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Influence of strain rate and water content on mechanical behavior of dam concrete
Construction and Building Materials 36 (2012) 448–457
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Influence of strain rate and water content on mechanical behavior of dam concrete Shengxing Wu, Xudong Chen ⇑, Jikai Zhou College of Civil and Transportation Engineering, Hohai University, Nanjing, China
h i g h l i g h t s " Concrete are subjected to four-point loading under different strain rates. " Strength and elastic modulus increases with increasing strain rate. " Dynamic increase factor is relative to strain rate and water content. " Increasing water content will increase elastic modulus, but lower strength. " Poisson’s ratio remains unchanged with strain rate and water content.
a r t i c l e
i n f o
Article history: Received 20 March 2012 Received in revised form 5 May 2012 Accepted 4 June 2012 Available online 29 June 2012 Keywords: Concrete Water content Strain rate Experimental Mechanical properties
a b s t r a c t The influence of strain rate and water content on the mechanical behavior of dam concrete has been investigated. Sieved concrete specimens with water-binder ratio (w/b) 0.45 are subjected to four-point loading at strain rates of 106, 105, 104 and 103 s1. All these tests were performed with a closed loop servo-controlled stiff testing machine. The tests provide stress–strain curves at the chosen strain rates. Strain rate sensitivity is measured with in terms of the stress–strain curves, the maximum stress (flexural strength), dynamic increase factor, elastic modulus and Poisson’s ratio. Strain rate sensitivities are compared for different water content (0%, 40%, 70% and 100%). The obtained results showed significant influences of strain rate and water content on materials behavior. Both flexural strength and elastic modulus increased with higher strain rates, while Poisson’s ratio remained unchanged. At same strain rate, increasing water content would increase elastic modulus, but lower the flexural strength. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction There are many examples [1–3] of structures or structural elements subjects to dynamic loading. A rapid rise of the external load from zero to the peak load requires the material in the structural element quickly develops the internal stresses necessary to balance the external load. Concrete, with its heterogeneous structure, is found to behave differently when it is subjected to dynamic loading, as compared to its behavior under static loading [4]. Understanding the dynamic behavior of concrete is an issue of great significance for application in civil engineering. A lot of efforts have been dedicated in this field. More emphasis has been placed on the compressive [5,6] and tensile [7,8] behavior, and less on flexural response. Some researchers have studied the behavior of plain, composite, recycled aggregated concrete beams under impact loading. Bentur et al. [9] reported that the peak load occurred within 1 ms after contact in both plain and conventionally reinforced concrete beams. Banthia et al. [10] and ⇑ Corresponding author. Tel.: +86 25 83786551; fax: +86 26 83786986. E-mail address: [email protected] (X. Chen). 0950-0618/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2012.06.046
Zhang et al. [11] concluded that high strength concrete had high impact strength and more brittle than normal concrete. Tang and Saadatmanesh [12] concluded that the impact resistance of concrete beams significantly improved and the deflection and crack width reduced with the composite laminates. Rao et al. [13] suggested that for a given impact energy the reactions and strains of recycled aggregated concrete (RAC) with 50% and 100% recycled coarse aggregates are significantly lower than those of normal concrete and recycled aggregated concrete with 25% recycled coarse aggregates. Compared to the impact/impulsive tests, much less information is available on moderate strain rate tests. The quasi-static and moderate strain rate regime (106–101 s1) is still largely under-researched. For concrete structures (dam, bridge, offshore platform, etc.) operating underwater for a long period of time, the water content of concrete will have a certain influence on the mechanical behavior. The effect of water content on the static strength of concrete has been analyzed for a while, and researchers have also conducted intensive studies achieving many satisfactory results [14–23]. All researchers have found a compressive strength increases on drying, and data have been reported that support strength gain upon
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drying for the cases of tensile and flexural strength. Meanwhile, experimental researches have also been carried out on the effect of water content on the dynamic behavior of concrete. Rossi [24] believed that water content was one of the main factors influencing the rate effect of materials. However, there seems to be no consensus as to whether an increase or decrease occurs in the dynamic behavior as the water content is changed. Yan and Lin [7], Suaris and Shah [25], Rossi et al. [26], Reinhardt et al. [27], Cadoni et al. [28] and Ross et al. [29] have found that substantial tensile strength increases for wet concrete in the regime with the moderate strain rate (i.e. 104 s1–1 s1), where dry concrete has been demonstrated to be relatively insensitive. Watstein [30], Kaplan [31], Logunova et al. [32] Ranjith et al. [33] and Forquin et al. [34] achieved the same conclusion for dynamic compressive strength of concrete through tests. Reinhardt et al. [27] even reported that no strain rate effect could be detected in dry specimens under moderate strain rates where a very remarkable strain rate effect only existed in the tensile strength of wet concrete. While Zielinski et al. [35], and Brara and Klepaczko [36,37] considered moisture condition had no effect on the tensile strength of concrete when the strain rate is higher than 1 s1. However, the results of Harris et al. [38] and Zhou et al. [39] indicated that water content tended to decrease the dynamic compressive strength, and increased the dynamic splitting tensile strengths. With few exceptions, concrete in situ is fully saturated by water, or have at least a water content. In spite of this, testing of concrete in the laboratory is often performed on dry specimens or specimens with uncontrolled water content [24,30,38]. Although moisture effects in concrete have been investigated by others, these studies have not quantified the moisture levels. With the aim of obtaining further information in this regime, an experimental investigation is undertaken. Concrete specimens with water-binder ratio (w/b) 0.45 are subjected to four-point loading at strain rates of 106, 105, 104 and 103 s1. The tests provide stress–strain curves at the chosen strain rates. Strain rate sensitivity is measured with in terms of the stress–strain curves, the maximum stress (flexural strength), dynamic increase factor, elastic modulus and Poisson’s ratio. Strain rate sensitivities are compared for different water content (0%, 40%, 70% and 100%). This paper presents a description of the test setup and obtained results, and proposes explanations for the observed key phenomena. 2. Experimental program 2.1. Specimens In this investigation, the concrete mixes were used for Xiaowan arch dam, China. The so-called ‘‘dam concrete’’ is a specific type of concrete used in the construction of concrete dams, which differs in that a larger size (80–150 mm) of aggregate is used in order to save cement and reduce the heat of hydration. Due to practical difficulties in performing a large size specimen test, dam concrete is usually sieved to remove aggregate larger than 40 mm. The passed fresh concrete was remixed to produce a uniform mix. The mix proportion of concrete used is given in Table 1, where Type 42.5R Portland cement was used in all mixes. The mixes contained
Fig. 1. Picture of test setup.
fly ash (ASTM Class F) to save cement and reduce the heat of hydration for practical application. The crushed granite rock was employed as coarse aggregate. The maximum sand grain size was 4 mm. The specific gravities of the fine and coarse aggregates were 2.40 and 2.58, respectively. The coarse aggregate and sand were air dried prior to mixing. Following casting, the specimens were covered with a plastic membrane to prevent the moisture from evaporating. Specimens were demolded after 24 h and moist cured for 6 months. During this investigation, prismatic (150 150 550 mm) specimens were used. A total of 36 beam specimens was prepared for tests. Also, several companion 150 mm cubes were cast for obtaining static compressive and split-tensile strength of concrete. The following values were obtained for the concrete at the age of 180 days: compressive strength = 51.8 MPa, and split tensile strength = 3.56 MPa. 2.2. Four-point bending tests As aforementioned, in order to study the dynamic properties of concrete, four-point bending tests on concrete beams were conducted over a wide range of strain rates, from 106 s1 to 103 s1. Dynamic testing was conducted using a dynamic loading system that applied a programmable controlled loading. All these tests were performed with a closed loop servo-controlled stiff testing machine of MTS System Corporation. The test setup is shown in Fig. 1. The load was applied at 0.25 kN/s, 2.5 kN/s, 25 kN/s, and 450 kN/s respectively. The measurement system consists of a strain amplifier, a tape recorder, and an intelligent signal processor. A 104 Hz sampling frequency can be achieved. Eleven pairs of foil strain gages, 5 mm in width and 50 mm in width, were used to monitor longitudinal and transverse strain histories. They were crossly glued onto the faces of the specimen. Each specimen was removed from the moist room 2 days before testing. Typical load-time curves for concrete beams tests at a static and dynamic loading rate are shown in Fig. 2a and b respectively. These
Table 1 Details of mix proportions (in kg per cubic meter of dam concrete). Cement
134
Fly ash
57
Water
86
Coarse aggregate 5–20 mm
20–40 mm
40–80 mm
80–150 mm
548
390
400
400
Fine aggregate
Superplasticizer
Air-entraining admixture
534
1.43
0.0105
Note: The sieved concrete was obtained by removing aggregates larger than 40 mm, i.e., aggregates larger than 40 mm must have been replaced by fine or coarse aggregates to keep the same mix proportion.
