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An experimental study on the lateral pressure of fresh concrete in formwork
Construction and Building Materials 111 (2016) 450–460
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
An experimental study on the lateral pressure of fresh concrete in formwork Wenxue Zhang, Jian Huang, Zengyin Li, Chun Huang ⇑ College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China
h i g h l i g h t s Four specifications to calculate lateral pressure are compared to obtain differences. The effects of factors on lateral pressure are tested and analyzed in experiments. A modification to the lateral pressure formula denoted in GB50666-2011 was proposed.
a r t i c l e
i n f o
Article history: Received 2 July 2015 Received in revised form 19 December 2015 Accepted 17 February 2016 Available online 21 March 2016 Keywords: Concrete Formwork Lateral pressure Concrete slump Vibration Casting speed
a b s t r a c t Most of the accidents related to concrete formwork are triggered by improper construction operations and the unsound lateral pressure estimations detailed in concrete formwork specifications. In this study a series of experiments was conducted to reveal the effect of different factors on lateral pressure. The results show that concrete slump, casting speed, and vibration mode can greatly influence the pressure; and the data obtained in the experiments differ greatly from the values yielded by different specifications. A modification is proposed to the GB50666 specification in order to improve the accuracy and reliability of pressure estimations. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Formwork is very critical to a building constructed by cast-inplace reinforced concrete and it comprises a high proportion of the total cost of concrete engineering. Extensive research has been conducted on the lateral pressure of concrete formwork recently. However, the components and mechanics of the lateral pressure in fresh concrete formwork have not been thoroughly understood. This can potentially cause design complications, poor construction quality, and accidents. Therefore, it is necessary to investigate the factors affecting the lateral pressure of fresh-concrete vertical formwork. Gardner and Quereshi [1] argued that the use of vibration to fluidize concrete can destroy the shear strength and eliminate the friction in formwork. Once concrete is completely fluidized, it behaves as a fluid because the lateral pressure is equal to the hydrostatic pressure produced by a fluid with the density of concrete. Gardner [2] stated that, as depth and time increase, concrete ⇑ Corresponding author. E-mail addresses: [email protected] (W. Zhang), [email protected] (C. Huang). http://dx.doi.org/10.1016/j.conbuildmat.2016.02.067 0950-0618/Ó 2016 Elsevier Ltd. All rights reserved.
develops internal shear strength and friction, causing the pressure to increase with depth at a lower rate than hydrostatic pressure. He also demonstrated that, for depths greater than 2 m, the magnitude of lateral pressure decreases near the base of a form. Santilli et al. [3,4] and Puente et al. [5] determined that, for low placement rates, a very low correlation coefficient exists between the concrete yield stress resulting from the slump cone and the maximum pressure reductions resulting from the hydrostatic cone. This relationship is even stronger for high placement rates. Arslan [6] and Arslan et al. [7] studied the influence of surface materials on lateral pressure and concluded that lateral pressure in concrete can be decreased by almost 40% by implementing a drainer system or a liner on the surfaces of formwork. Hurd [8] provided detailed suggestions concerning formwork design calculations. His work shows that lateral pressure overestimations increase the costs of formwork, which comprise about 60% of the costs of concrete structures [9]. This finding is confirmed by Kopczynski [10]. Studies concerning the lateral pressure of self-compacting concrete (SCC) formwork [11–14] have indicated that the pressure envelopes of SCC are similar to hydrostatic pressure. However, Omran et al. [15] reached a different conclusion—that the lateral pressure of SCC is obviously
W. Zhang et al. / Construction and Building Materials 111 (2016) 450–460
less than the hydrostatic pressure produced by a fluid with the density of concrete. The design standards of concrete formwork in different countries are based on industry standards [16–19] that are constrained by the economics of concrete construction and the requirements of concrete engineering quality and construction safety. Although formwork has been designed with more and more concern for safety recently, a number of accidents caused by the collapse of concrete formwork still occur. In order to provide a better reference for concrete formwork design, a series of experiments was conducted in this study to reveal the effects of critical factors on the lateral pressure values by comparing four standards: the ACI Committee 347 [16], CIRIA Report 108 [17], GB50666-2011 (China) [18] and TZ210-2005 (China) [19]. The critical factors include the concrete slump, rate of placement, initial setting time, environmental temperature, and vibration mode. On the basis of the experimental results, we propose some modifications to the GB50666 specification in order to improve the accuracy and reliability of pressure estimation through a regression analysis.
