Determination of mortar setting times using shear wave velocity evolution curves measured by the bender element technique

Cement and Concrete Research 106 (2018) 1–11

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Determination of mortar setting times using shear wave velocity evolution curves measured by the bender element technique

T

⁎

J. Zhua,b, J.N. Caob, B. Batec, , K.H. Khayatd a

Jones Lang LaSalle, 1 Zhongxinsi Road, Futian District, Shenzhen 518048, China Department of Civil, Architectural and Environmental Engineering, Missouri University of Science and Technology, Rolla, MO 65409, United States c Institute of Geotechnical Engineering, College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, China d University Transportation Center and the Center for Infrastructure Engineering Studies, Department of Civil, Architectural and Environmental Engineering, Missouri University of Science and Technology, Rolla, MO 65409, United States b

A R T I C L E I N F O

A B S T R A C T

Keywords: Mortar Early age Shear wave velocity Initial setting time Final setting time Bender element

Although identified as a good indicator to characterize freshly cast cementitious materials, shear wave velocity (Vs) alone has not been used successfully to determine the initial and final setting times (ti and tf). The challenge originates from the large Vs range that can vary from < 50 m/s to > 2000 m/s for cementitious materials at early age (typically < 24 h). To overcome these challenges, modifications to traditional bender element and to specimen geometry were made to obtain Vs versus time (Vs(t)) curves of six early age mortars at different water-tocement ratios, some with chemical admixtures. Derivative methods were then proposed to obtain ti and tf. The peak time (tpeak′) in the first-order derivative of Vs(t) curves correlate well to the final setting time (R2 = 0.979), while the peak time (tpeak″) of the second-order derivative of Vs(t) curves correspond well to the initial setting time (R2 = 0.950).

1. Introduction Monitoring freshly cast cementitious materials (paste, mortar, and concrete) at early age (approximately the first 24 h) is desired in quality assurance and quality control (QA/QC), and for long-term performance prediction. Initial and final setting times are the two key parameters to characterize cementitious material properties of early age. Initial setting time denotes the time when a cementitious material is sufficiently rigid to withstand a certain pressure and the material starts losing its plasticity. Final setting time denotes the time when the developments of strength and stiffness start, and the plasticity is completely lost. Both setting times are useful parameters in the transportation, casting, and consolidation of cementitious materials and are key parameters for strength development at early age and for formwork removal [1,2]. The standard methods of measuring setting times are based on the penetration resistance test (ASTM C403) for mortar or concrete and the Vicat needle test (ASTM C191) for paste. Both tests are destructive laboratory tests. The isothermal calorimetry method was employed to determine setting times from heat evolution curves [3–8]. The above methods are at the specimen scale. The ultrasonic pulse velocity measurement [9,10] is widely used in the field due to its non-destructive nature and its sensitivity to the presence of air pockets, abnormalities, or defects. However, water in the concrete leads to a high Vp value ⁎

(approximately 1490 m/s), which is on the same order of magnitude as that of the fresh cementitious material where Vp can vary from approximately 100 m/s in the fresh state to over 4000 m/s in the hardened state. Subsequently, P-wave velocity originating from the solid portion of the cement-based material during curing is shielded by water, which makes it a poor indicator of the curing process when used alone. Carette and Staquet [11] combined Vp and Vs results to determine setting time of mortars, and concluded that the P-wave is less sensitive to the setting process than S-wave. The hydraulic pressure method monitors the setting/hardening process using wall hydraulic pressure that are in contact with the concrete through the formwork (from hydrostatic to zero as the specimen cures from slump to fully hardening) [7,12]. Hydraulic pressure method can be implemented in the field. However, this method necessitates the use of high accuracy pressure sensors. Pore water pressure sensors in contact with concrete can then be used to evaluate the rate of setting. Previous studies suggest that shear wave velocity (Vs) is a good indicator of the curing process of cementitious materials, such as mortars [11] and cement-soil mixtures [13,14]. This is because shear waves propagate primarily through the solid skeleton of a material and is not significantly influenced by the presence of water or air. In spite of its use in evaluating characteristics of in-situ soils and cemented soil in the laboratory, shear wave velocity alone is not commonly used to

Corresponding author at: Institute of Geotechnical Engineering, College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, China. E-mail address: [email protected] (B. Bate).

https://doi.org/10.1016/j.cemconres.2018.01.013 Received 14 February 2017; Received in revised form 4 November 2017; Accepted 11 January 2018 0008-8846/ © 2018 Elsevier Ltd. All rights reserved.

