inverse Method for Determining the Tensile Strain Capacity of Strain Hardening Cementitious Composites

Transcription

1 Jornal of Advanced Concrete Technology Vol., No., -, Jne 7 / Copyright 7 Japan Concrete Institte Scientific paper Simplified Inverse Method for Determining the Tensile Strain Capacity of Strain Hardening Cementitios Composites Shnzhi Qian and Victor C. Li Received December, accepted 7 April 7 Abstract As emerging advanced constrction materials, strain hardening cementitios composites (SHCCs) have seen increasing field applications recently to take advantage of its niqe tensile strain hardening behavior, yet existing niaxial tensile tests are relatively complicated and sometime difficlt to implement, particlarly for qality control prpose in field applications. This paper presents a new simple inverse method for qality control of tensile strain capacity by condcting beam bending test. It is shown throgh a theoretical model that the beam deflection from a flexral test can be linearly related to tensile strain capacity. A master crve relating this easily measred strctral element property to material tensile strain capacity is constrcted from parametric stdies of a wide range of material tensile and compressive properties. This proposed method (UM method) has been validated with niaxial tensile test reslts with reasonable agreement. In addition, this proposed method is also compared with the Japan Concrete Institte (JCI) method. Comparable accracy is fond, yet the present method is characterized with mch simpler experiment setp reqirement and data interpretation procedre. Therefore, it is expected that this proposed method can greatly simplify the qality control of SHCCs both in exection and interpretation phases, contribting to the wider acceptance of this type of new material in field applications.. Introdction In the past decade, great strides have been made in developing strain hardening cementitios composite (SHCC), characterized by its niqe macroscopic psedo strain hardening behavior after first cracking when it is loaded nder niaxial tension. SHCCs, also referred to as high performance fiber reinforced cementitios composites (HPFRCCs, Naaman and Reinhardt 99), develop mltiple cracks nder tensile load in contrast to single crack and tension softening behavior of concrete and conventional fiber reinforced concrete. Mltiple cracking provides a means of energy dissipation at the material level and prevent catastrophic fractre failre at the strctral level, ths contribting to strctral safety. Meanwhile, material tensile strain hardening (dctility) has been gradally recognized as having a close connection with strctral drability (Li ) by sppressing localized cracks with large width. Many deterioration and prematre failre of infrastrctre can be traced back to the brittle natre of concrete. Therefore, SHCCs are considered as a promising material soltion to the global infrastrctre deterioration problem and tensile dctility is the most important property of this type of material. Research Assistant, Department of Civil and Environmental engineering, University of Michigan, USA. Professor, Department of Civil and Environmental engineering, University of Michigan, USA. vcli@mich.ed Engineered Cementitios Composites (ECC, Li 99) is a niqe representative of SHCCs, featring sperior dctility (typically > %, times that of normal concrete or FRC) (Li and Kanda 998; Li et al ), tight crack width (less than 8µm, Li ), and relatively low fiber content (% or less of short randomly oriented fibers). A typical tensile stress-strain crve of ECC is shown in Fig.. It attains high dctility with relatively low fiber content via systematic tailoring of the fiber, matrix and interface properties, gided by micromechanics principles. Enhanced with sch high tensile dctility and/or tight crack width, ECC has demonstrated sperior energy dissipation capacity, high damage tolerance, large deformation capacity, and exceptional drability in many recent experimental investigations (Li ). As a reslt, ECC is now emerging in the field and has seen increasing infrastrctre applications, sch as dam repair, bridge deck overlay and link slab, copling beam in high-rise bilding, and other strctral elements and systems (Li ). As aforementioned, tensile dctility is the most important material property of SHCC, yet relatively large variation of tensile dctility was observed in the literatre (Kanda et al, ; Wang and Li ). To address sch concern, Wang and Li () have proposed sing artificial flaws with prescribed size distribtion as defect site initiator to create more satrated mltiple cracks, reslting in more consistent tensile strain capacity among different specimens from the same batch. The overall tensile strain capacity shows mch more consistent reslts after implantation of artificial flaws, however, the variation of tensile strain capacity is still relatively large when compared with that