In this section, four specifications are selected as the standards to calculate pressure values using Eqs. (1)–(7). We analyze the effects of the rate of placement, concrete slump, initial setting time and environmental temperature on the lateral pressure values estimated using different specifications. (1) GB50666-2011 hhCode for the construction of concrete structuresii [18]. According to Appendix A.0.4 of the GB50666-2011 specification, when the concrete has a slump of no more than 180 mm and a normal internal vibration with a placement rate of less than 10 m/h, the smaller of the values yielded by Eqs. (1) and (2) should be selected as the lateral pressure value. 1
F ¼ 0:28Dc t 0 bR2
ð1Þ
F ¼ Dc h
ð2Þ
For concrete with a slump greater than 180 mm and a rate of placement greater than 10 m/h, the lateral pressure of the formwork can be calculated using Eq. (2). In Eqs. (1) and (2), Dc represents the weight density of the concrete (kN/ m3); and t0 indicates the initial setting time of the concrete—if there are no measured data, the initial setting time can be calculated from t0 = 200/(T + 15), where T is the environmental temperature in °C. The parameter b is the correction factor for the concrete slump (k): b = 0.85 when 50 mm < k 6 90 mm, b = 0.9 when 90 mm < k 6 130 mm, and b = 1.0 when 130 mm < k 6 180 mm; R represents the rate of placement (m/h), and h represents the depth of the concrete from the top of the placement to the point of consideration in the formwork. (2) TZ210-2005 Technical guide for construction of railway concrete engineering [19]. For new-site large-volume concrete and common concrete projects, the formwork lateral pressure can be calculated using Eq. (3), where R represents the placement rate (m/h).
F¼
72R P 19 R þ 1:6
the concrete and the concrete’s temperature. Furthermore, the concrete slump-correction is not considered in TZ210. (3) ACI Committee 347R-04, Guide to formwork for concrete [16]. For concrete with a slump of no more than 175 mm, and placed using normal internal vibration to a depth of no more than 1.2 m, the formwork lateral pressure can be calculated by using Eq. (4).
785R P max ¼ C w C c 7:2 þ T þ 18:7
ð3Þ
TZ210 primarily considers the influence of the rate of placement while neglecting the effects of the initial setting time of
ð4Þ
Eq. (4) can also be applied to calculate the pressure value of columns ranging from 30 Cw (kPa) to qgh and for walls with a rate of placement less than 2.1 m/h and a placement height less than 4.2 m. For walls with a placement rate that is less than 2.1 m/h and a placement height that is greater than 4.2 m, or all walls with a placement rate that ranges from 2.1 to 4.5 m/h, the pressure value can be calculated by using Eq. (5).
1156 224R P max ¼ C w C c 7:2 þ þ T þ 18:7 T þ 18:7
2. Comparison of the estimated formwork lateral pressure values using different specifications
451
ð5Þ
The minimum is 30 Cw (kPa) and the maximum is qgh; Pmax represents the maximum lateral pressure (kPa); R is the rate of placement (m/h); T is the temperature (°C) of the concrete during placement; Cw, Cc, and Dc indicate the unit weight coefficient, the chemistry coefficient, and the weight density of the concrete (kN/m3), respectively. (4) CIRIA Report No. 108 [17]. The maximum concrete pressure of a formwork is less than Dch and can be calculated by using Eq. (6).
pffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffi P max ¼ Dc C 1 R þ C 2 K H C 1 R
ð6Þ
pffiffiffi In Eq. (6), if C 1 R > H then the fluid pressure (Dch) equals the design pressure. The coefficient C1 depends on the size and shape of the formwork; for walls, C1 is set at 1, and for columns C1 is set at 1.5. The coefficient C2 depends on the constituent materials of the concrete; for ordinary Portland concrete (OPC) without a retardant, C2 is set at 0.3 and it is set at 0.45 for OPC with a retardant. H represents the height of the vertical formwork (in meters), and K is the temperature coefficient yielded by Eq. (7).
K¼
2 36 T þ 16
ð7Þ
In order to compare these pressure values calculated according to the four specifications, a real project was used to analyze the effects of the environmental temperature, concrete slump, initial setting time, and pouring speed on the lateral pressure values of concrete formwork. The concrete, which is mixed in a mixing plant, has a strength grade of C40 with a retardant. The weight density value of the concrete equals 3
Dc ¼ 25 kN=m and H = h = 9 m. The detailed results of the analysis are described in the following sections. 2.1. Placement rate The effects of different rates of placement (R) on the lateral pressure of formwork were analyzed under the conditions of an initial setting time of six hours, a 120 mm concrete slump, and a temperature of 20 °C. The correction factor of the concrete slump (b) is equal to 0.9 according to GB50666, and the unit weight coefficient (Cw) according to ACI347 is equal to 1.1. The chemistry coefficient (Cc) according to ACI347 is equal to 1.2. The coefficient