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monitor the early age properties of cementitious materials. This is because early-age cementitious materials have a larger range of stiffness variations during the curing process where Vs can vary from around 50 m/s in the fresh state to over 2000 m/s in the hardened stage. This is considerably greater than soils that normally vary from 30 m/s (kaolinite [15]) to 350 m/s (iron oxide-coated sand, [16]) under normal loading conditions (< 400 kPa). The quick stiffness (Vs) increment increases the resonant frequency of the specimen, which subsequently mandates the increment of the exciting frequency to ensure a good signal-to-noise ratio [17,18], reduces wavelength, and poses challenges in maintaining the wavelength ratio (Rd) requirement (Rd > 2) needed to minimize the near-field effect in < 24 h [19,20]. This is the major reason that existing studies using traditional piezoceramic materialbased tools, such as the traditional bender element (BE) [21] and piezoelectric ring actuator [7], provide only partial Vs evolution data (< 15 h) for cementitious materials generally with longer curing process (normally > 24 h). However, in view of its advantages, such as insitu and laboratory experimental capabilities and well-established approaches for soils, the bender element technique could be suitable to evaluate the stiffness of cement-based materials at early age. This study aims at modifying the traditional bender element to obtain Vs evolution curves of mortar at early-age spanning from 0 to > 24 h. The study also seeks to determine the initial and final setting times based on Vs evolution results. The following objectives are proposed accordingly: (1) modify the geometry of mortar specimen and change the geometry, alignment and coating of a traditional bender element used for soils to cover Vs variations at early-age of cementbased materials; and (2) measure the evolution of shear wave velocity of mortar specimens at early age (up to 96 h) with the modified bender element testing system. Six mortar mixtures of different water-to-cement ratios (w/c), including one with a set accelerator and two with set retarders were prepared to embrace a broad range of setting times. The evolution of Vs with time was analyzed to evaluate setting times, which were compared to values measured by ASTM standard penetration resistance test. In addition, a calorimetry test-based method was also evaluated and used to correlate to setting times determined from penetration resistance test.

Table 1 Mixture proportioning of tested mortars. Mixture

Mix 1a

Mix 2

Mix 3

Mix 4

Mix 5

Mix 6

w/c Cement (kg/m3) Sand (kg/m3) Water (kg/m3) Set retarder (ml/100kgc) Set accelerator (ml/100kgc) Unit weight (kN/m3)

0.50 673 1137 337 – – 21.34

0.43 713 1203 313 – – 22.28

0.37 751 1267 277 – – 22.63

0.43 713 1203 313 195 – 22.08

0.43 713 1203 313 – 1500 21.78

0.43 713 1203 313 220 – 22.08

a

Repeated three times to verify the repeatability of material properties.

close to the lower limit of the specification for aggregate used to make masonry mortar (ASTM C144). Two chemical admixtures were introduced to alter the range of setting times: a hydration controlling admixture that retards setting times by controlling the hydration of the cement, and a non-chloride accelerating admixture that accelerates cement hydration. 3. Mixing design Six mortar mixtures were used, as shown in Table 1. Mortar mixtures with w/c of 0.50, 0.43, and 0.37 are referred to as Mix 1, Mix 2, and Mix 3, respectively. The dosage rates of the admixtures (i.e., set accelerator and set retarder) were selected based on the criteria in ASTM C 494: Normal variation of delaying in the initial setting time is between 1 and 3.5 h when using a set retarder, or between 1 and 3.5 h earlier when using an accelerator. Mix 4 and Mix 6, modified from Mix 2 (w/c of 0.43), contained 3 fl oz./cwt (fluid ounce/cement hundredweight) (195 ml/100kgc) and 3.4 fl oz./cwt (220 ml/100kgc) hydration controlling admixture, respectively. Mix 5 was modified from Mix 2 with w/c of 0.43, and incorporated 23 fl oz./cwt (1500 ml/100 kg) accelerating admixture. The procedure used for mixing mortar is in compliance with ASTM C 305. A mechanical mixer was used. In each test, a batch of 25 l of mortar was prepared, and 21 l was placed in the formwork. 4. Bender element testing system

2. Materials A bender element (BE) testing system for measuring Vs of cementitious materials was used. The BE system consisted of three pairs of bender elements, a signal generation and acquisition system, and a wooden formwork measuring 0.61 × 0.305 × 0.14 m3 (length × width × height, inner geometry) (Fig. 2). The system was developed with modifications on a traditional bender element system. The details of each component and the rationale behind the corresponding modifications are discussed below.

A Type I portland cement was used. Missouri River sand. A well graded river-bed sand was used. The sand was sieved through No. 4 sieve with D50 of 0.7 mm and Cu (coefficient of uniformity, D60/D10) of 2.74. The grain-size distribution of the sand is shown in Fig. 1 and is 100 90

Missouri River Sand ASTM C144 lower limit

Cumulative Passing (%)

80

5. Bender element test setup

ASTM C144 upper limit

70

Two-layered brass-reinforced piezo actuators were cut into bender element plates with dimension of 23 × 11.5 × 2 mm3 (length × width × thickness). This size is larger than typical sizes ranging from 12 × 5 × 0.5 mm3 to 20 × 12.7 × 2 mm3 [22] used in soil testing. The selected larger size is expected to enhance signal strength given the long travel distance in a large specimen and the initially paste-type materials (possibly weak signal due to the few contacting points for Vs propagation). A parallel-type connection was also adopted over series-type connection for stronger received signals [23]. From inside out, coatings of a bender element that is typically used for geotechnical applications follow the order of polyurethane, silver conductive paint, and epoxy coatings (Fig. 2b) [15,17,23,24]. Modifications were made to these coatings to accommodate testing of cementitious materials, which are corrosive with high pH. For the

60 50 40 30 20 10 0 0.01

0.1

1

10

Sieve Size (mm) Fig. 1. Grain-size distribution of sand used in this study.