2 S. Qian and V. C. Li / Jornal of Advanced Concrete Technology Vol., No., -, 7 Tensile stress. 7 Tensile strain (%) Fig. Typical tensile stress-strain crve of ECC. of other properties, e.g., first cracking. Therefore, test method for qality control of SHCCs onsite shold logically focs on tensile strain capacity de to its importance in governing strctral response and potentially large variability. While most characterization of the tensile behavior of SHCCs was carried ot sing niaxial tensile test (UTT) in academia, this method is generally considered to be complicated, time-consming and reqire advanced eqipment and delicate experimental skills. Therefore, it is not sitable for onsite qality control prpose (Stang and Li, Ostergaard et al, Kanakbo ). First, special fixtres and/or treatments for the ends of specimens are sally needed in order to transfer tensile loads. Frthermore, the specimen is sensitive to stress concentration indced by misalignment and can fail near the end prematrely. Last bt not least, realistic dimensions for specimens large enogh to have - dimensional random fiber orientation make the UTT even more difficlt to condct. As a simpler alternative to the UTT, for point bending test (FPBT) was proposed by Stang and Li () for qality control on constrction sites, provided that an appropriate interpretation procedre for the test reslt is available. FPBT, in which the mid-span of the specimen ndergoes constant bending moment, may be carried ot to determine the moment-crvatre or momentdeflection crves. This type of test is mch easier to set p and condct in comparison to UTT, and a large amont of experience in bending test has been accmlated in the ser commnity of cementitios materials. The ltimate goal of this test is to se the momentcrvatre or moment-deflection crves so determined to invert for the niaxial tensile properties. It shold be noted, however, that the bending test is not meant to determine whether the material has tensile strainhardening behavior or tension-softening behavior, bt rather to constrain the tensile material parameters, e.g. the tensile strain capacity, as part of the qality control process in the field. Inverse analyses for FPBT have recently been attempted by Technical University of Denmark (DTU) and Japan Concrete Institte (Ostergaard et al ; Kanakbo ) with certain sccess. By adopting a simplified elastic-perfectly plastic tensile model, JCI method generally can predict platea tensile and tensile strain capacity from the FPBT reslts via a sectional analysis similar to that developed by Maalej and Li (99). On the other hand, hinge model, inclding both tensile strain hardening and tension softening effect, was employed in the DTU inverse method along with least sqare method to invert for tensile material properties from their bending response. The model can predict experimental load deflection crve fairly well and tensile properties derived based on this method agree well with that from FEM analysis, yet no direct comparison with UTT reslts has been made so far. Despite the sccesses mentioned above, frther simplification and/or validation are necessary to make the FPBT widely accepted for qality control of SHCCs. In case of JCI method, significant improvement is needed to simplify the experimental exection and data interpretation procedre. For instance, LVDTs are reqired in JCI method to measre the beam crvatre. This is somewhat brdensome in field conditions, considering qality control may involve a large nmber of specimens. Frthermore, the inverse process is not ser friendly, which reqire relatively complicated calclation (solving cbic eqation). As for the DTU method, firstly it needs complementary UTT reslts to trly validate the model. Secondly, the niqeness of soltion from sch inverse analysis is qestionable at times. Finally, the method will need to be packaged into sophisticated software, which may incr additional ser cost. A simple engineering chart with reasonable accracy may be more preferable. Keeping these considerations in mind, this paper looks to develop a greatly simplified yet reasonably accrate inverse method for determining tensile strain capacity of SHCCs. In the following sections, the research significance and overall research framework for the proposed method will be presented first, followed by parametric stdy to obtain the master crves for inverse analysis. Thereafter, the experimental program consisting of both FPBT and complementary UTT will be revealed in detail. The reslts from FPBT will then be converted to tensile strain capacity and validated with independent UTT test reslts. Finally, the proposed method will be compared with JCI inverse method, followed by overall conclsions.. Overall research framework The overall research framework is revealed in Fig., consisting of detailed procedre for development and exection of inverse method (top frame (a)) and validation and verification procedre (bottom frame (b)). As shown in the top frame (a), deflection capacity (deflection corresponding to peak bending stress, i.e., modls of rptre) can be obtained from FPBT. By condcting

3 S. Qian and V. C. Li / Jornal of Advanced Concrete Technology Vol., No., -, 7 7 FPBT Flexral model (Maalej & Li 99) UTT Flexral stress load point deflection crve Tensile strain capacity deflection capacity relation (master crve) Experimental tensile stress strain relation Validation/Verification Derived tensile strain capacity (a) (b) Fig. Overall research framework for proposed UM method. parametric stdies based on a flexral behavior model of SHCCs, master crve can be constrcted in terms of tensile strain capacity with respect to deflection capacity. Based on deflection capacity of FPBT and master crve from parametric stdy, tensile strain capacity of SHCCs can be derived. Additionally, companion UTT test sing specimens cast from the same batch of material is sed to validate and/or verify the proposed method in terms of the accracy of derived tensile strain capacity, which is shown in bottom frame (b). It is conceived that a large nmber of FPBT will be condcted at constrction sites on daily basis to ensre the qality of the SHCC material. The extra step of verification (Frame (b)) will not be necessary once the method is standardized and tilized in practice, except a very limited nmber of UTT specimens to be cast onsite and tested at advanced research laboratory to check whether this material is trly a strain hardening type dring trial mixing stage.. Flexral behavior model The flexral