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Fig. 3. Average water content of specimens versus time in water.
Fig. 4. Typical failure mode of concrete specimen. Fig. 2. Typical load time curves for concrete specimens: (a) loading rate 0.25 kN/s and (b) loading rate 450 kN/s.
illustrate that the linearity of loading was acceptable and that failure was easily recognized.
normalized by the cross sectional area exposed to water. The percentage of moisture content was found through interpolation by finding the mass of the specimen oven dried. The water content is 0% in an oven dried specimen and 100% in a saturated specimen. The water content of concrete specimens can be reflected by the degree of saturation. Water content was calculated as follows:
2.3. Water content of concrete During the phase of this investigation, the distribution and concentration of moisture in concrete specimens were manipulated by exposing the specimens to drying and wetting environments for various periods of time. The data collected during this moistureconditioning period formed and empirical basis for predicting the time required to cause given moisture change under various conditions. Concrete specimens were kept in an oven at 60 ± 1 °C after 180 days of moist curing. For oven-drying tests, drying operations (approximately 20 days in duration) were achieved in extremely well-controlled conditions. No heating rates were used for these drying procedures. After drying, specimens under test were placed on water reservoir again. Water, at room temperature, was then added to the reservoir. The specimens were then subsequently removed and dried until the moisture content of interest. The test at moisture content just involved drying the surface and immediately testing the specimen while its temperature remained 20 °C. This is important because the evaporative effect of water will cool the specimen. The mass of the specimen was measured at regular intervals using a balance accurate to one hundredth of a gram. The amount of water taken in from the specimen was calculated and
wr ¼
W Wd 100% Ww Wd
ð1Þ
where wr is the water content of the specimen (%), W is the mass of the specimen (g), Ww is the specimen water saturated mass (g), and Wd is the dried mass of a specimen (g). Fig. 3 shows water content as a function of exposure time for specimens that were oven-dried to zero moisture content and then immersed. Each data point is the average of three specimens. In this test, concrete specimens with four water contents of 0%, 40%, 70% and 100% were prepared for both static (106 s1) and dynamic (103 s1) loading. 2.4. Test procedure The beams were supported simply and were subjected to two-point loads, as shown in Fig. 1. The distance between the two-points was kept at 450 mm. Special bearing assemblies (roller, guide plates, etc.) were designed to facilitate the application of load to the test specimens. The load was applied to the beam by means of the hydraulic testing machine. All the tests were carried out in a
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laboratory of Hohai University, China. At least three specimens were tested for each loading condition to ensure the repeatability of the experimental results. To avoid changes in concrete strength due to aging of concrete specimens, all tests were carried out in succession within the period of 1–2 weeks. 3. Test results and discussion 3.1. Strain rate effects 3.1.1. Failure pattern Fig. 4 shows the typical flexural failure mode of concrete beam in this investigation. The crack pattern of all beam specimens under both static and dynamic loading is presented in Fig. 5. As shown in Fig. 5, the failure location of all concrete beams is at
Fig. 5. Crack pattern of concrete specimens.
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the mid-span, no effect of strain rate was observed. Thus it would appear that for concrete beams subjected to flexure, strain rates will not affect the failure mode. The failure locations of the beams tested were evenly distributed between the load carrier clamps suggesting that the loading during the test was as intended. Fig. 6 shows the fractured surfaces of concrete beams under different strain rates (from 106 s1 to 103 s1). It can be seen from Fig. 6 that the fractured surfaces of the specimens became more and more flattened with the increasing strain rate; and an increasing number of aggregates were broken along the fractured surface. Many researchers [40,41] have shown that a large number of bond micro-cracks exist at the interfaces between the matrix and the aggregates. In case of static loading, the bond cracks at the aggregate-matrix interface start to extend to owing to stress concentration at crack tips. Then, some cracks at nearby aggregate surfaces start to bridge in the form of matrix cracks, meanwhile, other bond cracks continue to grow slowly. Finally, the microcracks through the matrix coalesce together all the bond cracks and complete failure occurs. The fractured surface of the specimen mainly passes through the matrix and the aggregate-matrix interfaces. This leads to a rough surface (Fig. 6a and b). However, crack velocity in concrete has been shown to increase with strain rate [42,43]. Therefore, at low strain rates crack has time to seek the path of least resistance. However, when the specimens are subjected to rapid loading, the creation of new cracks is forced to propagate through regions of greater resistance, and a greater amount of micro-crack may be required before a continuous fractured surface be formed. Thus, a certain part of the aggregates are broken during loading and the fractured surfaces of the specimens become more flattened (Fig. 6d). 3.1.2. Stress–strain behavior Fig. 7 shows the typical stress–strain curves at four strain rates for concrete beams. A significant change in the stress–strain
Fig. 6. Failure surface of concrete beams under different strain rates: (a) 106 s1; (b) 105 s1; (c) 104 s1; and (d) 103 s1.
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S. Wu et al. / Construction and Building Materials 36 (2012) 448–457 Table 2 Comparison DIF with published experimental results. Strain rates (s1)
Four-point bending (average value from current work)
Tension [7]
Compression [47]
Three-point bending [25]
103 104 105 106
1.361 1.186 1.136 1.0
1.431 1.322 1.167 1.0
1.15 1.05 1.02 1.0
1.22 1.11 1.06 1.0
Table 3 Poisson’s ratio versus strain rate for concrete. Strain rate (s1) Poisson’s ratio (average)
Fig. 7. Typical stress–strain curves of concrete specimens under different strain rates.
response of the materials to increase in strain rate is clearly seen in Fig. 7. For concrete specimens, as the strain rate is increased, both the initial slope and the peak stress increase, while the nonlinearity of the initial response decreases. Specific aspects of the response of the material as a function of strain rate are discussed next. 3.1.3. Flexural strength and dynamic increase factor (DIF) The results of the tests at different strain rates carried out are shown in Fig. 8. The strain rate was calculated from the linear portion of the strain–time curves in tests where strain gages were used. It can be seen from Fig. 8 that the flexural strength of concrete beams increased gradually as strain rate increased from 106 s1 to 105 s1, 104 s1 to 103 s1. A relationship between flexural strength and strain rate was established using regression to fit test data:
f ¼ 0:70 lg ðe_ Þ þ 10:72
ð2Þ
where f is flexural strength (MPa), and e_ is strain rate (s1). On the basis of the results presented here, it is clear that concrete is a very strain rate sensitive material. Concrete beams showed high flexural strength at high strain rate (Table 3). Several explanations can be suggested to account for these trends. One explanation may be based on fracture mechanics concepts [43,44]. The phenomenon of strain rate sensitivity can be explained by combining the classical Griffith theory with the concept of
105 0.179
104 0.218
103 0.209
sub-critical crack growth. According to Griffith theory, failure in brittle materials occurs when a flaw exceeds the critical flaw size and failure will then occur. If the load is applied slowly, the subcritical flaws have time to grow and thus the failure occurs at a lower value of the load. However, if the load is applied at a high rate, there is little or no time available for the growth of the subcritical flaws, and a higher load can be reached by the structural element before failure occurs. John and Shah [44] reported that pre-peak crack growth is reduced at high rates of loading. An alternative explanation of the observed trend may be given on the basis of non-linear fracture mechanics. It has been recognized that immediately ahead of a moving crack is a zone of micro-cracking called the process zone. Reinhardt et al. [45] has suggested that the size of this zone of micro-cracking depends upon the velocity of the crack; a faster crack has a larger zone of micro-cracking ahead of it. At a higher strain rate the crack propagates faster, and therefore the process zone will be bigger. This increased micro-cracking may explain the higher energy requirements at higher strain rates. This argument, may, at first glance, seem to contradict with the argument presented above on the basis of sub-critical crack growth, which predicts less micro-cracking in high strain rate loading situations. However, these two phenomena occur on the opposite sides of the peak load. The concept of sub-critical crack growth is applicable prior to the peak load; the concept of a larger process zone applies in the post-peak load region, where the unstable crack propagation commences. The dynamic increase factor (DIF), defined as the ratio of the dynamic strength to the static strength, has been widely accepted as an important parameter to measure the strain rate effect on the strength of concrete-like materials [6,46]. The results of the tests in this paper are plotted in Fig. 9. A relationship between flexural strength and strain rate was established using regression to fit test data:
DIF ¼ 0:11 lg ðe_ Þ þ 1:65
Fig. 8. Flexural strength versus strain rate for concrete specimens.