2

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purple primer

PVC 3 days later cement

Installed on a socket

traditional coating

modified coating

Fig. 2. Bender element testing system for monitoring of early age stiffening of cementitious materials: (a) bender element coatings, (b) coating comparison, (c) signal generation and receiving system, and (d) mortar specimen and formwork.

7000

Mix-1 (w/c=0.50) Mix-2 (w/c=0.43) Mix-3 (w/c=0.37) Mix-4 (w/c=0.43+1.95 mL/kg retarder) Mix-5 (w/c=0.43+ accelerator) Mix-6 (w/c=0.43+2.20 mL/kg retarder)

Penetration Resistance (psi)

6000

5000

Fig. 3. Penetration resistance evolution with time for the six investigated mortars.

4000

3000

2000

1000

0 100

200

300

400 500 Elapsed Time (min)

600

700

800

grounding (drain wire embedded into the testing material) [23,24]. (2) PVC cement was used instead of epoxy due to its higher moisture resistance, good flexibility, chemical resistance and durability. A layer of Oatey purple primer was used to roughen up the surface of the polyurethane-coated piezoceramic plate, and to provide better mechanical bonds between the polyurethane and PVC cement [19] (Fig. 2b). (3) Outside of the previously mentioned coatings, a plastic sheet was tightly wrapped around bender element unit to further protect the unit in a corrosive environment.

modified BE system, polyurethane was still used in direct contact with the piezoceramic plate as the insulation and waterproofing coating. Three to five polyurethane layers were painted onto the piezoceramic plate to strengthen the coating and to avoid possible electricity shorting path. Outside the polyurethane coating, however, the following modifications to the traditional coatings were made: (1) Silver paint coating was not used in this study, despite its electrical shielding ability that prevents cross-talking [23]. This is because: (i) no obvious improvement in the quality of signals was observed using silver painting in a side-by-side comparison test on dry sands using bender elements with and without silver conductivity coating; (ii) the BEs are more prone to electrical short-circuiting during the silver coating procedure, which leads to low success rate of BE fabrication; and (iii) a sufficient electrical shield seemed to be provided by parallel BE made with twisted coaxial cable with

To sum up, the coatings on a BE unit follow the order of (from inside to outside): polyurethane; purple primer; PVC cement; and plastic wrap (Figs. 2a–b). Several bender element tests were performed on three individual specimens with Mix 1 to evaluate repeatability. 3

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Input (V)

Output (mV)

Input (V)

Fig. 4. Heat evolution versus time for the six tested mortars.

12 8 4 0 -4 -8 -12 0.10 0.05

Fig. 5. Example input and output signals of (a–b) square function and (c–d) sine function for a mortar specimen with 0.5 w/c (Mix I) determined after 8 h of age.

(a)

(b)

0.00

travel time = 0.40 ms

-0.05 -0.10 12 8 4 0 -4 -8 -12

(c)

Output (mV)

0.10 0.05

(d)

0.00 -0.05

travel time = 0.43 ms

-0.10 -0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6 0.7 0.8 Time (ms)

0.9

1.0

1.1

6. Formwork

1.2

1.3

1.4

1.5

required to ensure the travel time sufficiently larger than the system lag. (3) On the other hand, in order to receive clear signals, travel distance should not be too long. (4) To avoid near-field effect, the travel distance to wavelength ratio (Rd ratio) should be no less than two [25]. In this study, the tip-to-tip travel distance was chosen to be 0.27 m, which gave a travel time at least 8 times greater than the system lag while satisfying the wavelength ratio requirement for the majority of the time (resonant frequency and wavelength evolve over time, see also the last paragraph of this section). Subsequently, the inner dimensions of the formwork were 0.61 × 0.305 × 0.14 m3 (length × width × height) (Fig. 2d).