behavior model sed in this investigation is based on the work of Maalej and Li (99). Compared with other models, the major distinction of this model is that the contribtion of tensile strain hardening property of SHCCs was inclded. The actal SHCC considered in the model is Polyethylene ECC (PE-ECC) material. To simplify the analysis, the stress strain behavior of the ECC was assmed as bilinear crves in both tension and compressive. Based on a linear strain profile and eqilibrim of forces and moment in a section, the relation between flexral stress and tensile strain at the extreme tension fiber (Simplified as critical tensile strain hereafter) can be determined as a fnction of basic material properties. Overall, the model predicts experimentally measred flexral response qite well. For more detail, the readers are referred to Maalej and Li (99). Based on geometrical considerations, the beam crvatre can be compted as the ratio of critical tensile strain to the distance from the extreme tension fiber to the netral axis. This can be expressed in following eqation: ε t φ = = () ρ c whereφ, ρ, ε, and c are beam crvatre, beam radis t of crvatre, critical tensile strain, and the distance from the extreme tension fiber to the netral axis. In a FPBT of SHCC material, according to strctral mechanics, we can obtain following eqation to relate the deflection of the beam to the crvatre at the load point and therefore critical tensile strain. The load point. Parametric stdy and master crves h ρ = φ Fig. Definition of load point displacement, span length L, beam height h and crvatreφ in a schematic FPBT test (crvatre is constant along the middle third span between the two load points). L

4 8 S. Qian and V. C. Li / Jornal of Advanced Concrete Technology Vol., No., -, 7 deflection for a beam with span length L is given by: * φ * L φ * L h L = + ( ) () The definitions for,φ, L and h are shown in Fig.. The first term incldes the flexral deformation from pre bending span and shear span while the second term incldes the shear deformation from shear span. It shold be noted that the shear deformation is strongly related with the ratio of beam height over span length as shown in the second term. The specimens sed in this stdy have a height and span length of mm, mm while corresponding vales are mm and mm for JCI method. Therefore, the second term in Eqation () for the UM method is at least an order of magnitde smaller than the first term, so that () can be simplified as follows: =.* φ * L () Since the relation between flexral stress and ε t is already established, we can predict the flexral stress and load point deflection relation based on Eqations () and (). The maximm flexral stress (MOR) and corresponding deflection (deflection capacity) are reached once the strain capacity of the SHCCs is exhasted either at the extreme tensile fiber or at the extreme compression fiber, which is the assmed failre criterion in this model. The strain capacity is defined as tensile/compressive strain corresponding to ltimate tensile/compressive (maximm stress in stressstrain crve). The model was originally developed based on material behavior of PE-ECC, it wold be desirable to check its applicability for other SHCCs, sch as PVA-ECC, which has been extensively investigated in the past decade. PVA-ECC, with mix proportion and material tensile and compressive properties shown in Table, was tilized to check the applicability of the model. As shown in Fig., the analytical reslt from the model predicts the experimental flexral stress-deflection crves reasonably well, particlarly in terms of average MOR and deflection capacity prediction. This seems to sggest that the model is qite versatile in predicting the flexral behavior of SHCCs.. Constrction of master crves Parametric stdy was condcted to investigate the inflence of material niaxial tensile and compressive properties (parametric vales) on the flexral response of SHCCs based on the aforementioned flexral model. The correlation between tensile strain capacity and load point deflection was established and constrcted as master crve. All tensile and compressive properties were varied within a wide range of parametric vales (Table ), covering the normal range of test reslts of SHCC specimens at UM and JCI (Kanakbo ). It is expected that the master crves based on this wide range of parametric stdy can be directly tilized for qality control prpose in field. With material parameters shown in Table, five cases of parametric stdy were plotted in Fig. as examples. The material parameters varied in first cracking, ltimate tensile, modls of elasticity and compressive compared with Case in Table. Figre shows the flexral stress, load point Cement Sand Table Mix proportion and material properties of PVA-ECC. Mix proportion Fly Ash Water Sperplasticizer Fiber First cracking Material properties Tensile strain capacity (%) Ultimate tensile Compressive..7..±..7±..±..7±. Note: Mix proportion is by weight except PVA fiber by volme. The modls of elasticity and the ltimate compressive strain are assmed to be 8 GPa and., respectively. Table Range of material parameters sed in parametric stdies to constrct the tensile strain capacity deflection capacity (crvatre) relation. Material parameters First cracking Tensile properties Ultimate Tensile tensile strain capacity (%) Modls of elasticity (GPa) Compressive properties Compressive Compressive strain capacity (%) Range.~..~. ~ ~ ~.~ * Note: Parameters are in the normal range of test reslts of SHCC specimens at UM and JCI; Tensile and compressive modls of elasticity are assmed to be eqal; Beam dimensions are x7xmm/xxmm with span length of mm/mm for UM and JCI specimens, respectively; * : Estimated range.