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dependent on the size and the shape of the formwork (C1) is equal to 1.5 according to CIRIA.108, and the coefficient dependent on the constituent materials of the concrete (C2) is equal to 0.45. The temperature coefficient (K) is 1.0. The formwork lateral pressure values, calculated by using different equations with different rates of placement, are shown in Fig. 1. The figure shows the following. (1) The lateral pressure values of formwork calculated using different specifications are different. The differences vary according to the different rates of placement. The biggest difference observed among the pressure values is a magnitude of 3.75 within the same placement rate. The values calculated using the standard TZ210 specification are significantly smaller than the values obtained using the other three specifications; this can potentially cause safety risks. (2) Although the placement rate is considered in all four of the specifications, the effect on the pressure value is different. The value calculated using the ACI347 specification is the highest when the placement rate is 6 m/h. The values calculated using the specifications ACI347 and GB50666 are around 181.4 kPa and 73.2 kPa within the calculated placement rate range, respectively. The pressure value obtained using the TZ210 specification is about 37.8 kPa and is the least affected by the rate of placement. (3) For a placement rate less than 3.0 m/h, the value calculated using the CIRIA.108 specification is larger than the value obtained using the other three specifications. Thus, this set of guidelines may yield a more conservative estimate. When the rate of placement is relatively high, the largest value is obtained using the ACI347 specification. Thus, the estimates yielded by this set of guidelines are too conservative. These results are consistent with the results obtained by Santilli et al. [3,4] and Puente et al. [5]. 2.2. Concrete slump The effects of different concrete slump values on the formwork lateral pressure were analyzed under the conditions of an initial setting time of six hours, a rate of placement of 2 m/h, and an environmental temperature of 20 °C. The unit weight coefficient (Cw) and the chemistry coefficient (Cc) according to ACI347 are 1.1 and 1.2. The coefficient dependent on the size and shape of the formwork (C1) according to CIRIA.108 is 1.5, the coefficient dependent on the constituent materials of the concrete (C2) is 0.45 and the temperature coefficient (K) is 1.0. The formwork
lateral pressure values, calculated with different concrete slump values, are shown in Fig. 2. (1) Only the formula specified by GB50666 takes into account the influence of the concrete slump on the lateral pressure. For the same concrete slump, the values yielded by the various formulas are significantly different. The value calculated using the TZ210 specification is the lowest, and the value calculated using the CIRIA.108 specification is the highest. The highest value is almost three times greater than the lowest value. (2) Although the formula given in GB50666 allows for the influence of the concrete slump, the values calculated by using the CIRIA.108 specification are almost twice as high as those calculated by using the GB50666 specification. Thus, using the CIRIA.108 specification can result in an unnecessary waste of resources. 2.3. Initial setting time The effects of different initial setting times on the framework lateral pressure were analyzed under the conditions of a concrete slump of 120 mm, a casting speed of 2 m/h, and an environmental temperature of 20 °C. The correction factor of the concrete slump (b) according to GB50666 is 0.9. The unit weight coefficient (Cw) and the chemistry coefficient (Cc) according to ACI347 are 1.1 and 1.2, respectively. The coefficient dependent on the size and shape of the formwork (C1) according to CIRIA.108 is 1.5; the coefficient dependent on the constituent materials of the concrete (C2) is 0.45 and the temperature coefficient (K) is 1.0. The lateral pressure values of formwork, calculated by using different formulas and with different initial setting times, are shown in Fig. 3. Of the four specification guidelines, only the GB50666 specification considers the effects of the initial setting time on formwork lateral pressure. The lateral pressure of formwork rises as the initial setting time of the concrete increases; it is a linear relationship. 2.4. Environmental temperature The effects of the environmental temperature on the lateral pressure during concrete pouring were analyzed with a concrete slump of 120 mm, a casting speed of 2 m/h, and an initial setting time of six hours. The correction factor of the concrete slump (b) according to GB50666 is equal to 0.9. The unit weight coefficient (Cw) and the chemistry coefficient (Cc) of ACI347 are equal to 1.1 120
225
GB50666
100
TZ210 ACI347
175
Lateral pressure (kPa)
Lateral pressure (kPa)
200
CIRIA.108
150 125 100 75 50
80 60 40 20
GB50666 ACI347
25 0
TZ210 CIRIA.108
0 0.5
2.0
4.0
6.0
Rate of placement (m/h) Fig. 1. Relationship between the placement rate and lateral pressure.
0
20
40
60
80
100
120
140
160
Slump (mm) Fig. 2. Relationship between the concrete slump and lateral pressure.
Lateral pressure (kPa)
W. Zhang et al. / Construction and Building Materials 111 (2016) 450–460
453
120
3. Lateral pressure experimental session
100
This experiment consisted of 16 specimens. Ten of the specimens had dimensions of 60 cm 120 cm; two had dimensions of 30 cm 120 cm; one of them was 15 cm 120 cm; and the last three had dimensions of 60 cm 60 cm. All of the specimens were 300 cm in height. C30 concrete was used for the experiment; its main ingredients included JINYU brand P.O42.5 cement, river sand, and graded crushed stone. Due to the material supply, formwork processing, and garbage treatment characteristics, Beijing’s Yun Meng Bridge, which was under construction at the time, was selected as the site of the experiment.