There are a few considerations in choosing the dimensions of the formwork. (1) There is inherent system time lag due to the bender element plate, coatings, wiring, and the electrical equipment [19,20]. Kang et al. [20] determined the system lag of the same bender element testing system with a smaller BE (12.7 × 8.0 × 0.6 mm, length × width × thickness) to be 6–11 μs. (2) The stiffness of hardened cementitious materials, such as mortar in this study, is usually higher than that of common soils. Therefore, long wave travel distance is 4

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10 MHz signal generator, a linear amplifier, a 4 pole LP/HP filter, and a 100 MHz oscilloscope. The stiffness and attenuation (energy dissipation) of cement paste, mortar, and concrete at early age (up to 72 h) evolve rapidly as they change from slurry state to a semi-solid state. Consequently, their resonant frequencies increase drastically (estimated to be from 100 Hz to 14,000 Hz), while the attenuation of the received electrical signals likely decrease over time. To receive strong signal and weak noise, the exciting frequency of the input sine wave was also adjusted to be close to the resonant frequencies. Square wave, containing a wide frequency range that covers the evolving natural frequency of the mortar, was also used. Cutoff frequencies were 1 Hz (high pass) and 50 kHz (low pass), respectively. The amplitude of the waveform generator was 10 V. 7. Penetration resistance test To determine the initial and final setting times of mortar, penetration resistance test was performed in accordance to ASTM C403 and AASHTO T197. Loading apparatus, penetration needles with bearing areas of 645, 323, 161, 65, 32, and 16 mm2, and tamping rod were used. The penetration resistance was calculated by dividing the recorded force by the needle bearing area. Six to nine undisturbed penetration readings of penetration resistance were recorded at different elapsed times for each test. The time taken to penetrate 25.4 mm depth was about 10 ± 2 s. Elapsed time was calculated from the time when water was added to cement. Initial and final setting times are determined to be the elapsed times at penetration resistance of 3.5 MPa and 27.6 MPa, respectively.

Fig. 6. Shear wave velocity versus elapsed time curves from bender element tests on three individual mortar specimens with Mix 1.

Thick (0.038 m in thickness) wooden board was chosen as the formwork material for the following two reasons: (1) it is rigid enough to resist any lateral movement due to the lateral pressure exerted by the fresh mortar; (2) its thickness can ensure tight fixation of the BEs on the wall and provided good contacts between the bender and mortar. Wooden boards were assembled together by screws, which is easily removed after each test. Oil lubrication along the inside wall of the formwork, together with screw connections, enabled the reuse of wooden formwork. Three pairs of BEs were installed in pre-drilled holes (diameter, 0.022 m), aligning perpendicularly to the bottom of the formwork to prevent possible voids immediately underneath the benders during mortar placement. The vertical alignment of the benders also avoided interference by compressive waves reflected from sidewalls because of their elongated travel path [20]. The distance between the center of a BE and the mortar surface was 0.038 m. The signal generation and acquisition system consisted of a 1 mHz-

8. Calorimetry test A calorimetry test was carried out, in compliance with ASTM C1679 to evaluate the heat flow generated by the hydration reaction of cement over time. I-Cal 8000 Isothermal Calorimeter and the accompanying CalCommander software were used. Fifty to 150 g of mortar sample was placed in a clean reusable plastic cup. The lid was closed until testing to minimize heat exchange with the surrounding air. TheArrhenius' law (Eq. 1) was used to describe the temperature dependency of the hydration rate of cement: Fig. 7. Shear wave velocity versus elapsed time curves.

5

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Fig. 8. Vs evolution over time of mortars with different w/c. Legends beginning with “Carette”, “Liu” and “Soliman” refer to Carette and Staquet [11], Liu et al. [21], and Soliman et al. [7], respectively.

Table 2 Initial and final setting times determined from different methods. Mortar

Mix-1 Mix-2 Mix-3 Mix-4 Mix-5 Mix-6 R2

Initial setting time (h)

Final setting time (h)

Penetration resistance

BE (tpeak″)

BE (a)

Calorimetry

Penetration resistance

BE (tpeak′)

Calorimetry

5.00 4.33 3.28 6.53 3.28 9.58 –

4.59 5.32 3.03 6.78 3.13 9.17 0.950

5.16 4.20 3.85 6.36 2.88 9.56 0.981

4.48 4.14 3.46 7.75 3.46 8.71 0.910

6.42 5.67 4.83 8.08 4.38 11.50 –

6.50 6.20 5.10 8.50 3.80 11.50 0.979

6.56 5.78 5.07 9.30 3.83 10.34 0.908

Fig. 9. The rate of heat evolution curve and its first-order derivative curve for Mix 1.