5 S. Qian and V. C. Li / Jornal of Advanced Concrete Technology Vol., No., -, 7 9 Flexral stress. 8 8 Load point deflection (mm) Fig. Comparison of experimental reslts and analytical prediction of flexral stress-load point deflection for PVA-ECC. Flexral stress. 8 % % % % % Critical tensile strain Analytical prediction Experimental reslts Case Case Case Case Case 8 Load point deflection (mm) Fig. Parametric stdy for SHCCs with different material parameters (Dashed line boxes inclde markers corresponding to same critical tensile strain (tensile strain at the extreme tension fiber); markers are plotted on % strain interval after % strain for all cases) (Notice Case and Case are almost coincided). deflection and corresponding critical tensile strain relation. Beam dimensions are x7xmm with span length of mm. From the Figre, load point deflections were observed to correlate very well with critical tensile strains, regardless of the actal parametric material properties. Once the critical tensile strain reaches the tensile strain capacity, the beam reaches peak load and the corresponding load point deflection is the deflection capacity. Therefore, it appears that the deflection capacity and tensile strain capacity can be linearly correlated regardless of the vales of other material properties. The overall reslts from the parametric stdy indeed show a linear relation between tensile strain capacity and deflection capacity, as revealed in Fig. (a). Totally cases were investigated in the parametric stdy, with the range of material parameters shown in Table. All linear crves lie in a narrow band regardless of the vales of other material properties, which sggests that the beam deflection capacity is most sensitive to tensile strain capacity for a fixed geometry. For ease of qality control on site, a master crve was constrcted as a line with niform thickness to cover all parametric case stdies, as shown in Fig. (b). The top edge of the master crve is made to coincide with the pper bondary of all crves in Fig. (a) for conservativeness. Additionally, another master crve correlating tensile strain capacity with crvatre was constrcted by parametric stdy in order to compare the proposed UM method with JCI method, in which ltimate bending moment and crvatre was tilized to derive tensile strain capacity. The range of parametric vales is the same as the aforementioned parametric stdy, as shown in Table. The dimension of specimen sed in this parametric stdy is xxmm, with a span length of mm (JCI-S--). As expected, this set of master crve also characterizes a linear relation within a very narrow band regardless of actal material properties (Figs. 7 (a) and (b)). Since crvatre may be linearly correlated with deflection sing Eqation (), this master crve can be easily transformed into tensile strain capacity to deflection capacity relation, even thogh the slope shold be different from Fig. de to different dimensions sed in the two parametric stdies. In the case when specimens with different dimensions have to be sed for qality control, e.g. de to different fiber length, a different set of master crve shold be constrcted. Table Assmed material properties for different cases of SHCCs. Tensile properties Compressive properties First Ultimate Tensile Modls Compressive cracking tensile strain of capacity elasticity (%) (GPa) Compressive strain capacity (%) Case.. % 8. Case.. %. Case.. % 8 7. Case.. % 8. Case.. % 8.

6 S. Qian and V. C. Li / Jornal of Advanced Concrete Technology Vol., No., -, 7 Strain capacity (%). Strain capacity (%). 8 Deflection capacity (mm) (a) Upper bond Average vale Lower bond Master crve Predicted Deviation Deflection capacity (mm) (b) Fig. (a) Tensile strain capacity deflection capacity relation obtained from parametric stdy ( cases); (b) Master crve transforming deflection capacity into tensile strain capacity.. Discssion on the niqe behavior of master crves The master crve reveals a linear behavior within a narrow band width. In the following, discssions will be presented to provide some nderstanding of this niqe phenomenon. As shown in Eqations () and (), for a given span length L, it can be observed that middle span deflection () and crvatre (φ ) wold be linearly related to ε t if c (the distance from extreme tension fiber to netral axis) is constant with respect toε t. It trns ot that this is approximately correct when ε t is larger than %, as shown in Fig. 8, where parametric reslts are plotted for five cases of SHCCs (Table ) in terms of distance from extreme tension fiber to netral axis with tensile strain relation. It shold be noted that the vertical axis (distance from extreme tension fiber to netral axis) is normalized by the beam height. On the other hand, it is observed that these normalized distance (normalized c vale) near platea are very close (ranging from.8 to.9) for cases with drastically different material properties. This explains the narrow band width of the master crve. The close platea vales for different cases may be de to the fact that most of the SHCC materials have a very high ratio between compressive and tensile, ths pshing the netral axis very close to the extreme compressive fiber. Comparison between Fig. 8 and Table sggests that the higher the ratio, the higher the normalized c vale. Nevertheless, the small difference between these normalized c vales sggests that narrow band width may characterize the master crve for most SHCC materials, in which ratio of compressive over tensile is abot.. Use method of master crves Based on the master crves obtained from parametric stdy, the deflection capacity from simple beam bending test can be easily converted to material tensile strain capacity, with detailed procedre schematically shown in Fig. (b) and explained below. Assming a deflection capacity of 8 mm with standard deviation of. mm already known from FPBT, the predicted average tensile strain capacity can be derived by taking the averaged strain vale corresponding to 8 mm deflection. The Strain capacity (%). Strain capacity (%). 7 8 Crvatre (µ/mm) (a) 7 8 Crvatre (µ/mm) (b) Fig. 7 (a) Tensile strain capacity crvatre capacity relation obtained from parametric stdy ( cases); (b) Master crve transforming crvatre capacity into tensile strain capacity.