106 0.194
ð3Þ
These results are compared with those of compressive [47], tensile [7] and three-point bending [25] DIF of other researchers, as shown in Table 2. It can be seen that the tensile response is the most strain rate sensitivity, the compressive the least and the response of beam specimens subjected to increasing strain rate falls between those of tension and compression. This means that any constitutive law which assumes isotropic strain rate sensitivity may not be very accurate. From Table 2, it appears that the specimens tested in the fourpoint loading arrangement exhibit higher strain rate sensitivity than those tested a three-point loading arrangement. However, the difference cannot be solely attributed to the different testing
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Fig. 9. Strain rate influence on the DIF of concrete specimens.
Fig. 10. Elastic modulus versus strain rate for concrete specimens.
configuration since the specimens tested in a four point loading arrangement also had lower static strength. 3.1.4. Elastic modulus and Poisson’s ratio The elastic modulus is typically calculated as either a secant or a chord modulus. A secant modulus is calculated from the origin to a defined point on the stress–strain curve, usually within 30% to 60% of the specimen’s peak stress [5]. The chord modulus is usually evaluated between the stress and strain pairs at 50 millionths strain and at 40% of the peak stress [7]. In this study, the dynamic and static elastic modulus was measured as the chord modulus according to [7]. Fig. 10 shows the change in the values of elastic modulus as a function of strain rate. As with strength, elastic modulus increases approximately with an increase in strain rate. In this study, the average values of the modulus observed in strain rate 106 s1 to 105 s1, 104 s1 and 103 s1 are 50.83 GPa, 52.8 GPa, 56.15 GPa and 60.83 GPa respectively. A linearly elastic material like steel shows little strain rate sensitivity for elastic modulus [48,49], while concrete shows an enhanced elastic modulus at higher strain rates. The enhancement of elastic modulus can be explained by a decrease in internal micro-cracking (for a given level of stress) with the increased strain rate, resulting in a stress– strain curve that linear up to higher values of stress. However, the increase in only about half of the corresponding percent increases in strength. The lower strain rate sensitivity of elastic modulus compared to strength is consistent with similar observations in
Fig. 11. Effect of water content on stress–strain curves of concrete: (a) strain rate: 106 s1 and (b) 103 s1.
studies of other researchers [7,50]. The relationship between modulus of elasticity and strain rate can obtained by the following equation:
E ¼ 3:11 lg ðe_ Þ þ 69:11
ð4Þ
where E is modulus of elasticity (GPa). The Poisson’s ratio illustrated here is calculated at 30% of the strength. Table 3 illustrates the variation in the average Poisson’s ratios of the concrete beams as a function of strain rate. From the test results obtained, it seems that there is no definite increasing or decreasing tendency for Poisson’s ratio with increase in strain rate. Very little information concerning the strain rate effect on Poisson’s ratio is available. CEB recommendations [5] assume that the Poisson’s ratio is independent of loading rate, because of the scarcity of results. Harsh et al. [51] noticed that an increase in Poisson’s ratio for cement paste and mortar loading in tension during rapid loading. While Yan and Lin [7] did not observe any changes in Poisson’s ratio for strain rate as high as 0.2 s1. 3.2. Water content effects 3.2.1. Stress–strain behavior Not only the stress–strain behavior of concrete under static loading was measured, the dynamic loading behavior was also
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the gel, em-brittled the concrete system and consequently facilitated the propagation of bond cracks [59]. Moisture thus assists both the initiation and propagation of pre-existing drying induced cracks. The flexural strength evolution with the water content observed here follows the same results from those obtained by Pihlajavaara [14] and Okajima et al. [60] who tested respectively the mortars with w/c = 0.5 and 0.65 after obtaining a good maturity. They performed their flexural tests at uniform environmental humidity increasing, and register increasing of 58% and 39% respectively. Kanna et al. [19] reported an increase of 36% in flexural strength of a mortar with w/c = 0.45 after 6 days of over-drying at 105 °C. It has been shown that drying increases the strength of concrete for all forms of loading [15,61]. This process was termed dryingstrengthening by Pihlajavaara [14] though it had been observed experimentally earlier by Gonnermann [62], in a paper of great interest, showed that the strength of dried concrete on re-soaking reduced to the same value as that of concrete continuously moist cured. Matsushita and Onoue [63] also showed that re-saturation of dried concrete by a fluid with molecular sizes larger than water produced strength reductions related to the size of the molecule. The process of strength reduction in sorption was termed wetting-weakening by Pihlajavaara [14] who proposed a relationship between water content and the strength of the form: 2
½fw =f0 ¼ 1 cwr
Fig. 12. Effect of water content on flexural strength of concrete: (a) strain rate: 106 s1 and (b) 103 s1.
determined. As shown in Fig. 11a, when the static stress–strain curves of the four different water contents are compared, it is observed that the peak load of the four water content is decreasing with higher water content. Fig. 11b shows four stress–strain curves of concrete under dynamic loading (strain rate 103 s1). The shape of the stress–strain curves seem not to be influenced by the higher strain rate. For all four water contents, the strain rate effect seems to more pronounced for the saturated specimens. 3.2.2. Flexural strength and dynamic increase factor (DIF) Fig. 12 gives the evolution of the flexural strength of different water content and strain rates (Fig. 12a strain rate 106 s1; and Fig. 12b strain rate 103 s1). The flexural strength increases with the water content decreased. The marked reduction in the flexural strength of the concrete specimen highlights the role played by water content. The decrease in strength of a cement-based material versus its water content increase may be explained by means of capillary depression (or capillary suction) variations [52–54], disjoining pressures variations [55] and surface energy variations [56,57]. According to Yurdas et al. [58] and Burlion et al. [18], capillary suction, generated during the evaporation of free water in capillary pores, can be considered as the dominated mechanism. This effect leads to a stiffening of the material, which acts like an isotropic pre-stress of the granular skeleton. In addition, it is proposed that physio-chemi-sorption lowered the surface energy of
ð5Þ
where fw is the flexural strength at water content w (MPa); f0 is the flexural strength at water content 0% (MPa); c is a constant; and wr is the water content (%). This form of relationship is confirmed by the test results in this investigation, as shown in Fig. 12. The concept of wetting-weakening and drying-strengthening has been questioned because of the effect of differential shrinkage or swelling. Popovics [15] pointed out in discussing Pihlajavaara’s work [14] that drying produces tensile stresses in the exterior ‘‘shell’’ of the specimen; these stresses would be superimposed on applied tensile forces or could result in surface cracking. Both these latter effects would reduce the flexural strength of concrete. Wetting and subsequent swelling would impose a reversed stress state to drying, i. e., compressive stresses in the exterior ‘‘shell’’ and tensile in the interior. However, the influence of wetting or drying is governed by the rate at which the moisture movement occurs. Rapid moisture transfer results in severe stress gradients which have a dominant influence on apparent determinations. On the other hand, if the moisture loss is gradual, any stress gradient would be small and would dissipate with time as internal and external hygral equilibrium was achieved. Fig. 13 shows the dynamic increase factor (DIF) of concrete under different water content. From the results as shown in Fig. 13, the following conclusion can be drawn immediately: that wet concrete is more rate-dependent than dry concrete. This result has also been confirmed by other researchers [7,24,26]. Rossi [24] observed that the moisture condition of concrete had a definite effect on dynamic increase factor, with a wet concrete showing larger increases than an air-dried concrete. Yan [7] also found larger relative increases for wet concrete. Weerheijm and Van Doormaal [64] have noted that the strain rate effect, for the range of loading rates (11–10 s1), diminishes as the moisture content decreases as a result of longer periods of air-drying. Because the concrete specimens have the same skeleton strength, thus the difference in strength is mainly caused by water content. It is reported that for concrete, the main factor that induces the rate dependence of concrete strength is the viscous cohesive stress, rv of free water in the pores [7,24,26,65–67]. This stress can be expressed as:
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455
Fig. 13. Effect of water content on dynamic increase factor of concrete.