6

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constant temperature (20.0 °C) was maintained during all calorimetry tests to avoid inconsistent results induced by temperature variation. 9. Results The penetration resistance versus elapsed time curves for six mixtures is shown in Fig. 3. The rate of heat evolution versus elapsed time relationship for the six fresh mortars measured by calorimetry test is shown in Fig. 4. The process of cement hydration can be broken down into five stages. In the first stage, a large amount of heat is rapidly generated after cement contacts with water. Hydration activity slows down in Stage 2, which is also known as the dormant period. Mortars with set retarder (Mix 4 and Mix 6) have longer dormant periods. In Stage 3, heat release accelerates followed by a rapid reaction between calcium hydrate (CH) and calcium silicate hydrate (CSH) [7]; both the initial setting (beginning of solidification) and final setting (complete solidification and beginning of hardening) occur in Stage 3. Hydration products are formed at slower rates during Stage 4 (deceleration) and Stage 5 (diffusion limited). The received BE signals from both the sine and square wave forms are plotted in Fig. 5. The time of arrival of the received shear wave was determined using the zero-crossing point with the x-axis of the half peak before the first major peak (Fig. 5b and d). Then, the travel time was determined from time zero to the time of arrival, and the shear wave velocity was calculated by dividing the tip-to-tip distance by the travel time. The travel times determined from square and sine wave forms should be the same [17,26]. In practice, however, minor differences (< 10% in this study) in the travel time by different wave forms exist. For instance, in the case of the Mix 1 mortar made with 0.5 w/c, a 7% difference in travel time was observed between square and sine wave forms at 8 h of age. In such a case, an average shear wave velocity was reported. Three repeated Vs versus time relationships for Mix 1 agrees well with each other (Fig. 6), which suggests good repeatability of the BE system. The variations of shear wave velocity with elapsed time for the six mortar mixtures are illustrated in Figs. 7 and 8. The results show that: (1) shear wave velocity increased monotonically with time during the first 24 h. Three phases of the Vs evolution curve can be observed: a gentle slope before approximately 5 to 8 h, a steep increment from about 5 to 15 h, and a gentle slope approximating to a plateau value after about 10 to 15 h. (2) Shear wave velocity of hardened (> 20 h) mortar ranged from 1700 to 2100 m/s. (3) At the same elapsed time in mortar made without a set accelerator or retarder, Vs of fresh mortar with low w/c was higher. The use of a set retarder significantly delayed hydration reaction of cement by approximately 3 h and 5 h when incorporated of dosage rates of 195 ml/100 kg and 220 ml/100 kg, respectively (Table 2). (5) The use of a set accelerator increased Vs in the initial 9 h, and then registered a lower Vs value than the mortar made without any set accelerator did (Fig. 7), which suggests that the use of set accelerator decreased the Vs of the hardened mortar.

Fig. 10. Comparison between final setting times obtained from the penetration resistance and those from shear wave velocity derivative method. Solid symbols are experimental data from this study; open symbols are from Carette and Staquet [11].

10. Discussion 10.1. Comparison of Vs evolution at early age to previous studies Fig. 11. Comparison between initial setting times obtained from penetration resistance and those either from Vs evolution methods (tpeak″ and parameter a) or from calorimetry method. Solid symbols are experimental data from this study; open symbols are from Carette and Staquet [11].

k = Ze−Ea RT

Compared to the shear wave velocity (Vs) measurements of mortar mixtures previously reported by Soliman et al. [7], Liu et al. [21], and Carette and Staquet [11], it can be observed that for the same curing time, the range of the magnitude of Vs in this study (0–2100 m/s) is similar to that in previous studies, and that the variations of Vs with elapsed time curves in this study share the same S-shaped feature as those in the literature (Fig. 8). It can also be noted that Vs of the mortar made with w/c of 0.50 (1697 m/s) after 24 h of curing in this study is lower than that of a hardened mortar at the same w/c (2260 m/s) reported by Vipulanandan and Garas [27]. In addition to the longer curing time in the latter study, a higher Vs value could also originate

(1)

where k is the hydration rate constant, Z is a proportionality constant, Ea is the activation energy for the reaction, R is the ideal gas constant in J/(mol.K), and T is the temperature in Kelvin. Eq. 1 suggests that the warmer the mortar, the faster the hydration reaction is. Therefore, a 7

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Fig. 12. Fitting curves using Weibull, the lognormal, and Gamma cumulative distributions, and modified Fredlund and Xing equation. Data labeled “measured” refers to the measured Vs data in this study.

subsequent time steps can be taken directly from the calorimetry test results to achieve sufficient accuracy since approximately 500 time steps were recorded between the valley of Stage 2 and the peak of Stage 3. The rate of heat evolution versus elapsed time curve and its first order derivative curve for Mix 1 is shown in Fig. 9 as an example. The initial and final setting times of all six mortar specimens obtained using the Ge et al. [3] method are presented in Table 2, and were correlated to those measured from the penetration resistance test, as shown in Figs. 10 and 11, respectively. For the calorimetry measurement in this study, both tcp and tcp′ values correlate to the final and initial setting times obtained from standard penetration tests reasonably well (with R2 of 0.910 and 0.908, respectively). These good correlations seem to suggest that the calorimetry method, albeit yielding slightly lower R2 values (0.908–0.910) than those (0.950–0.981) from the proposed Vs-based method in this study, is viable. For the calorimetry measurement in Carette and Staquet [11], however, both tcp and tcp′ values correlate poorly to tf and ti values obtained from standard penetration tests (Figs. 10–11). It is not clear whether the poor correlations origin from the narrow range of the initial and final setting times for the mortars in Carette and Staquet [11] or the calorimetry method proposed by Ge et al. [3]. Further calorimetry testing and analysis are warranted before conclusions can be drawn regarding the validity and limitations of the calorimetry method.