80 60 40 20 0
3
GB50666
TZ210
ACI347
CIRIA.108
5
7
9
11
Initial setting time (h) Fig. 3. Relationships between the initial setting time and lateral pressure.
and 1.2, respectively. The coefficient dependent on the size and shape of the formwork (C1) according to CIRIA.108 is equal to 1.5 and the coefficient dependent on the constituent materials of the concrete (C2) is equal to 0.45. The formwork lateral pressure values, calculated using the different formulas for different environmental temperatures, are shown in Fig. 4. (1) At the same environmental temperature, there are significant differences among the lateral pressure values of concrete formwork. The minimum value is obtained from the TZ210 specifications. At low environmental temperatures, the pressure values yielded by the various formulas vary significantly. This may result in accidents during construction. (2) The GB50666 and TZ210 specifications do not take into account the influence of environmental temperature on lateral pressure directly, but both the ACI347 and CIRIA.108 specifications do take into account the temperature effects. However, the formwork lateral pressure values that are obtained using the ACI347 and CIRIA.108 specifications can vary significantly when the environmental temperature decreases, and the obtained values drop at different rates. When the environmental temperature increases from 5 °C to 30 °C, the values obtained using ACI347 decrease by 47% while the values obtained using CIRIA.108 decline by 61%.
3.1. Formwork design and measuring point arrangements The formwork required sufficient strength and stiffness to avoid large template deformation, which would affect the accuracy of the test results. In accordance with our preliminary calculations, 6 mm thick steel plate was used as the formwork’s faceplate and 8 mm 60 mm steel plate was used for stiffening ribs at every 300 mm both vertically and horizontally. The edge rib was L63 8 mm angle steel; M20 high-strength bolts, spaced 150 mm apart, were used for connecting the formwork. The layouts of the pressure measure cells are shown in Fig. 5. From the bottom of the formwork to a height of 200 cm, pressure measure cells were located at a regular distance of 50 cm. A single cell was used for a side 60 cm wide and a side 30 cm wide. Two cells were used for a side 120 cm long. No cell was used with a side 15 cm wide. To analyze the influence of the edges of the 30 cm 120 cm specimens on the lateral pressure, tests were conducted on both sides. The detailed information about the specimens is listed in Table 1. 3.2. Data acquisition system In order to ensure the reliability of the data, two kinds of pressure measure cell (made by the DANDONG experimental instrument factory and JINMA Hi Tech Co. Ltd.) were simultaneously utilized in this experiment. In Fig. 5, ‘J’ and ‘D’ represent JINMA and DANDONG cells, respectively. The main performance index of these two kinds of cells is as follows. (1) The range, resolution, nonlinear error, repeatability error, and hysteresis error of the JINMA JM-5006X double membrane intelligent string type digital pressure cell are 0.6 MPa, 60.2% F.S., 61.2% F.S., 61.0% F.S., and 61.0% F.S., respectively. (2) The range, resolution, nonlinear error, repeatability error, and hysteresis error of the DANDONG DY-110 single membrane pressure cell are 0.4 MPa, 60.3% F.S., 62.0% F.S., 60.5% F.S., and 61.0% F.S., respectively. 3.3. Experimental process
Fig. 4. Relationship between the environmental temperature and lateral pressure.
A slump experiment was conducted on each specimen before casting and the pertinent data were recorded in detail. Once the concrete had been poured to a height of 0.5 m, the changes in the lateral pressure, environmental temperature, casting time, and other parameter values were recorded. The initial setting time of the concrete was recorded at the same time. The experiment required approximately 35 m3 of concrete and took 36 days to complete. Some of the steps in the experiment are shown in Fig. 6. To accurately simulate the real construction environment, the whole experiment was conducted in an outdoor environment.
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values of the formwork at the same height on the long walls were averaged. Then the maximum formwork lateral pressure values during the pouring of the concrete were determined. The relationships between the lateral pressure values and the placement heights of typical specimens are shown in Fig. 7. The data regarding the 16 specimens are shown in Table 1 and Fig. 8. In Table 1 ‘position’ represents the place, measured vertically from the bottom surface, where the lateral pressure reached a maximum; and ‘placement height’ indicates the corresponding height of the pouring concrete. For example, 0.5(2.5) means that the lateral pressure reached a maximum 0.5 m from the bottom surface and the corresponding height of the pouring concrete was 2.5 m. (1) The maximum values of the formwork lateral pressure did not necessarily occur at the bottom of the formwork but at some elevation above the base of the formwork. The impact of the lateral pressure values on formwork increased as the pouring height rises; this resulted in the outward deformation of formwork. In addition, the shear strength of the poured concrete increased, due to vibration and setting. The increased shear strength allowed the concrete to support vertical loads. (2) The formwork lateral pressure values increase as the pouring height rises. However, once the pouring height reaches a certain value, the growth of lateral pressure values stops and the values even diminish as the pouring height continues to increase. (3) The average of the maximum values of the formwork lateral pressure on the short sides of specimens 1–12 was 31.1 kPa. The average of the maximum values of the formwork lateral pressure on the long sides of specimens 1–12 was 30.1 kPa. Four of the average formwork lateral pressure values that were recorded on the long sides were greater than those recorded on the short sides. Thus, the shape of the formwork structures did not significantly influence the lateral pressure values of the concrete. These results are consistent with those reported by Santilli et al. [14]. (4) Table 1 lists the data for the concrete slump, rate of placement, and vibration mode; these factors significantly influence formwork lateral pressure. Therefore, a detailed analysis of the concrete slump, rate of placement, and vibration mode is conducted in the following section. 4. Analysis of the experimental results 4.1. Comparison of the calculated and measured formwork lateral pressure values
Fig. 5. Pressure test point arrangements.