Fig. 14. Influence of water viscous cohesive force on the strength of specimen.
rv ¼
3pgR2 dh 3 dt 2h
ð6Þ
where g is the viscosity of the water, R is the radius of crack, and h is the height of crack (Fig. 14). To relate the viscous stress to the strain rate, we have to further link the displacement to the stress. The displacement of crack Dh can be calculated using the linear fracture mechanics:
pffiffiffi Dh / K I R
ð7Þ
where KI is the mode I intensity factor, which is proportional to r. Thus
rv /
dh / e_ dt
ð8Þ
From Eqs. (7), (8), we can see that the viscous cohesive force is proportional to the strain rate, thus contributing to more sensitive rate dependence for the moisture and saturated specimens. Concrete is a porous material, thus the above model can be used to explain the observed difference in strain rate sensitive (DIF) among specimens with various water content. Cadoni claims to give a different explanation for the influence of moisture content. Cadoni et al. [28] used Hopkinson Bar Bundle (HBB) to carry out experiments on large sized concrete specimens with aggregates from powder to 25 mm maximum size. The specimens were subjected to different curing conditions to study the effect of internal humidity conditions on strain rate enhancement. They confirmed that the level of free water inside concrete had an important influence on the strain rate sensitivity of concrete. In addition, they proposed a wave propagation concept for the physical explanation of the phenomenon. His interpretation is
Fig. 15. Effect of water content on elastic modulus of concrete: (a) strain rate: 106 s1 and (b) 103 s1.
based on the principle of wave propagation in concrete. When a pore is not filled with water, it will locally reflect the incoming stress wave. The multiple reflections of all pores together can cause a considerable increase in stress. When a stress wave meets a pore that is filled with liquid the reflected stress is not big not enough to cause the increase in stress that locally provokes the damage of the material. Therefore the wet concrete will exhibit a more pronounced rate effect than the dry concrete. This interpretation of Cadoni et al. [28] only gives an explanation of the difference between wet and dry concrete and does not explain the increase in strength between static and dynamic loading.
3.2.3. Elastic modulus and Poisson’s ratio The effect of water content on elastic modulus is shown in Fig. 15. The main feature of the results is that both the dynamic and static elastic modulus increases on higher water content. The significant change in the elastic modulus, in particular, highlights the effects of water content. It is proposed that decreasing of micro-cracking is a possible mechanism responsible for the increase of the modulus on rewetting. The partial recovery of the modulus on rewetting can be attributed to entry of interlayer water into the tobermorite gel and to some major crack healing due to water sorption. As reported in the last section, the flexural strength of concrete, however, decrease on water sorption. Evans and Marthe [68] drew the complete stress–strain curves for concrete in direct
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Table 4 Poisson’s ratio of concrete versus water content under different strain rates.
4. Conclusions
Strain rate (s1)
Water content 0%
Water content 40%
Water content 70%
Water content 100%
106 103
0.182 0.192
0.196 0.205
0.187 0.213
0.202 0.177
tension and observed that there was a reduction in the modulus as the strain in the concrete increased. They also attributed this reduction in the static modulus of micro-crack propagation. Haque and Cook [69], while investigating the effects of drying on the bulk modulus of hardened cement paste also concluded that rewetting causes a increase of the modulus. Parrot [70] however, attributed to the reduction in the elastic modulus of hardened cement paste on drying to the dehydration of the calcium silicate hydrate. Overall, the reduction in the elastic modulus, observed in this investigation, can be attributed to micro-cracking. In addition, the presence of moisture in concrete may also increase material stiffness; the increased stiffness with moisture present is evidenced by higher elastic modulus obtained for wet specimens, as reported by Reinhardet et al. [27]. Cook and Haque [20] indicated that the changes in mechanical properties such as strength and creep, as a function of water content, can be explained on the premise of time-dependent micro-cracking, surface free energy and redistribution of the interlayer water. The present results establish that the elastic modulus of concrete is also a function of the water content and any study into the strength and deformation should take into account the concomitant variation of the elastic modulus. Average Poisson’s ratio for most of the tests was between 0.177 and 0.213 according to Table 4 for concrete specimens. Notice there is no significant variation of Poisson’s ratio was measured for concrete with different water content. These results of this investigation show quite similar trend to those of static tests reported by other investigators [71]. Tests on saturated and ovendried cement pastes at an age of 30 days for water–cement ratios of 0.3–0.5 showed that Poisson’s ratio remained remarkably constant at 0.25 for increase rewetting time [71]. Persson [72]’s results showed that Poisson’s ratio of mature of high performance concrete decreased with higher relative humidity in concrete. He linked the results to the self-desiccation of high performance concrete. However, he also showed that the significance of the influence of moisture was low.
3.3. Multi-parameter statistical analysis In this investigation, the flexural strength and elastic modulus of concrete were determined for different strain rates and water content. Multiple regression analysis of the flexural strength f (in MPa), dynamic increase factor DIF and the elastic modulus E (in GPa) with strain rate e_ (s1) and water content w (%), as independent variables were performed. The following regression equations were derived:
f ¼ 11:71 þ 0:21 ln ðe_ Þ 2:49w R ¼ 0:96
ð9Þ
DIF ¼ 0:94 þ 129:49e_ þ 0:25w R ¼ 0:87
ð10Þ
E ¼ 38:12 þ 3; 623; 080:55e_ 2 þ 19:73w R ¼ 0:88
ð11Þ
where R is the correlation coefficient. Reasonable fits are observed from Eqs. (9)–(11).
In this study, the mechanical behavior of concrete is evaluated by tests using concrete specimens with different strain rates (106, 105, 104 and 103 s1) and different water content (0%, 40%, 70% and 100%). From this work the following conclusions are made: The fractured surfaces of the specimens became more and more flattened with the increasing strain rate; and an increasing number of aggregates were broken along the fractured surface. As the strain rate is increased, both the initial slope and the peak stress increase, while the nonlinearity of the initial response decreases. The flexural strength, dynamic increase factor (DIF), and elastic modulus of concrete beams increased gradually as strain rate increased from 106 s1 to 103 s1. There is no definite increasing or decreasing tendency for Poisson’s ratio to increase in strain rate. The flexural strength increases with the water content decreased. The marked reduction in the flexural strength of the concrete specimen highlights the role played by water content. At same strain rate, increasing water content would increase elastic modulus and dynamic increase factor (DIF). Both the dynamic and static elastic modulus increases with higher water content. There is no significant variation of Poisson’s ratio was measured in concrete with different water content. There are many other factors which may affect the mechanical behavior of concrete as strain rate is increased, such as mix proportions, aggregate type (stiffness, surface texture, size, shape and strength) and content, grading, cement content, age and curing conditions. Further work, in particular more test data, is needed. Acknowledgement The authors are grateful to the National Natural Science Foundation (Nos. 50979032 and 51178162) for the financial support. References [1] Fu HC, Erki MA, Seckin M. Review of effects of loading rate on reinforced concrete. J Struct Eng 1991;117(12):3660–79. [2] Tanimura S, Mimura K, Nonaka T, Zhu W. Dynamic failure of structures due to great Hanshin-Awaji earthquake. Int J Impact Eng 2000;26(6–7):583–96. [3] Ozbolt J, Sharma A. Numerical simulation of reinforced concrete beams with different shear reinforcements under dynamic impact loads. Int J Impact Eng 2011;38(12):940–50. [4] Suaris W, Shah SP. Constitutive model for dynamic loading of concrete. J Struct Eng 1984;111(3):563–76. [5] Bischoff PH, Perry SH. Compressive behavior of concrete at high strain rates. Mater Struct 1991;24:425–50. [6] Fu HC, Erki MA, Seckin M. Review of effects of loading rate on concrete in compression. J Struct Eng 1991;117(12):3645–9. [7] Yan D, Lin G. Dynamic properties of concrete in direct tension. Cem Concr Res 2006;36(7):1371–8. [8] Malvar LJ, Ross CA. Review of strain rate effects for concrete in tension. ACI Mater J 1998;95(6):735–9. [9] Bentur A, Mindess S, Banthia N. The behavior of concrete under impact loading: experimental procedures and method of analysis. Mater Struct 1987;20(4):371–8. [10] Banthia N, Mindess S, Bentur A. Impact behavior of concrete beams. Mater Struct 1987;20(4):293–302. [11] Zhang XX, Ruiz G, Yu RC, Tarifa M. Fracture behavior of high-strength concrete at a wide range of loading rates. Int J Impact Eng 2009;36(10–11):1204–9. [12] Tang T, Saadatmanesh H. Behavior of concrete beams strengthened with fiberreinforced polymer laminates under impact loading. J Compos Constr 2003;7(3):209–18. [13] Rao MC, Bhattacharyya SK, Barai SV. Behavior of recycled aggregate concrete under drop weight impact load. Constr Build Mater 2011;25:69–80. [14] Pihlajavaara SE. A review of some of the main results of a research on the aging phenomena of concrete: effect of moisture conditions on strength, shrinkage and creep of mature concrete. Cem Concr Res 1974;4:761–71. [15] Popovics S. Effect of curing method and final moisture condition on compressive strength of concrete. J Am Concr Inst 1986;83:650–7. [16] Barlett FM, MacGregor JG. Effect of moisture condition on concrete core strength. ACI Mater J 1993;91(3):227–36. [17] Glucklich J, Korin U. Effect of moisture content on strength and strain energy release rate of cement mortar. J Am Ceram Soc 1975;58(11–12):517–21.