7 S. Qian and V. C. Li / Jornal of Advanced Concrete Technology Vol., No., -, 7 Normalized distance from extreme. tension fiber to netral axis pper and lower bond of the predicted tensile strain capacity can be obtained by taking maximm or minimm strain vale corresponding to 8. mm or 7. mm deflection, respectively. The predicted deviation of tensile strain capacity is simply the difference between the pper/lower bond and average vale. A set of eqations has been developed to simplify the conversion procedre, as shown below, where Eqations () and () can be sed to calclate the average tensile strain capacity and its deviation, respectively. ' ε. δ. () t =.9.8 SHCC SHCC SHCC SHCC SHCC Tensile strain (%) Fig. 8 Normalized distance from extreme tension fiber to netral axis tensile strain relation for SHCCs (distance normalized by the beam height). PD =. SD +.8 () where ε ' is the predicted average tensile strain capacity t (%); δ is the average deflection capacity obtained from FPBT (mm) (In Fig. (b), δ is assmed to be 8mm); PD is the predicted deviation for tensile strain capacity (%) considering the standard deviation of the deflection capacity, as shown in Fig. (b) and SD is the standard deviation of the deflection capacity (mm) (assmed to be. mm). To be conservative, the lower bond eqals to the lowest strain capacity vale corresponding toδ SD, which is assmed to be 7.mm. Likewise, the pper bond eqals to the highest strain capacity vale corresponding to δ + SD (assmed to be 8.mm). Therefore, the Predicted Deviation is the difference of pper bond/lower bond with predicted average tensile strain capacity. It shold be noted that this eqation can only be applied to specimen with the same geometry and same loading conditions as that sed by the athors (see Experimental Program section). Shold any of these geometry and/or loading conditions change, another set of master crves and corresponding conversion eqations shold be developed for that prpose. Once the proposed method (or its modified version) is standardized and widely accepted, there shold be no need for change in geometry and loading conditions. A similar procedre can also be sed to convert the crvatre to strain capacity for the specimens tested according to the JCI method. A set of eqation has also been developed according to Fig. 7 to simplify the conversion procedre. Eqations () and (7) can be sed to calclate the average tensile strain capacity and its deviation, respectively. ε.9 φ. () t, c =, c PD.9 SD +.9 (7) c = c where ε is the predicted average tensile strain capacity (%); φ is the average crvatre capacity obtained t, c, c from FPBT (µ/mm); PD c is the predicted deviation for tensile strain capacity (%) and SD c is the standard deviation of the crvatre capacity (µ/mm). The same limitation as mentioned above for Eqations () and () also applies to Eqations () and (7), except that the specimen geometry and loading profile shold follow those in the JCI method.. Experimental program. Materials, Specimen Preparation and Testing The mix proportion of SHCC materials investigated in Table Comparison of ratio of compressive over average tensile for different SHCCs (material properties are assmed parametric vales). Modls of Elasticity (GPa) First cracking Ultimate tensile Average tensile Comp. Ratio of comp. /Average tensile SHCC SHCC SHCC SHCC SHCC Note: All data are assmed vales, in the normal range of test reslts at UM and the JCI rond robin tests (Kanakbo ). For all cases, tensile and compressive strain capacity are assmed to be % and.%.