The formwork lateral pressure values (Fc) calculated using the formulas detailed in the GB50666-2011, TZ210-2005, CIRIA.108, and ACI347 specifications are compared with the measured formwork lateral pressure values (Ft). The results are shown in Fig. 9; the absolute error and the relative error are calculated as Ea ¼ F c F t and Er ¼ EFat 100%, respectively. Fig. 9 shows the following.
3.4. Estimated formwork lateral pressure values First, the data obtained from the experiment were processed. For the specimens with dimensions of 60 cm 60 cm 300 cm, the average formwork lateral pressure at the same height was calculated. For the specimens with dimensions of 60 cm 120 cm 300 cm and 30 cm 120 cm 300 cm, the lateral pressure values of the formwork at the same height on the long and short walls were averaged separately. For the specimens with dimensions of 15 cm 120 cm 300 cm, only the lateral pressure
(1) The values of the relative errors calculated using the GB50666 specification range from 11% to +78%; the average relative error is 21%. The absolute error values of SP.4, SP.7, and SP.8 are 4.5 kPa, 2.5 kPa, and 0.8 kPa, respectively. The probability that the obtained value is less than the corresponding measured value is 23%. (2) The values of the relative errors calculated using the TZ210 specification range from 38% to +76%; the average relative error is 0.8%. The calculated values of seven of the
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W. Zhang et al. / Construction and Building Materials 111 (2016) 450–460 Table 1 Specimen parameters and maximum lateral pressure values. Specimen number
Size (m) (L * W * H)
Slump (mm)
Placement rate (m/h)
Temperature (°C)
Vibration mode
1 2 3 4 5 6 7 8 9 10 11 12 13 14
0.6 1.2 3 0.6 1.2 3 0.6 1.2 3 0.6 1.2 3 0.6 1.2 3 0.6 1.2 3 0.6 1.2 3 0.6 1.2 3 0.6 1.2 3 0.6 1.2 3 0.3 1.2 3 0.3 1.2 3 0.15 1.2 3 0.6 0.6 3
155 203 240 210 154 154 155 86 157 150 157 159 160 159
1.29 1.29 1.33 0.93 1.16 1.16 0.45 0.80 1.45 1.16 1.97 3.30 6.38 1.5
13 24 17 19 24 16 21 20 22 16 18 8 20 17
15
0.6 0.6 3
159
2.36
9
16
0.6 0.6 3
160
5.17
20
1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 2 full vibrations in the end 1 vibration/1 m Final full vibration No vibration during pouring Final full vibration
specimens are less than the corresponding measured values. The probability that the obtained value is less than the corresponding measured value is 54%. (3) The values of the relative errors calculated using the ACI347 specification range from 0% to +47%; the average relative error is 25%. Thus, these results are conservative. (4) The relative errors of the values calculated using the CIRIA.108 specification range from +5% to +116%; the average relative error is 58%. Thus, these results are overlyconservative. (5) The results demonstrate that numerous factors affect the lateral pressure values of formwork and significant differences exist between the measured and calculated values regardless of the specification used. The values calculated by using the CIRIA.108 specification are significantly larger than the corresponding measured values. Thus, the use of the CIRIA.108 specification may result in an unnecessary waste of resources. In addition, there is a very high probability that a value calculated using the TZ210 specification is less than the corresponding measured value. Thus, the TZ210 specification is not adequately conservative. 4.2. Fractional analysis of the experimental data 4.2.1. Regression analysis Since the experiment was conducted in an outdoor environment, several factors—such as the temperature, sunshine, and wind speed—may have influenced the results. In order to study the individual effects of the main factors on the formwork lateral pressure, some of the variables were normalized by multi-parameter fitting. First, on the basis of an analysis of the environment, the parameters that may possibly have affected the results were determined. Then, the nlinfit function of Matlab and Eq. (8) were used to subject the data to nonlinear least-squares fitting. The rate of placement, environmental temperature, and concrete slump were normalized and grouped according to Eq. (8). Thus, while the variables of one parameter were studied, the other two parameters were adjusted to certain values using Eq. (8) so that the influence of a single particular parameter could be analyzed. The sectional area (x1), formwork length (x2), rate of placement (x3), environmental temperature (x4), and concrete slump (x5) were
Long side
Short side
Measured value (kPa)
Position (placement height)
Measured value (kPa)
Position (placement height)
27.0 26.0 37.5 41.5 30.5 21.5 27.5 28.5 38.2 27.2 24.8 31.3 33.0 36.2 54.7 47.7 52.9 17.1 43.7
0.5 (2.5) 1.0 (3.0) 0.5 (3.0) 0.5 (3.0) 0.5 (3.0) 1.0 (2.5) 0.5 (2.0) 0.5 (2.0) 0.5 (2.5) 0.5 (2.0) 1.0 (3.0) 0 (1.5) 0 (3.0)
25.0 32.0 42.1 37.0 32.0 24.0 26.0 30.0 39.0 28.1 24.1 34.0
0.5 1.0 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
(2.5) (3.0) (3.0) (2.5) (3.0) (2.0) (2.0) (2.5) (2.0) (2.0) (2.0) (1.5)
0.5 (2.5) 0 (second full vibration) 0.5 (3.0) 0 (full vibration) 0 (1.5) 0.5 (full vibration)
considered during the multi-parameter fitting. Because the vibration modes of SP.14 and SP.16 were different from those of the other specimens, the related data were not included in the analysis. The determination coefficient (Rs) was 0.92. So the regression equation, or Eq. (8), was capable of predicting the formwork lateral pressure values precisely.