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Influence of strain rate and water content on mechanical behavior of dam concrete Shengxing Wu, Xudong Chen ⇑, Jikai Zhou College of Civil and Transportation Engineering, Hohai University, Nanjing, China
h i g h l i g h t s " Concrete are subjected to four-point loading under different strain rates. " Strength and elastic modulus increases with increasing strain rate. " Dynamic increase factor is relative to strain rate and water content. " Increasing water content will increase elastic modulus, but lower strength. " Poisson’s ratio remains unchanged with strain rate and water content.
a r t i c l e
i n f o
Article history: Received 20 March 2012 Received in revised form 5 May 2012 Accepted 4 June 2012 Available online 29 June 2012 Keywords: Concrete Water content Strain rate Experimental Mechanical properties
a b s t r a c t The influence of strain rate and water content on the mechanical behavior of dam concrete has been investigated. Sieved concrete specimens with water-binder ratio (w/b) 0.45 are subjected to four-point loading at strain rates of 106, 105, 104 and 103 s1. All these tests were performed with a closed loop servo-controlled stiff testing machine. The tests provide stress–strain curves at the chosen strain rates. Strain rate sensitivity is measured with in terms of the stress–strain curves, the maximum stress (flexural strength), dynamic increase factor, elastic modulus and Poisson’s ratio. Strain rate sensitivities are compared for different water content (0%, 40%, 70% and 100%). The obtained results showed significant influences of strain rate and water content on materials behavior. Both flexural strength and elastic modulus increased with higher strain rates, while Poisson’s ratio remained unchanged. At same strain rate, increasing water content would increase elastic modulus, but lower the flexural strength. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction There are many examples [1–3] of structures or structural elements subjects to dynamic loading. A rapid rise of the external load from zero to the peak load requires the material in the structural element quickly develops the internal stresses necessary to balance the external load. Concrete, with its heterogeneous structure, is found to behave differently when it is subjected to dynamic loading, as compared to its behavior under static loading [4]. Understanding the dynamic behavior of concrete is an issue of great significance for application in civil engineering. A lot of efforts have been dedicated in this field. More emphasis has been placed on the compressive [5,6] and tensile [7,8] behavior, and less on flexural response. Some researchers have studied the behavior of plain, composite, recycled aggregated concrete beams under impact loading. Bentur et al. [9] reported that the peak load occurred within 1 ms after contact in both plain and conventionally reinforced concrete beams. Banthia et al. [10] and ⇑ Corresponding author. Tel.: +86 25 83786551; fax: +86 26 83786986. E-mail address: [email protected] (X. Chen). 0950-0618/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2012.06.046
Zhang et al. [11] concluded that high strength concrete had high impact strength and more brittle than normal concrete. Tang and Saadatmanesh [12] concluded that the impact resistance of concrete beams significantly improved and the deflection and crack width reduced with the composite laminates. Rao et al. [13] suggested that for a given impact energy the reactions and strains of recycled aggregated concrete (RAC) with 50% and 100% recycled coarse aggregates are significantly lower than those of normal concrete and recycled aggregated concrete with 25% recycled coarse aggregates. Compared to the impact/impulsive tests, much less information is available on moderate strain rate tests. The quasi-static and moderate strain rate regime (106–101 s1) is still largely under-researched. For concrete structures (dam, bridge, offshore platform, etc.) operating underwater for a long period of time, the water content of concrete will have a certain influence on the mechanical behavior. The effect of water content on the static strength of concrete has been analyzed for a while, and researchers have also conducted intensive studies achieving many satisfactory results [14–23]. All researchers have found a compressive strength increases on drying, and data have been reported that support strength gain upon
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drying for the cases of tensile and flexural strength. Meanwhile, experimental researches have also been carried out on the effect of water content on the dynamic behavior of concrete. Rossi [24] believed that water content was one of the main factors influencing the rate effect of materials. However, there seems to be no consensus as to whether an increase or decrease occurs in the dynamic behavior as the water content is changed. Yan and Lin [7], Suaris and Shah [25], Rossi et al. [26], Reinhardt et al. [27], Cadoni et al. [28] and Ross et al. [29] have found that substantial tensile strength increases for wet concrete in the regime with the moderate strain rate (i.e. 104 s1–1 s1), where dry concrete has been demonstrated to be relatively insensitive. Watstein [30], Kaplan [31], Logunova et al. [32] Ranjith et al. [33] and Forquin et al. [34] achieved the same conclusion for dynamic compressive strength of concrete through tests. Reinhardt et al. [27] even reported that no strain rate effect could be detected in dry specimens under moderate strain rates where a very remarkable strain rate effect only existed in the tensile strength of wet concrete. While Zielinski et al. [35], and Brara and Klepaczko [36,37] considered moisture condition had no effect on the tensile strength of concrete when the strain rate is higher than 1 s1. However, the results of Harris et al. [38] and Zhou et al. [39] indicated that water content tended to decrease the dynamic compressive strength, and increased the dynamic splitting tensile strengths. With few exceptions, concrete in situ is fully saturated by water, or have at least a water content. In spite of this, testing of concrete in the laboratory is often performed on dry specimens or specimens with uncontrolled water content [24,30,38]. Although moisture effects in concrete have been investigated by others, these studies have not quantified the moisture levels. With the aim of obtaining further information in this regime, an experimental investigation is undertaken. Concrete specimens with water-binder ratio (w/b) 0.45 are subjected to four-point loading at strain rates of 106, 105, 104 and 103 s1. The tests provide stress–strain curves at the chosen strain rates. Strain rate sensitivity is measured with in terms of the stress–strain curves, the maximum stress (flexural strength), dynamic increase factor, elastic modulus and Poisson’s ratio. Strain rate sensitivities are compared for different water content (0%, 40%, 70% and 100%). This paper presents a description of the test setup and obtained results, and proposes explanations for the observed key phenomena. 2. Experimental program 2.1. Specimens In this investigation, the concrete mixes were used for Xiaowan arch dam, China. The so-called ‘‘dam concrete’’ is a specific type of concrete used in the construction of concrete dams, which differs in that a larger size (80–150 mm) of aggregate is used in order to save cement and reduce the heat of hydration. Due to practical difficulties in performing a large size specimen test, dam concrete is usually sieved to remove aggregate larger than 40 mm. The passed fresh concrete was remixed to produce a uniform mix. The mix proportion of concrete used is given in Table 1, where Type 42.5R Portland cement was used in all mixes. The mixes contained
Fig. 1. Picture of test setup.
fly ash (ASTM Class F) to save cement and reduce the heat of hydration for practical application. The crushed granite rock was employed as coarse aggregate. The maximum sand grain size was 4 mm. The specific gravities of the fine and coarse aggregates were 2.40 and 2.58, respectively. The coarse aggregate and sand were air dried prior to mixing. Following casting, the specimens were covered with a plastic membrane to prevent the moisture from evaporating. Specimens were demolded after 24 h and moist cured for 6 months. During this investigation, prismatic (150 150 550 mm) specimens were used. A total of 36 beam specimens was prepared for tests. Also, several companion 150 mm cubes were cast for obtaining static compressive and split-tensile strength of concrete. The following values were obtained for the concrete at the age of 180 days: compressive strength = 51.8 MPa, and split tensile strength = 3.56 MPa. 2.2. Four-point bending tests As aforementioned, in order to study the dynamic properties of concrete, four-point bending tests on concrete beams were conducted over a wide range of strain rates, from 106 s1 to 103 s1. Dynamic testing was conducted using a dynamic loading system that applied a programmable controlled loading. All these tests were performed with a closed loop servo-controlled stiff testing machine of MTS System Corporation. The test setup is shown in Fig. 1. The load was applied at 0.25 kN/s, 2.5 kN/s, 25 kN/s, and 450 kN/s respectively. The measurement system consists of a strain amplifier, a tape recorder, and an intelligent signal processor. A 104 Hz sampling frequency can be achieved. Eleven pairs of foil strain gages, 5 mm in width and 50 mm in width, were used to monitor longitudinal and transverse strain histories. They were crossly glued onto the faces of the specimen. Each specimen was removed from the moist room 2 days before testing. Typical load-time curves for concrete beams tests at a static and dynamic loading rate are shown in Fig. 2a and b respectively. These
Table 1 Details of mix proportions (in kg per cubic meter of dam concrete). Cement
134
Fly ash
57
Water
86
Coarse aggregate 5–20 mm
20–40 mm
40–80 mm
80–150 mm
548
390
400
400
Fine aggregate
Superplasticizer
Air-entraining admixture
534
1.43
0.0105
Note: The sieved concrete was obtained by removing aggregates larger than 40 mm, i.e., aggregates larger than 40 mm must have been replaced by fine or coarse aggregates to keep the same mix proportion.