Table 3 Parameters of Weibull, lognormal, and Gamma cumulative distributions, and Fredlund and Xing equation. Equation

Parameters

Mix 1

Mix 2

Mix 3

Mix 4

Mix 5

Mix 6

Weibull

α β R2 μ σ R2 α β R2 a n m R2

2.178 9.953 0.996 2.097 0.516 0.998 3.934 2.295 0.998 8.068 3.015 2.266 0.999

2.651 8.933 0.995 2.031 0.416 0.996 5.795 1.405 0.996 6.696 5.019 1.656 0.995

2.303 8.124 0.994 1.904 0.486 0.998 4.422 1.665 0.997 6.190 3.464 1.921 0.999

3.018 11.286 0.998 2.285 0.411 0.994 6.447 1.617 0.996 9.778 3.683 2.162 0.997

1.773 6.955 0.992 1.695 0.637 0.997 2.707 2.341 0.995 4.817 2.677 1.825 0.998

3.384 14.083 0.999 2.511 0.331 0.996 9.227 1.396 0.998 14.346 4.047 3.707 0.999

Lognormal

Gamma

Modified Fredlund and Xing

from the larger maximum size of the aggregate, better quality cement and mixing, as well as the systematic shift in the measurement method and first arrival time determination [20]. In the following sections, the initial and final setting times are determined from the penetration resistance, calorimetry test method, and shear wave velocity (Vs) test. The ti and tf values deducted from the calorimetry and Vs tests are compared to those obtained from the penetration resistance test, which was used as a benchmark.

10.4. ti and tf determined from Vs evolution curves The evolution of Vs versus elapsed time could be used to determine the initial and final setting times [7]. Soliman et al. [7] plotted the first derivative of Vs (dVs/dt) versus time curve, and defined the times corresponding to the “lower concave point” and the “highest convex point” in the major Vs increment portion of the dVs/dt versus time curve as the initial and final setting times, respectively. However, it is not always possible to obtain the ‘lower concave point’ and the ‘highest convex point’ because dVs/dt versus time curve is often monotonic in the major Vs increment portion (see also Fig. 13). This is because the dVs/dt versus time curves in this study and that reported by Carette and Staquet [11] do not have such local peak or valley points (Fig. 13) and noise (or fluctuation due to the variation of measured Vs values) could be misinterpreted as such local points due to the discrete nature of the dVs/dt versus time curves.

10.2. ti and tf determined from penetration resistance test The initial and final setting times determined from penetration resistance test (ASTM C403) ranged from 197 to 575 min and from 263 to 690 min, respectively as shown in Table 2 and Fig. 3. 10.3. ti and tf determined from calorimetry test Ge et al. [3] proposed that the initial setting time correlates to the peak time (tcp′) of the first-order derivative curve of Stage 3 of the rate of heat evolution versus elapsed time curve, while the final setting time correlates to the peak (tcp) of Stage 3 of the rate of heat evolution versus elapsed time curve. Instead of curve fitting, differences between two 8

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Fig. 13. Original, first, and second derivatives of Vs versus elapsed time curves.

Table 4 Fitting parameters of lognormal and modified Fredlund and Xing equations for experimental data of mortars with clinkers (REF), municipal solid waste incineration electrostatic precipitator fly ash at different ratios (EFA-1 and EFA-2), thermal power station fly ash at different ratios (TFA-1 and TFA-2), reduced water/binder ratio of 0.4 (R-0.4), and air entraining agent (R-AEA) in Carette and Staquet [11]. Equation

Parameters

REF

TFA-1

TFA-2

EFA-1

EFA-2

R-0.4

R-AEA

Lognormal

Vs,max Vs,min Μ Б R2 Vs,max Vs,min a n m R2

1782 66 1.996 0.613 0.9999 3907 57 4.575 3.079 0.383 0.9999

1784 67 2.173 0.598 0.9998 2817 52 6.062 2.947 0.686 0.9999

1666 85 2.257 0.533 0.9994 1539 62 10.959 2.855 4.002 0.9998

1803 64 2.072 0.596 0.9999 2968 50 5.388 2.993 0.629 0.9999

1538 83 2.043 0.456 0.9997 1741 70 6.777 3.583 1.548 0.9999

2075 66 1.966 0.654 0.9992 95,670 72 3.799 3.271 0.012 0.9996

1682 44 2.094 0.597 0.9997 8140 40 4.756 3.328 0.140 0.9998

Modified Fredlund and Xing

above-mentioned equations give satisfactory accuracy with high R2 values of 0.992 to 0.999 (Table 3). Furthermore, it is recommended to calculate the first and second derivatives of the fitted cumulative equations. Take lognormal cumulative equations for example (Fig. 13), the time at the peak (tpeak′) of the first derivative curve (Vs′), i.e. the inflection point of the original Eq. 3, was used to correlate to the final setting time (tf) measured from the standard penetration resistance test:

To solve the above challenges, new methods have been proposed to determine the initial and final setting times, as elaborated below. The fitted Vs versus elapsed time curves with commonly seen S-shaped cumulative distribution equations, such as the Weibull cumulative eq. [28] (Eq. 2), the lognormal cumulative equation [29] (Eq. 3), or the Gamma cumulative equation [30] (Eq. 4). The modified Fredlund and Xing [31] equation (Eq. 5) is also used because it's a parameter characterizes the onset of the major increment of Vs from the initial gentle slope (dormant period), and therefore can be used to estimate the initial setting time (see below for details).

′ + 0.17 t f = 0.96tpeak

with R2 = 0.979 (Fig. 10). A similar procedure for modified Fredlund and Xing equation gives:

α

y=1−e

y=

−⎛ x ⎞ ⎝β⎠

1 xσ 2π

e

−

(2)

′ − 0.09 t f = 0.96tpeak

(ln x − μ)2 2σ 2

(3)

1 y= γ (α, βx ) Γ (α )

(7)

2

with R = 0.982 (Fig. 10). Applying the same methods to the Vs evolution curves reported by Carette and Staquet [11] yielded reasonable good fitting results, with R2 = 0.861. The fitting results shown here suggest that the proposed inflection point method is valid to estimate the final setting time. The time (tpeak″) corresponding to the peak of second derivative (Vs″) of lognormal distribution correlates to the initial setting time (ti) determined from standard penetration resistance test as follows (Fig. 11):

(4) m

1 ⎤ y = θs − θs ⎡ ⎢ + ln( e (x/ a)n ⎥ ⎣ ⎦

(6)

(5)

where α, β, μ, σ, a, n and m are fitting coefficients for Eqs. 2–5. The fitted curves are shown in Fig. 12, and the fitting parameters and the coefficient of determination (R2) are listed in Table 3. All of the

t i = 1.04t′′ peak + 1.05 9

(8)

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Table 5 Fitting coefficients and R2 values of the proposed correlation between initial and final setting times to and the fitted parameters in the Vs evolution methods. Fitting method

Cumulative lognormal Modified Fredlund and Xing Cumulative lognormal Modified Fredlund and Xing Modified Fredlund and Xing

Correlation to ti/tf

tf = k ⋅ tpeak′ + b ″

ti = k ⋅ tpeak + b ti = k ⋅ a + b

Data in this study

Data from Carette and Staquet [11]

k

b

R2

k

b

R2

0.96 0.96 1.04 1.03 0.70

0.17 −0.09 1.05 1.09 −0.50

0.979 0.982 0.950 0.937 0.981

1.37 1.13 1.39 1.45 0.75

−0.11 1.09 1.92 1.25 1.59

0.861 0.836 0.742 0.648 0.697

with R2 = 0.950. Similarly, for modified Fredlund and Xing equation we have

t i = 1.03t′′ peak + 1.09

setting time than the experimental method used in Carette and Staquet [11]. With the non-destructive nature and reliable results, the proposed bender element is a promising tool to determine initial and final setting times and to monitor early age characteristics of mortars as well as other cementitious materials.

(9)

2

with R = 0.937. Besides, the parameter a in modified Fredlund and Xing equation correlates to ti as

t i = 0.70a − 0.50

Acknowledgement

(10)

with R2 = 0.981. Applying the same approach to the measured shear wave velocity versus elapsed time curves in Carette and Staquet [11] resulted in correlations shown in Fig. 11 with R2 values of 0.742 and 0.697 for the lognormal and modified Fredlund and Xing equation, respectively (Table 4). It should be noted that one of the mixtures in the Carette and Staquet [11] evaluation was removed from the fitting of modified Fredlund and Xing equation because the initial fluctuating segment of the measured Vs evolution curve resulted in fitting disagreeable with the visual judgment (e.g., the two tangent line method) and gave an unreasonably high a value. Two reasons accounting for the low R2 values are postulated. Firstly, the initial fluctuating segment of the measured Vs evolution curves by Carette and Staquet [11] caused a large variation in initial setting time estimation (e.g. the R-0.4 sample); Secondly, the range of initial setting times was narrower than that measured in this study, causing a larger variation. That said, both tpeak″ and parameter a from the shear wave velocity evolution monitoring method can give reasonable estimation of the initial setting time (Table 5). The above results and analysis also suggest Vs evolution curve measured by the BE method in this study can offer more reliable predictions of both the initial and final setting times than that measured by the method used in Carette and Staquet [11] does.