F ¼ 86:3 þ 36:8x0:39 x0:024 x0:06 x0:19 1 2 3 4 1:71 0:87 sinð5:2 þ 6:1x0:51 Þ 5
ð8Þ
As is shown in Table 1, the influence of the sectional dimensions on the formwork lateral pressure was negligible. Thus, the effects of the sectional dimensions were ignored when grouping the experimental data. Since the effects of the concrete slump, rate of placement, and environmental temperature were the primary consideration during the analysis, the specimens were divided into three experimental groups. 4.2.2. Influence of the concrete slump The concrete slumps of SP.8, SP.9, SP.12, SP.4, and SP.3 were equal to 86 mm, 157 mm, 159 mm, 210 mm, and 240 mm, respectively. The rate of placement and environmental temperature values of these five specimens were revised using Eq. (8). The temperature values and the rate of placement values were changed to 20 °C and 1.20 m/h in order to obtain the corrected lateral pressure values of the formwork. The corrected results are shown in Table 2, and the effects of the concrete slump on the formwork lateral pressure values are shown in Fig. 10. The results indicate that the concrete slump significantly influences the formwork lateral pressure in that the formwork lateral pressure rises as the concrete slump increases, under the same conditions; the relationship is linear. The determination coefficient of the linear regression function is Rs = 0.93; this can be used to characterize the relationship between the lateral pressure and the concrete slump. 4.2.3. Influence of the rate of placement The placement rates of SP.7, SP.8, SP.4, SP.10, SP.2, SP.3, and SP.9 were 0.45 m/h, 0.80 m/h, 0.93 m/h, 1.16 m/h, 1.29 m/h, 1.33 m/h, and 1.45 m/h, respectively. The concrete slump and environmental temperature of these seven specimens were revised using Eq. (8).
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(a) Formwork assembly
(b) Test site Fig. 8. Maximum lateral pressure of all specimens at different test points.
(c) Specimens Fig. 6. Experimental process.
Fig. 7. Relationships between the lateral pressure values of typical specimens and the placement height.
The environmental temperature and concrete slump values were corrected to 20 °C and 150 mm in order to obtain the corrected formwork lateral pressure values. The corrected results are listed
in Table 3, and the influence of the rate of placement on the formwork lateral pressure is shown in Fig. 11. The results indicate that the formwork lateral pressure increases as the placement rate increases, under the same conditions, and that the formwork lateral pressure values exhibit an exponential relationship with the placement rate. The determination coefficient of the exponential function is equal to Rs = 0.99; this can be used to characterize the relationship between the lateral pressure and the rate of placement. 4.2.4. Influence of the environmental temperature The environmental temperatures of SP.10, SP.4, SP.8, SP.7, and SP.2 were 16 °C, 19 °C, 20 °C, 21 °C, and 24 °C, respectively. The concrete slump and placement rate values of these five specimens were revised using Eq. (8). The rate of placement and concrete slump values were corrected to 1.20 m/h and 150 mm, respectively, in order to obtain the corrected formwork lateral pressure values. The corrected results are shown in Table 4, and the influence of the environmental temperature on the formwork lateral pressure is shown in Fig. 12. The results indicate that the environmental temperature influenced the formwork lateral pressure significantly less than the concrete slump and placement rate. These results are consistent with those reported by Santilli et al. [14]. The environmental temperature does not directly influence the formwork lateral pressure, but it affects the initial setting time of the concrete. According to Omran et al. [15], environmental temperature does not influence the rate of lateral pressure variation. As the temperature increases, however, both the initial setting time and the concrete slump are affected. 4.2.5. Influence of the vibration mode In order to analyze the maximum formwork lateral pressure values, which were influenced by the vibration method during the concrete casting, the vibration modes of SP.14, SP.15, and SP.16 were changed during the process of the experiment. Specimen 14 was vibrated once after each 50-cm increment of concrete
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Fig. 10. Influence of the concrete slump on the lateral pressure.