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Fig. 3. Average water content of specimens versus time in water.
Fig. 4. Typical failure mode of concrete specimen. Fig. 2. Typical load time curves for concrete specimens: (a) loading rate 0.25 kN/s and (b) loading rate 450 kN/s.
illustrate that the linearity of loading was acceptable and that failure was easily recognized.
normalized by the cross sectional area exposed to water. The percentage of moisture content was found through interpolation by finding the mass of the specimen oven dried. The water content is 0% in an oven dried specimen and 100% in a saturated specimen. The water content of concrete specimens can be reflected by the degree of saturation. Water content was calculated as follows:
2.3. Water content of concrete During the phase of this investigation, the distribution and concentration of moisture in concrete specimens were manipulated by exposing the specimens to drying and wetting environments for various periods of time. The data collected during this moistureconditioning period formed and empirical basis for predicting the time required to cause given moisture change under various conditions. Concrete specimens were kept in an oven at 60 ± 1 °C after 180 days of moist curing. For oven-drying tests, drying operations (approximately 20 days in duration) were achieved in extremely well-controlled conditions. No heating rates were used for these drying procedures. After drying, specimens under test were placed on water reservoir again. Water, at room temperature, was then added to the reservoir. The specimens were then subsequently removed and dried until the moisture content of interest. The test at moisture content just involved drying the surface and immediately testing the specimen while its temperature remained 20 °C. This is important because the evaporative effect of water will cool the specimen. The mass of the specimen was measured at regular intervals using a balance accurate to one hundredth of a gram. The amount of water taken in from the specimen was calculated and
wr ¼
W Wd 100% Ww Wd
ð1Þ
where wr is the water content of the specimen (%), W is the mass of the specimen (g), Ww is the specimen water saturated mass (g), and Wd is the dried mass of a specimen (g). Fig. 3 shows water content as a function of exposure time for specimens that were oven-dried to zero moisture content and then immersed. Each data point is the average of three specimens. In this test, concrete specimens with four water contents of 0%, 40%, 70% and 100% were prepared for both static (106 s1) and dynamic (103 s1) loading. 2.4. Test procedure The beams were supported simply and were subjected to two-point loads, as shown in Fig. 1. The distance between the two-points was kept at 450 mm. Special bearing assemblies (roller, guide plates, etc.) were designed to facilitate the application of load to the test specimens. The load was applied to the beam by means of the hydraulic testing machine. All the tests were carried out in a
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laboratory of Hohai University, China. At least three specimens were tested for each loading condition to ensure the repeatability of the experimental results. To avoid changes in concrete strength due to aging of concrete specimens, all tests were carried out in succession within the period of 1–2 weeks. 3. Test results and discussion 3.1. Strain rate effects 3.1.1. Failure pattern Fig. 4 shows the typical flexural failure mode of concrete beam in this investigation. The crack pattern of all beam specimens under both static and dynamic loading is presented in Fig. 5. As shown in Fig. 5, the failure location of all concrete beams is at
Fig. 5. Crack pattern of concrete specimens.
451
the mid-span, no effect of strain rate was observed. Thus it would appear that for concrete beams subjected to flexure, strain rates will not affect the failure mode. The failure locations of the beams tested were evenly distributed between the load carrier clamps suggesting that the loading during the test was as intended. Fig. 6 shows the fractured surfaces of concrete beams under different strain rates (from 106 s1 to 103 s1). It can be seen from Fig. 6 that the fractured surfaces of the specimens became more and more flattened with the increasing strain rate; and an increasing number of aggregates were broken along the fractured surface. Many researchers [40,41] have shown that a large number of bond micro-cracks exist at the interfaces between the matrix and the aggregates. In case of static loading, the bond cracks at the aggregate-matrix interface start to extend to owing to stress concentration at crack tips. Then, some cracks at nearby aggregate surfaces start to bridge in the form of matrix cracks, meanwhile, other bond cracks continue to grow slowly. Finally, the microcracks through the matrix coalesce together all the bond cracks and complete failure occurs. The fractured surface of the specimen mainly passes through the matrix and the aggregate-matrix interfaces. This leads to a rough surface (Fig. 6a and b). However, crack velocity in concrete has been shown to increase with strain rate [42,43]. Therefore, at low strain rates crack has time to seek the path of least resistance. However, when the specimens are subjected to rapid loading, the creation of new cracks is forced to propagate through regions of greater resistance, and a greater amount of micro-crack may be required before a continuous fractured surface be formed. Thus, a certain part of the aggregates are broken during loading and the fractured surfaces of the specimens become more flattened (Fig. 6d). 3.1.2. Stress–strain behavior Fig. 7 shows the typical stress–strain curves at four strain rates for concrete beams. A significant change in the stress–strain
Fig. 6. Failure surface of concrete beams under different strain rates: (a) 106 s1; (b) 105 s1; (c) 104 s1; and (d) 103 s1.
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S. Wu et al. / Construction and Building Materials 36 (2012) 448–457 Table 2 Comparison DIF with published experimental results. Strain rates (s1)
Four-point bending (average value from current work)
Tension [7]
Compression [47]
Three-point bending [25]
103 104 105 106
1.361 1.186 1.136 1.0
1.431 1.322 1.167 1.0
1.15 1.05 1.02 1.0
1.22 1.11 1.06 1.0
Table 3 Poisson’s ratio versus strain rate for concrete. Strain rate (s1) Poisson’s ratio (average)
Fig. 7. Typical stress–strain curves of concrete specimens under different strain rates.
response of the materials to increase in strain rate is clearly seen in Fig. 7. For concrete specimens, as the strain rate is increased, both the initial slope and the peak stress increase, while the nonlinearity of the initial response decreases. Specific aspects of the response of the material as a function of strain rate are discussed next. 3.1.3. Flexural strength and dynamic increase factor (DIF) The results of the tests at different strain rates carried out are shown in Fig. 8. The strain rate was calculated from the linear portion of the strain–time curves in tests where strain gages were used. It can be seen from Fig. 8 that the flexural strength of concrete beams increased gradually as strain rate increased from 106 s1 to 105 s1, 104 s1 to 103 s1. A relationship between flexural strength and strain rate was established using regression to fit test data:
f ¼ 0:70 lg ðe_ Þ þ 10:72
ð2Þ
where f is flexural strength (MPa), and e_ is strain rate (s1). On the basis of the results presented here, it is clear that concrete is a very strain rate sensitive material. Concrete beams showed high flexural strength at high strain rate (Table 3). Several explanations can be suggested to account for these trends. One explanation may be based on fracture mechanics concepts [43,44]. The phenomenon of strain rate sensitivity can be explained by combining the classical Griffith theory with the concept of
105 0.179
104 0.218
103 0.209
sub-critical crack growth. According to Griffith theory, failure in brittle materials occurs when a flaw exceeds the critical flaw size and failure will then occur. If the load is applied slowly, the subcritical flaws have time to grow and thus the failure occurs at a lower value of the load. However, if the load is applied at a high rate, there is little or no time available for the growth of the subcritical flaws, and a higher load can be reached by the structural element before failure occurs. John and Shah [44] reported that pre-peak crack growth is reduced at high rates of loading. An alternative explanation of the observed trend may be given on the basis of non-linear fracture mechanics. It has been recognized that immediately ahead of a moving crack is a zone of micro-cracking called the process zone. Reinhardt et al. [45] has suggested that the size of this zone of micro-cracking depends upon the velocity of the crack; a faster crack has a larger zone of micro-cracking ahead of it. At a higher strain rate the crack propagates faster, and therefore the process zone will be bigger. This increased micro-cracking may explain the higher energy requirements at higher strain rates. This argument, may, at first glance, seem to contradict with the argument presented above on the basis of sub-critical crack growth, which predicts less micro-cracking in high strain rate loading situations. However, these two phenomena occur on the opposite sides of the peak load. The concept of sub-critical crack growth is applicable prior to the peak load; the concept of a larger process zone applies in the post-peak load region, where the unstable crack propagation commences. The dynamic increase factor (DIF), defined as the ratio of the dynamic strength to the static strength, has been widely accepted as an important parameter to measure the strain rate effect on the strength of concrete-like materials [6,46]. The results of the tests in this paper are plotted in Fig. 9. A relationship between flexural strength and strain rate was established using regression to fit test data:
DIF ¼ 0:11 lg ðe_ Þ þ 1:65
Fig. 8. Flexural strength versus strain rate for concrete specimens.