8 S. Qian and V. C. Li / Jornal of Advanced Concrete Technology Vol., No., -, 7 this stdy is shown in Table, inclding PVA-ECC, and. These SHCC materials featre high amont of fly ash in the mix proportion, with fly ash to cement ratios of.,., and.8, respectively. Additionally, PVA- ECC and Dctal from JCI rond robin test (Kanakbo ) are also listed in Table, which will be sed for comparison between UM method and JCI method. A Hobart mixer was sed in this investigation, with a fll capacity of liters. All beam, niaxial tensile and compressive specimens were cast from the same batch. The beam and niaxial tensile specimens were cast horizontally and compressive cylinder specimens were cast vertically. At least specimens were prepared for each test. After demolding, all specimens were cred in a sealed container with abot 99% hmidity nder room temperatre for 8 days before testing. For point bending test was condcted with a MTS 8 machine. The beam specimen has a dimension of mm long, mm high, and 7 mm deep, all dimensions are more than times that of the PVA fiber length (8mm), which is the largest length scale among the ingredients of PVA-ECC. The loading span between two spports is mm with a constant moment span length of mm. The beam was tested nder displacement control at a loading rate of. mm/second. The flexral stress was derived based on simple elastic beam theory and the beam deflection at the loading points was measred from machine displacement directly. The test setp is shown in Fig. 9 (a) in comparison with the JCI method (Fig. 9 (b)). As shown in Fig., niaxial tensile test (UTT) was also carried ot to directly verify the derived tensile LVDT 8 mm LVDT Fig. Setp for niaxial tensile test. strain capacity from for point bending test. The copon specimen sed herein measred.8 x 7. x.7 mm. Alminm plates were gled at both ends of the copon specimen to facilitate gripping (both ends are fixed). Tests were condcted in an MTS 8 machine with a kn capacity nder displacement control, with a loading rate of.mm/second throghot the test. Two external linear variable displacement transdcers (LVDTs) were attached to specimen srface with a gage length approximately 8mm to measre the displacement.. Experimental reslts The material tensile and compressive properties for dif- Table Mix proportion for different SHCCs. Cement Sand Fly Water/cementitios ash materials Sperplasticizer Fiber PVA-ECC PVA-ECC.... PVA-ECC PVA-ECC * Dctal* Note: * : Data from JCI rond robin test (Kanakbo, ) Bearing Test Specimen (a) (b) LVDT Fig. 9 Comparison of test setp for the (a) UM method and (b) JCI method (Beam deflection at the loading points was obtained from machine displacement directly in UM method).

9 S. Qian and V. C. Li / Jornal of Advanced Concrete Technology Vol., No., -, 7 Table Material tensile and compressive properties from experiment for different SHCCs. First cracking Ultimate tensile Tensile strain capacity (%) Compressive PVA-ECC.±. (7%).±. (%).±. (%).±. (%) PVA-ECC.9±. (%).±. (%).±. (9%).±.8 (8%) PVA-ECC.±. (%).9±. (%).7±. (%) 7.±.7 (%) PVA-ECC *.7±.8 (%).±. (%).7±.7 (%).±.8 (%) Dctal*.7±.9 (7%).±. (7%).±. (%) 98.±.7 (%) Note: * : Experimental data from JCI rond robin test (Kanakbo, ); Nmber in parenthesis is coefficient of variation (COV). Table 7 Comparison between predicted tensile strain capacity from FPBT and tensile strain capacity from UTT. Tensile strain capacity from UTT (%) Deflection capacity from FPBT (mm) Predicted tensile strain capacity (%) Difference between prediction and test reslt (%) PVA-ECC.±..8±..±.8 % PVA-ECC.±. 7.±..±. -% PVA-ECC.7±. 9.±.9.±. 9% ferent SHCCs can be fond in Table. With increasing amont of fly ash in PVA-ECC -, the compressive contines to decrease as expected, yet PVA- ECC still has a compressive of abot 8 MPa. For all SHCCs the typical coefficient of variations (COV) of first cracking and ltimate tensile Flexral stress. Flexral stress PVA-ECC FA/C=. 8 Load point deflection (mm) (a) PVA-ECC FA/C=. 8 Load point deflection (mm) (b) Fig. Experimental flexral stress load point deflection relation for PVA-ECC (a) before and (b) after correction of the initial loading stage. are less than %, similar to that of compressive. Conversely, the COV of tensile strain capacity are in the range of %-% except for PVA- ECC and, where the robstness of tensile dctility increased (in the form of redced COV) de to the sage of high volme fly ash (Wang ). This general trend relatively low COV for tensile and high COV for tensile strain capacity can also be fond in Kanakbo (). This frther confirmed the rationale of qality control for the tensile strain capacity instead of tensile. The flexral stress-load point deflection crves for PVA-ECC were shown in Fig.. If the specimen was not flly contacted with the test apparats, the initial loading stage may show nrealistic low stiffness in some case as shown in Fig. (a). This can be easily corrected by disconting this part of deflection from the load point deflection, as revealed in Fig. (b). The initial deflection with low stiffness, if any, is typically less than. mm, comprising of less than % of the deflection capacity. Similar to PVA-ECC in Fig., PVA-ECC and also show typical deflection hardening behavior nder FPBT, with the bottom srface of the specimens after bending test shown in Fig.. More and more satrated microcrack is revealed from PVA-ECC to, along with gradal increase of deflection capacity (Table 7). The modls of rptre for PVA-ECC - ranges from - MPa, abot.-. times that of their first cracking. This is consistent with the finding of Maalej and Li (99) that this ratio shold be abot.7 for elastic-perfectly plastic material (for tensile portion of beam), sch as the PVA-ECCs investigated in this stdy.