Table 3 Influence of the casting speed on the lateral pressure. Specimen number
Placement rate (m/h)
Measured data (kPa)
Correction coefficient
Corrected result (kPa)
7 8 4 10 2 3 9
0.45 0.80 0.93 1.16 1.29 1.33 1.45
27.5 30.0 37.0 28.1 32.0 42.0 39.4
0.93 0.96 0.79 1.07 0.95 0.73 0.78
25.6 28.7 29.2 30.0 30.4 30.5 30.8
Fig. 9. Comparison of the measured values and the values calculated using the GB50666, ACI347, CIRIA.108 and TZ210 specifications. Fig. 11. Influence of the casting speed on the lateral pressure. Table 2 Influence of the concrete slump on the lateral pressure. Specimen number
Slump (mm)
Measured data (kPa)
Correction coefficient
Corrected result (kPa)
8 9 12 4 3
86 157 159 210 240
30.0 39.4 34.3 37.0 42.0
1.08 0.98 1.17 1.03 0.99
32.4 37.8 38.0 38.8 41.6
was poured. Once the pouring process was complete, a vibrating rod was inserted in the bottom of the specimen and vibrated twice from the bottom to the top. Specimen 15 was vibrated once after every 100-cm increment of concrete was poured. Once the pouring process was complete, a vibrating rod was inserted in the bottom of the specimen and vibrated once from the bottom to the top.
Table 4 Influence of the environmental temperature on the lateral pressure. Specimen number
Temperature (°C)
Measured data (kPa)
Correction coefficient
Corrected result (kPa)
10 4 8 7 2
16 19 20 21 24
28.1 37.0 30.0 27.5 26.0
0.99 0.80 1.01 1.08 1.20
27.7 29.6 29.2 29.7 31.1
Specimen 16 was not vibrated during the pouring process. Once the pouring process was completed, a vibrating rod was inserted in the bottom of the specimen and vibrated from the bottom to the top. The lateral pressure values recorded at the 0-cm and 50cm measurement points of these three specimens are shown in Fig. 13, which shows the following.
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W. Zhang et al. / Construction and Building Materials 111 (2016) 450–460
with the measured values, a modification of the formwork lateral pressure calculation formula given in the GB50666 specification is proposed. First, the relationship between the maximum formwork lateral pressure and the rate of placement (R) is revised with regard to the casting speed items in the GB50666 formula. Next, the relationship between the maximum formwork lateral pressure and the slump (k) is revised in order to include in the formula the influence of the concrete slump. Then, the modified formula to calculate the formwork lateral pressure is obtained. 5.1. Revision of the placement rate In accordance with Fig. 11, the relationship between the lateral pressure and the placement rate can be expressed as Eq. (9). 1
Fig. 12. Influence of the environmental temperature on the lateral pressure.
F ¼ 30R4
ð9Þ
The determination coefficient of the fitting function (Rs) is 0.99; this function can be applied to characterize the relationship between the lateral pressure and the rate of placement. The values of the absolute errors, calculated using Eq. (9), are listed in Table 5. In order to ensure that the calculated values are larger than the measured values, when the placement rate is less than 10 m/h Eq. (9) is modified to: 1
F ¼ 31R4
ð10Þ
The effects of the concrete’s weight density and the initial setting time are also considered. When the weight density of the concrete (Dc) is equal to 24 kN/m3 and the temperature is 20 °C, the initial setting time can be expressed as t0 ¼ 200=ðT þ 15Þ ¼ 5:71. Thus, Eq. (11) can be obtained by substituting Dc and t0 into Eq. (10). 1
F ¼ 0:23Dc t 0 R4
ð11Þ
5.2. Revision of the concrete slump correction factor Fig. 13. Influence of the vibration mode on the lateral pressure.
(1) The vibration depth significantly influences the maximum formwork lateral pressure. The maximum formwork lateral pressure of SP.15, which was vibrated once after each 100cm increment of concrete was poured, is 47.4% higher than that of SP.14, which was vibrated once after each 50-cm increment of concrete was poured. (2) The maximum formwork lateral pressure of SP.14 increases by 89.3% after the first vibration by the vibrating rod from the bottom to the top, then it increases by 92.6% after the second vibration by the vibrating rod from the bottom to the top. The maximum formwork lateral pressure of SP.15 increases by 29.0% after vibration by the vibrating rod from the bottom to the top. (3) The maximum values of the formwork lateral pressure of SP.14, SP.15, and SP.16—after the vibration by the vibrating rod from the bottom to the top—are different.
5. Formula modifications The results and analysis demonstrate that the concrete slump and rate of placement can significantly influence the maximum formwork lateral pressure and that the influence of the environmental temperature on the maximum formwork lateral pressure is relatively minor. Existing specifications may yield highly inaccurate formwork lateral pressure values. As the parameters in the experiment were consistent with the parameters in the GB50666 specification and the calculated values were in good agreement
In accordance with Fig. 10, the relationship between the lateral pressure and the concrete slump can be expressed as Eq. (12).