106 0.194
ð3Þ
These results are compared with those of compressive [47], tensile [7] and three-point bending [25] DIF of other researchers, as shown in Table 2. It can be seen that the tensile response is the most strain rate sensitivity, the compressive the least and the response of beam specimens subjected to increasing strain rate falls between those of tension and compression. This means that any constitutive law which assumes isotropic strain rate sensitivity may not be very accurate. From Table 2, it appears that the specimens tested in the fourpoint loading arrangement exhibit higher strain rate sensitivity than those tested a three-point loading arrangement. However, the difference cannot be solely attributed to the different testing
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Fig. 9. Strain rate influence on the DIF of concrete specimens.
Fig. 10. Elastic modulus versus strain rate for concrete specimens.
configuration since the specimens tested in a four point loading arrangement also had lower static strength. 3.1.4. Elastic modulus and Poisson’s ratio The elastic modulus is typically calculated as either a secant or a chord modulus. A secant modulus is calculated from the origin to a defined point on the stress–strain curve, usually within 30% to 60% of the specimen’s peak stress [5]. The chord modulus is usually evaluated between the stress and strain pairs at 50 millionths strain and at 40% of the peak stress [7]. In this study, the dynamic and static elastic modulus was measured as the chord modulus according to [7]. Fig. 10 shows the change in the values of elastic modulus as a function of strain rate. As with strength, elastic modulus increases approximately with an increase in strain rate. In this study, the average values of the modulus observed in strain rate 106 s1 to 105 s1, 104 s1 and 103 s1 are 50.83 GPa, 52.8 GPa, 56.15 GPa and 60.83 GPa respectively. A linearly elastic material like steel shows little strain rate sensitivity for elastic modulus [48,49], while concrete shows an enhanced elastic modulus at higher strain rates. The enhancement of elastic modulus can be explained by a decrease in internal micro-cracking (for a given level of stress) with the increased strain rate, resulting in a stress– strain curve that linear up to higher values of stress. However, the increase in only about half of the corresponding percent increases in strength. The lower strain rate sensitivity of elastic modulus compared to strength is consistent with similar observations in
Fig. 11. Effect of water content on stress–strain curves of concrete: (a) strain rate: 106 s1 and (b) 103 s1.
studies of other researchers [7,50]. The relationship between modulus of elasticity and strain rate can obtained by the following equation:
E ¼ 3:11 lg ðe_ Þ þ 69:11
ð4Þ
where E is modulus of elasticity (GPa). The Poisson’s ratio illustrated here is calculated at 30% of the strength. Table 3 illustrates the variation in the average Poisson’s ratios of the concrete beams as a function of strain rate. From the test results obtained, it seems that there is no definite increasing or decreasing tendency for Poisson’s ratio with increase in strain rate. Very little information concerning the strain rate effect on Poisson’s ratio is available. CEB recommendations [5] assume that the Poisson’s ratio is independent of loading rate, because of the scarcity of results. Harsh et al. [51] noticed that an increase in Poisson’s ratio for cement paste and mortar loading in tension during rapid loading. While Yan and Lin [7] did not observe any changes in Poisson’s ratio for strain rate as high as 0.2 s1. 3.2. Water content effects 3.2.1. Stress–strain behavior Not only the stress–strain behavior of concrete under static loading was measured, the dynamic loading behavior was also
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the gel, em-brittled the concrete system and consequently facilitated the propagation of bond cracks [59]. Moisture thus assists both the initiation and propagation of pre-existing drying induced cracks. The flexural strength evolution with the water content observed here follows the same results from those obtained by Pihlajavaara [14] and Okajima et al. [60] who tested respectively the mortars with w/c = 0.5 and 0.65 after obtaining a good maturity. They performed their flexural tests at uniform environmental humidity increasing, and register increasing of 58% and 39% respectively. Kanna et al. [19] reported an increase of 36% in flexural strength of a mortar with w/c = 0.45 after 6 days of over-drying at 105 °C. It has been shown that drying increases the strength of concrete for all forms of loading [15,61]. This process was termed dryingstrengthening by Pihlajavaara [14] though it had been observed experimentally earlier by Gonnermann [62], in a paper of great interest, showed that the strength of dried concrete on re-soaking reduced to the same value as that of concrete continuously moist cured. Matsushita and Onoue [63] also showed that re-saturation of dried concrete by a fluid with molecular sizes larger than water produced strength reductions related to the size of the molecule. The process of strength reduction in sorption was termed wetting-weakening by Pihlajavaara [14] who proposed a relationship between water content and the strength of the form: 2
½fw =f0 ¼ 1 cwr
Fig. 12. Effect of water content on flexural strength of concrete: (a) strain rate: 106 s1 and (b) 103 s1.
determined. As shown in Fig. 11a, when the static stress–strain curves of the four different water contents are compared, it is observed that the peak load of the four water content is decreasing with higher water content. Fig. 11b shows four stress–strain curves of concrete under dynamic loading (strain rate 103 s1). The shape of the stress–strain curves seem not to be influenced by the higher strain rate. For all four water contents, the strain rate effect seems to more pronounced for the saturated specimens. 3.2.2. Flexural strength and dynamic increase factor (DIF) Fig. 12 gives the evolution of the flexural strength of different water content and strain rates (Fig. 12a strain rate 106 s1; and Fig. 12b strain rate 103 s1). The flexural strength increases with the water content decreased. The marked reduction in the flexural strength of the concrete specimen highlights the role played by water content. The decrease in strength of a cement-based material versus its water content increase may be explained by means of capillary depression (or capillary suction) variations [52–54], disjoining pressures variations [55] and surface energy variations [56,57]. According to Yurdas et al. [58] and Burlion et al. [18], capillary suction, generated during the evaporation of free water in capillary pores, can be considered as the dominated mechanism. This effect leads to a stiffening of the material, which acts like an isotropic pre-stress of the granular skeleton. In addition, it is proposed that physio-chemi-sorption lowered the surface energy of
ð5Þ
where fw is the flexural strength at water content w (MPa); f0 is the flexural strength at water content 0% (MPa); c is a constant; and wr is the water content (%). This form of relationship is confirmed by the test results in this investigation, as shown in Fig. 12. The concept of wetting-weakening and drying-strengthening has been questioned because of the effect of differential shrinkage or swelling. Popovics [15] pointed out in discussing Pihlajavaara’s work [14] that drying produces tensile stresses in the exterior ‘‘shell’’ of the specimen; these stresses would be superimposed on applied tensile forces or could result in surface cracking. Both these latter effects would reduce the flexural strength of concrete. Wetting and subsequent swelling would impose a reversed stress state to drying, i. e., compressive stresses in the exterior ‘‘shell’’ and tensile in the interior. However, the influence of wetting or drying is governed by the rate at which the moisture movement occurs. Rapid moisture transfer results in severe stress gradients which have a dominant influence on apparent determinations. On the other hand, if the moisture loss is gradual, any stress gradient would be small and would dissipate with time as internal and external hygral equilibrium was achieved. Fig. 13 shows the dynamic increase factor (DIF) of concrete under different water content. From the results as shown in Fig. 13, the following conclusion can be drawn immediately: that wet concrete is more rate-dependent than dry concrete. This result has also been confirmed by other researchers [7,24,26]. Rossi [24] observed that the moisture condition of concrete had a definite effect on dynamic increase factor, with a wet concrete showing larger increases than an air-dried concrete. Yan [7] also found larger relative increases for wet concrete. Weerheijm and Van Doormaal [64] have noted that the strain rate effect, for the range of loading rates (11–10 s1), diminishes as the moisture content decreases as a result of longer periods of air-drying. Because the concrete specimens have the same skeleton strength, thus the difference in strength is mainly caused by water content. It is reported that for concrete, the main factor that induces the rate dependence of concrete strength is the viscous cohesive stress, rv of free water in the pores [7,24,26,65–67]. This stress can be expressed as:
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Fig. 13. Effect of water content on dynamic increase factor of concrete.