10 S. Qian and V. C. Li / Jornal of Advanced Concrete Technology Vol., No., -, 7. Validation and verification of the proposed method To validate the proposed inverse method, the deflection capacity obtained from FPBT is converted to tensile strain sing Eqations () and () (derived for the same beam size as sed in the FPBT experiments) and then compared with tensile strain capacity obtained directly from niaxial tensile test for PVA-ECC -. As revealed in Table 7 and Fig., the tensile strain capacity derived from FPBT predicts the niaxial tensile test reslts with reasonable accracy, with less than % difference. This agreement demonstrates the validity of the proposed inverse method. To frther verify the proposed UM method, comparison between UM method and JCI method was condcted based on JCI rond robin test data (Kanakbo ). As mentioned previosly, bending test reslts from JCI rond robin test are presented in the form of moment crvatre relation. To facilitate the comparison, the crvatre capacity can be converted to tensile strain capacity sing Eqations () and (7) in UM method. Within the JCI method, the tensile strain capacity is obtained by solving following eqations (JCI-S- -): ε = φ D ( x ) (8) t, b nl x + x m = nl nl (9) m M max = E φ B D (a) PVA-ECC (b) PVA-ECC (c) PVA-ECC Fig. Beam bottom srface shown increasingly satrated microcracks after bending test for PVA-ECC - (Microcracks are magnified with thick pen for the constant moment span length only). () where ε t, b is the predicted tensile strain capacity (%); φ is the crvatre capacity (/mm), which can be calclated from two LVDTs measrements (Fig. 9 (b)); D is depth of the test specimen (= mm); x nl is the ratio of the distance from compressive edge (extreme compression fiber) to netral axis over depth of test specimen, which needs to be solved from Eqation (9); M max is maximm moment ( N mm) ; E is the static modls of elasticity (N/mm ); B is the width of test specimen ( mm). For more details, readers are referred to the Appendix to JCI-S--. As shown in Table 8 and Fig., predictions based on both the UM method and the JCI method reveal comparable reslts with those from niaxial tensile tests. Frthermore, the UM method shows slightly smaller discrepancy with the niaxial tensile test reslt (Table 8) based on limited data. The consistency between the UM method and the JCI method and verification by independent JCI rond robin test data frther demonstrate the validity of the proposed UM method. The advantage of the UM method over the JCI method lies in its simplicity, both in the experiment and data interpretation phases. In the experiment phase, the UM method only reqires machine displacement to be measred. This is not the case for the JCI method, where complicated setp sch as LVDTs is needed to measre crvatre, as revealed in Fig. 9 (a) and (b). In Tensile strain capacity (%). Tensile test reslts Prediction PVA-ECC. PVA-ECC PVA-ECC.8 FA/C Fig. Comparison of tensile strain capacity from UTT test with prediction from proposed UM method for different PVA-ECCs. Tensile strain capacity (%). Tensile test reslts Prediction (JCI method) Prediction (UM method) PVA-ECC Dctal Different SHCCs Fig. Comparison of tensile strain capacity from UTT with predictions from JCI method and proposed UM method for different SHCCs. (Experimental data for both UTT and FPBT are from JCI rond robin test and only two FPBT specimens were reported for Dctal.)

11 S. Qian and V. C. Li / Jornal of Advanced Concrete Technology Vol., No., -, 7 Table 8 Comparison between niaxial tensile test reslts with predictions based on the JCI method and the UM method. Tensile strain capacity from UTT (%) Crvatre Capacity from FPBT (µ/mm) Predicted tensile strain capacity (JCI method) (%) Predicted tensile strain capacity (UM method) (%) PVA-ECC.7±.7 9.±9..±.9 ().±. () Dctal.±. 8. *. * (). * () Note: * : Only two bending specimens were reported. The nmber in parenthesis is the difference (in percentage) between the predictions and test reslts from niaxial tensile test. the data interpretation phase, the UM method only needs a simple master crve or linear eqation to convert deflection capacity directly into tensile strain capacity, while the JCI method reqires relatively complicated procedres (solving cbic eqation) to obtain tensile strain capacity. Considering the large amont of specimens needed to be tested dring constrction, the UM method seems to be more sitable for qality control prpose de to its simplicity, efficiency and reasonable accracy.. Conclsions To facilitate the qality control of the strain hardening cementitios composites on site, a simplified inverse method is proposed to covert the deflection capacity from simple beam bending test to tensile strain capacity throgh linear transformation. The linear transformation (in the form of master crves) is derived from parametric stdy with a wide range of parametric vales of material tensile and compressive properties based on a theoretical model. This proposed method has been experimentally validated with niaxial tensile test reslts with reasonable agreement. In addition, this proposed method compares favorably with the JCI method in accracy, bt withot the