The authors would like to thank the United States Department of Transportation and the Center for Infrastructures Engineering Studies for the financial support to Mr. Jianfeng Zhu for his master studies. The authors would also like to thank the One-Thousand-Young-Talents Program of the Organization Department of the CPC Central Committee as well as the 100-Talents Program of Zhejiang University for their financial support. This work is also partially sponsored by the National Natural Science Foundation of China (Award No.: 51779219). In addition, the Key Laboratory of Soft Soils and Geoenvironmental Engineering of the Ministry of Education is acknowledged. References [1] V. Garnier, G. Corneloup, J.M. Sprauel, J.C. Perfumo, Setting time study of roller compacted concrete by spectral analysis of transmitted ultrasonic signals, NDT&E Int. 28 (1995) 15–22. [2] Z. Li, L. Xiao, X. Wei, Determination of concrete setting time using electrical resistivity measurement, J. Mater. Civ. Eng. 19 (2007) 423–427. [3] Z. Ge, K. Wang, P.J. Sandberg, J.M. Ruiz, Characterization and performance prediction of cement-based materials using a simple isothermal calorimeter, J. Adv. Concr. Technol. 7 (2009) 355–366. [4] M.P. Hofmann, S.N. Nazhat, U. Gbureck, Real-time monitoring of the setting reaction of Brushite-forming cement using isothermal differential scanning calorimetry, J. Biomed. Mater. Res. 79B (2006) 360–364. [5] V. Rahhal, R. Talero, Calorimetry of Portland cement with silica fume, diatomite and quartz additions, Constr. Build. Mater. 23 (2009) 3367–3374. [6] J.P. Sandberg, S. Liberman, Monitoring and Evaluation of Cement Hydration by Semi-Adiabatic Field Calorimetry, Concrete Heat Development: Monitoring, Prediction, and Management, vol. 241, Curran Associates. Inc., NY, 2007, pp. 13–24. [7] N.A. Soliman, K.H. Khayat, M. Karray, A.F. Omran, Piezoelectric ring actuator technique to monitor early-age properties of cement-based materials, Cem. Concr. Compos. 63 (2015) 84–95. [8] G. Zhang, J. Zhao, P. Wang, L. Xu, Effect of HEMC on the early hydration of Portland cement highlighted by isothermal calorimetry, J. Therm. Anal. Calorim. 119 (2015) 1833–1843. [9] C.-W. Chung, P. Suraneni, J.S. Popovics, L.J. Struble, Setting time measurement using ultrasonic wave reflection, ACI Mater. J. 101 (2012) 109–118. [10] G. Trtnik, G. Turk, F. Kavčič, V.B. Bosiljkov, Possibilities of using the ultrasonic wave transmission method to estimate initial setting time of cement paste, Cem. Concr. Res. 38 (2008) 1336–1342. [11] J. Carette, S. Staquet, Monitoring the setting process of mortars by ultrasonic P and S-wave transmission velocity measurement, Constr. Build. Mater. 94 (2015) 196–208. [12] S. Amziane, Setting time determination of cementitious materials based on measurements of the hydraulic pressure variations, Cem. Concr. Res. 36 (2006) 295–304. [13] J. Silva, M. Azenha, A.G. Correia, C. Ferreira, Continuous stiffness assessment of cement-stabilised soils from early age, Geotechnique 63 (2013) 1419–1432. [14] J. Silva, M. Azenha, A.G. Correia, J. Granja, Continuous monitoring of sand–cement stiffness starting from layer compaction with a resonant frequency-based method: issues on mould geometry and sampling, Soils Found. 54 (2014) 56–66. [15] X. Kang, G.C. Kang, B. Bate, Measurement of stiffness anisotropy in kaolinite using bender element tests in a floating wall consolidometer, Geotech. Test. J. 37 (2014) 1–16. [16] J.M. Larrahondo, H. Choo, S.E. Burns, Laboratory-prepared iron oxide coatings on

11. Summary In this study, a method is proposed for the use of the shear wave velocity (Vs) evolution curves of freshly cast mortar to estimate the initial and final setting times using a specially designed bender element system. The traditional bender element testing system used in geotechnical engineering was modified to obtain Vs versus elapsed time relationship of the cement-based materials, whose stiffness increased quickly at early age (from 0 to > 24 h). Details of the modifications of the bender element system and their rationales were elaborated. Cumulative distribution equations, such as the lognormal equation and modified Fredlund and Xing equation were used to fit the measured Vs evolution curves determined in this study as well as data reported by Carette and Staquet [11] for mortars made with w/c of 0.4 to 0.5. The test results were compared to the initial and final setting times obtained from the standard penetration resistance test. Test results indicated that the time corresponding to the first inflection point of the Vs evolution curve can correlate well to the final setting time (R2 = 0.979). The initial setting time was found to correlate well either to the peak time of the second derivative of the Vs evolution curve or to the parameter a in the modified Fredlund and Xing equation (R2 = 0.950 and 0.981, respectively). Correlation results also suggested that the modified bender element used in this study can yield a more reliable estimation of the 10

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