Fig. 14. Influence of water viscous cohesive force on the strength of specimen.
rv ¼
3pgR2 dh 3 dt 2h
ð6Þ
where g is the viscosity of the water, R is the radius of crack, and h is the height of crack (Fig. 14). To relate the viscous stress to the strain rate, we have to further link the displacement to the stress. The displacement of crack Dh can be calculated using the linear fracture mechanics:
pffiffiffi Dh / K I R
ð7Þ
where KI is the mode I intensity factor, which is proportional to r. Thus
rv /
dh / e_ dt
ð8Þ
From Eqs. (7), (8), we can see that the viscous cohesive force is proportional to the strain rate, thus contributing to more sensitive rate dependence for the moisture and saturated specimens. Concrete is a porous material, thus the above model can be used to explain the observed difference in strain rate sensitive (DIF) among specimens with various water content. Cadoni claims to give a different explanation for the influence of moisture content. Cadoni et al. [28] used Hopkinson Bar Bundle (HBB) to carry out experiments on large sized concrete specimens with aggregates from powder to 25 mm maximum size. The specimens were subjected to different curing conditions to study the effect of internal humidity conditions on strain rate enhancement. They confirmed that the level of free water inside concrete had an important influence on the strain rate sensitivity of concrete. In addition, they proposed a wave propagation concept for the physical explanation of the phenomenon. His interpretation is
Fig. 15. Effect of water content on elastic modulus of concrete: (a) strain rate: 106 s1 and (b) 103 s1.
based on the principle of wave propagation in concrete. When a pore is not filled with water, it will locally reflect the incoming stress wave. The multiple reflections of all pores together can cause a considerable increase in stress. When a stress wave meets a pore that is filled with liquid the reflected stress is not big not enough to cause the increase in stress that locally provokes the damage of the material. Therefore the wet concrete will exhibit a more pronounced rate effect than the dry concrete. This interpretation of Cadoni et al. [28] only gives an explanation of the difference between wet and dry concrete and does not explain the increase in strength between static and dynamic loading.
3.2.3. Elastic modulus and Poisson’s ratio The effect of water content on elastic modulus is shown in Fig. 15. The main feature of the results is that both the dynamic and static elastic modulus increases on higher water content. The significant change in the elastic modulus, in particular, highlights the effects of water content. It is proposed that decreasing of micro-cracking is a possible mechanism responsible for the increase of the modulus on rewetting. The partial recovery of the modulus on rewetting can be attributed to entry of interlayer water into the tobermorite gel and to some major crack healing due to water sorption. As reported in the last section, the flexural strength of concrete, however, decrease on water sorption. Evans and Marthe [68] drew the complete stress–strain curves for concrete in direct
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Table 4 Poisson’s ratio of concrete versus water content under different strain rates.
4. Conclusions
Strain rate (s1)
Water content 0%
Water content 40%
Water content 70%
Water content 100%
106 103
0.182 0.192
0.196 0.205
0.187 0.213
0.202 0.177
tension and observed that there was a reduction in the modulus as the strain in the concrete increased. They also attributed this reduction in the static modulus of micro-crack propagation. Haque and Cook [69], while investigating the effects of drying on the bulk modulus of hardened cement paste also concluded that rewetting causes a increase of the modulus. Parrot [70] however, attributed to the reduction in the elastic modulus of hardened cement paste on drying to the dehydration of the calcium silicate hydrate. Overall, the reduction in the elastic modulus, observed in this investigation, can be attributed to micro-cracking. In addition, the presence of moisture in concrete may also increase material stiffness; the increased stiffness with moisture present is evidenced by higher elastic modulus obtained for wet specimens, as reported by Reinhardet et al. [27]. Cook and Haque [20] indicated that the changes in mechanical properties such as strength and creep, as a function of water content, can be explained on the premise of time-dependent micro-cracking, surface free energy and redistribution of the interlayer water. The present results establish that the elastic modulus of concrete is also a function of the water content and any study into the strength and deformation should take into account the concomitant variation of the elastic modulus. Average Poisson’s ratio for most of the tests was between 0.177 and 0.213 according to Table 4 for concrete specimens. Notice there is no significant variation of Poisson’s ratio was measured for concrete with different water content. These results of this investigation show quite similar trend to those of static tests reported by other investigators [71]. Tests on saturated and ovendried cement pastes at an age of 30 days for water–cement ratios of 0.3–0.5 showed that Poisson’s ratio remained remarkably constant at 0.25 for increase rewetting time [71]. Persson [72]’s results showed that Poisson’s ratio of mature of high performance concrete decreased with higher relative humidity in concrete. He linked the results to the self-desiccation of high performance concrete. However, he also showed that the significance of the influence of moisture was low.
3.3. Multi-parameter statistical analysis In this investigation, the flexural strength and elastic modulus of concrete were determined for different strain rates and water content. Multiple regression analysis of the flexural strength f (in MPa), dynamic increase factor DIF and the elastic modulus E (in GPa) with strain rate e_ (s1) and water content w (%), as independent variables were performed. The following regression equations were derived:
f ¼ 11:71 þ 0:21 ln ðe_ Þ 2:49w R ¼ 0:96
ð9Þ
DIF ¼ 0:94 þ 129:49e_ þ 0:25w R ¼ 0:87
ð10Þ
E ¼ 38:12 þ 3; 623; 080:55e_ 2 þ 19:73w R ¼ 0:88
ð11Þ
where R is the correlation coefficient. Reasonable fits are observed from Eqs. (9)–(11).
In this study, the mechanical behavior of concrete is evaluated by tests using concrete specimens with different strain rates (106, 105, 104 and 103 s1) and different water content (0%, 40%, 70% and 100%). From this work the following conclusions are made: The fractured surfaces of the specimens became more and more flattened with the increasing strain rate; and an increasing number of aggregates were broken along the fractured surface. As the strain rate is increased, both the initial slope and the peak stress increase, while the nonlinearity of the initial response decreases. The flexural strength, dynamic increase factor (DIF), and elastic modulus of concrete beams increased gradually as strain rate increased from 106 s1 to 103 s1. There is no definite increasing or decreasing tendency for Poisson’s ratio to increase in strain rate. The flexural strength increases with the water content decreased. The marked reduction in the flexural strength of the concrete specimen highlights the role played by water content. At same strain rate, increasing water content would increase elastic modulus and dynamic increase factor (DIF). Both the dynamic and static elastic modulus increases with higher water content. There is no significant variation of Poisson’s ratio was measured in concrete with different water content. There are many other factors which may affect the mechanical behavior of concrete as strain rate is increased, such as mix proportions, aggregate type (stiffness, surface texture, size, shape and strength) and content, grading, cement content, age and curing conditions. Further work, in particular more test data, is needed. Acknowledgement The authors are grateful to the National Natural Science Foundation (Nos. 50979032 and 51178162) for the financial support. References [1] Fu HC, Erki MA, Seckin M. Review of effects of loading rate on reinforced concrete. J Struct Eng 1991;117(12):3660–79. [2] Tanimura S, Mimura K, Nonaka T, Zhu W. Dynamic failure of structures due to great Hanshin-Awaji earthquake. Int J Impact Eng 2000;26(6–7):583–96. [3] Ozbolt J, Sharma A. Numerical simulation of reinforced concrete beams with different shear reinforcements under dynamic impact loads. Int J Impact Eng 2011;38(12):940–50. [4] Suaris W, Shah SP. Constitutive model for dynamic loading of concrete. J Struct Eng 1984;111(3):563–76. [5] Bischoff PH, Perry SH. Compressive behavior of concrete at high strain rates. Mater Struct 1991;24:425–50. [6] Fu HC, Erki MA, Seckin M. Review of effects of loading rate on concrete in compression. J Struct Eng 1991;117(12):3645–9. [7] Yan D, Lin G. Dynamic properties of concrete in direct tension. Cem Concr Res 2006;36(7):1371–8. [8] Malvar LJ, Ross CA. Review of strain rate effects for concrete in tension. ACI Mater J 1998;95(6):735–9. [9] Bentur A, Mindess S, Banthia N. The behavior of concrete under impact loading: experimental procedures and method of analysis. Mater Struct 1987;20(4):371–8. [10] Banthia N, Mindess S, Bentur A. Impact behavior of concrete beams. Mater Struct 1987;20(4):293–302. [11] Zhang XX, Ruiz G, Yu RC, Tarifa M. Fracture behavior of high-strength concrete at a wide range of loading rates. Int J Impact Eng 2009;36(10–11):1204–9. [12] Tang T, Saadatmanesh H. Behavior of concrete beams strengthened with fiberreinforced polymer laminates under impact loading. J Compos Constr 2003;7(3):209–18. [13] Rao MC, Bhattacharyya SK, Barai SV. Behavior of recycled aggregate concrete under drop weight impact load. Constr Build Mater 2011;25:69–80. [14] Pihlajavaara SE. A review of some of the main results of a research on the aging phenomena of concrete: effect of moisture conditions on strength, shrinkage and creep of mature concrete. Cem Concr Res 1974;4:761–71. [15] Popovics S. Effect of curing method and final moisture condition on compressive strength of concrete. J Am Concr Inst 1986;83:650–7. [16] Barlett FM, MacGregor JG. Effect of moisture condition on concrete core strength. ACI Mater J 1993;91(3):227–36. [17] Glucklich J, Korin U. Effect of moisture content on strength and strain energy release rate of cement mortar. J Am Ceram Soc 1975;58(11–12):517–21.
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