associated complexity. The following specific conclsions can be drawn from this stdy:. A simple inverse method has been sccessflly developed to derive tensile strain capacity of SHCC from beam bending deflection capacity by sing a master crve. This method is expected to greatly ease the on-site qality control for SHCC in terms of mch simpler experiment setp reqirement (compared with both UTT and the JCI inverse method) and data interpretation procedre (compared with the JCI method), yet with reasonable accracy (within %);. The master crve featres simple linear transformation with a narrow band width. The master crve decoples the dependence of tensile strain capacity on the moment capacity in contrast with the JCI method where tensile strain capacity is dependent on both crvatre capacity and moment capacity. Therefore, this method allows simple linear eqations (Eqation () and ()) to be sed for easy data interpretation;. A linear relation between the deflection capacity and the tensile strain capacity is observed based on parametric stdies. It has been shown that this linear relation is closely related to the fact that the netral axis of the SHCCs nder bending rapidly approaches the extreme compression fiber and qickly stabilizes (the platea distance from extreme tension fiber to netral axis is abot 9% of the beam depth);. All linear crves relating tensile strain capacity and deflection capacity lie in a narrow band regardless of actal material properties. This sggests that beam deflection capacity is most sensitive to tensile strain capacity for a given FPBT geometric dimensions, and mch less sensitive to other properties sch as compressive, Yong s Modls, etc. This cold be explained by the fact that the distance from extreme tension fiber to netral axis stabilizes to abot 9% of the beam depth for all SHCCs with different material properties. It shold be noted that the following assmptions are made when the proposed UM method is sed: (a) The tested material is trly a strain hardening type; (b) The major target for qality control for this material is tensile dctility; and (c) For this method to be most effective, a standardized beam with fixed geometric dimensions shold be agreed pon by the ser commnity. Acknowledgements The athors thank the Michigan Department of Transportation, and the National Science Fondation for fnding portions of this research (CMS-97, CMS- 9). References JCI-S--. (). Method of test for bendingmoment crvatre crve of fiber reinforced cementitios composites. Japan Concrete Institte Standard, 7. Kanakbo, T. (). Tensile characteristics evalation method for DFRCC. Jornal of Advanced Concrete Technology, (), -7. Kanda, T., Kanakbo, T., Nagai, S. and Marta, M. (). Technical consideration in prodcing ECC Pre-cast strctral element. Proceedings of

12 S. Qian and V. C. Li / Jornal of Advanced Concrete Technology Vol., No., -, 7 International RILEM workshop on HPFRCC in strctral applications, Pblished by RILEM SARL, 9-. Kanda, T., Saito, T., Sakata, N. and Hiraishi, M. (). Fndamental properties of direct sprayed ECC. Proceedings of the JCI International Workshop on Dctile Fiber Reinforced Cementitios Composites (DFRCC) - Application and Evalation (DRFCC- ), Takayama, Japan, -. Li, V. C. (). Engineered cementitios composites. Proceedings of ConMat', Vancover, Canada, Agst -, CD-docments/-/SS-GF-_FP.pdf. Li, V. C. (). Strategies for high performance fiber reinforced cementitios composites development. Proceedings of International Workshop on Advances in Fiber Reinforced Concrete, Bergamo, Italy, Li, V. C. (). On engineered cementitios composites (ECC) A review of the material and its applications. Jornal of Advanced Concrete Technology, (), -. Li, V. C., Wang, S. and W, C. (). Tensile strainhardening behavior of PVA-ECC. ACI Materials Jornal, 98 (), 8-9. Li, V. C. and Kanda, T. (998). Engineered cementitios composites for strctral applications. Innovations Form in ASCE, Jornal of Materials in Civil Engineering, -9. Li, V. C. (99). From micromechanics to strctral engineering--the design of cementitos composites for civil engineering applications. JSCE Jornal of Strctral mechanics and Earthqake Engineering, (), 7-8. Maalej, M. and Li, V. C. (99). Flexral/tensile ratio in engineered cementitios composites. ASCE Jornal of Materials in Civil Engineering, (), -8. Naaman, A. E. and Reinhardt, H. W. (99). Characterization of high performance fiber reinforced cement composites (HPFRCC). in High Performance Fiber Reinforced Cementitios Composites, RILEM Proceedings, Eds. A. E. Naaman and H. W. Reinhardt, -. Ostergaard, L., Walter, R. and Olesen, J. F. (). Method for determination of tensile properties of engineered cementitios composites (ECC). Proceedings of ConMat', Vancover, Canada. Stang, H. and Li, V. C. (). Classification of fiber reinforced cementitios materials for strctral applications. Proceedings of BEFIB, Varenna, Lake Como, Italy, Wang, S. and Li, V. C. (). Tailoring of pre-existing flaws in ECC matrix for satrated strain hardening. Proceedings of FRAMCOS-, Vail, Colorado, U S A, -. Wang, S. (). Micromechanics based matrix design for engineered cementitios composites, PhD Thesis, Univ of Michigan, Ann Arbor, MI,.