F ¼ 0:055k þ 28:32
ð12Þ
The determination coefficient of the fitting function (Rs) is 0.93; this function can be used to characterize the relationship between the lateral pressure and the concrete slump. The absolute errors of the values, calculated using Eq. (12), are listed in Table 6. In order to ensure that the calculated values are larger than the measured values, Eq. (12) is modified to F ¼ 0:055k þ 28:32 þ DF; from the data in Table 6, DF is found to be 0.92. In order to allow for the effects of the concrete slump, the following Eq. (13) is upgraded by introducing the concrete slump correction factor bðkÞ into Eq. (11). Thus, the lateral pressure formula can be expressed as: 1
F ¼ 0:23Dc bðkÞt 0 R4
ð13Þ
Table 5 Influence of the casting speed on Ff and Ft (kPa). Specimen number
Measured value Ft
Calculated value Ff
Error Ft Ff
7 8 4 10 2 3 9
25.59 28.67 29.21 29.99 30.36 30.46 30.76
26.63 28.61 29.15 29.97 30.37 30.48 30.82
1.0189 0.3002 0.2520 1.1475 1.6153 1.7543 2.1590
W. Zhang et al. / Construction and Building Materials 111 (2016) 450–460 Table 6 Influence of the concrete slump on Ff and Ft (kPa). Specimen number
Measured value Ft
Calculated value Ff
Error Ft Ff
8 9 12 4 3
32.35 37.78 38.01 38.83 41.6
33.06 36.98 37.09 39.91 41.56
0.72 0.79 0.92 1.08 0.04
459
A further analysis of the results indicates that the placement rates of SP.4, SP.7, and SP.8 are 0.93 m/h, 0.45 m/h, and 0.8 m/h, respectively. Thus, there may be safety risks if the formwork is designed using the GB50666 specification when the placement rate is relatively low. (2) The average relative error of the values yielded by the modified formula Eq. (15) is 21%. The average relative error of the values yielded by the ACI347 specification is 25%, and the average relative error of the values yielded by the CIRIA.108 specification is 58.3%. Thus, both of these guidelines yield higher average errors than the modified formula proposed in this paper. 6. Conclusions The results in this study lead to the following conclusions.
Fig. 14. Comparison of the absolute error values of the modified and original formulas.
Here, Dc = 24 kN/m3; T = 20 °C; t 0 ¼ 200=ðT þ 15Þ ¼ 5:71; and R = 1.2 m/h. bðkÞ was solved by the use of two Eqs. (12) and (13).
bðkÞ ¼ 1:75 103 k þ 0:93
ð14Þ
In this way, the formula given in the GB50666 specification is modified on the basis of the experimental data. For R 6 10 m/h and 50 mm 6 k 6 240 mm, the modified formula for the formwork lateral pressure can be expressed as Eq. (15); the smaller value should be adopted as the design value.
(
1
F ¼ 0:23Dc bt0 R4
ð15Þ
F ¼ Dc H
Here, Dc represents the weight density of the concrete (kN/m3); t0 represents the initial setting time of the concrete; R represents the rate of placement (m/h); and b represents the concrete slump correction factor (b = 1.10 when 50 mm < k 6 90 mm, b = 1.25 when 90 mm < k 6 180 mm, and b = 1.40 when 180 mm < k 6 240 mm).
1
(F ¼ 0:23Dc bt0 R4 ) is more capable of effectively ensuring formwork engineering security and yielding accurate formwork lateral pressure values. (4) The vibration mode and depth have significant effects on the maximum formwork lateral pressure. Increasing the depth of vibration and/or repeating vibration greatly increase the formwork lateral pressure and should be avoided. (5) The concrete slump and the placement rate significantly affect the maximum lateral pressure. However, in previous research the influence of environmental temperature has not been thoroughly studied and remains unclear, especially in the cases when the casting process is completed before the initial setting of the concrete starts. The effects of environmental temperature should be investigated further.
Acknowledgement The research is supported and funded by the grants Natural Science Foundation of China: 51378034 and 5150081022.
5.3. Comparison of the modified and original formulas Due to the formula modifications, the specification coefficient changed from 0.28 to 0.23, the applicable range of the concrete slump increased from 50–180 mm to 50–240 mm, the corresponding concrete slump correction factor was revised, and the partial 1
(1) The values of the relative errors yielded by the TZ210 specification are small, but the probability of a value yielded by the TZ210 specification being less than the corresponding measured value is very high. (2) The experimental results demonstrate that the ACI347 and CIRIA.108 specifications are conservative. (3) The formula given in the GB50666 specification is modified in such a way that the applicable range of the concrete slump is extended, and the corresponding concrete slump adjustment factor is revised. Compared to the formula given in the GB50666 specification, the modified formula
1
coefficient of the placement rate changed from R2 to R4 . The formwork lateral pressure values calculated using the modified formula Eq. (15) and the formulas detailed in the GB506662011, CIRIA.108, and ACI347 specifications were compared with the measured lateral pressure values of the specimens. The relative errors are shown in Fig. 14. This figure shows the following. (1) All of the SP.4, SP.7, and SP.8 values yielded by the GB50666 specification are smaller than the corresponding measured values, but all of the values yielded by the modified formula are no less than the corresponding measured values.
References [1] N.J. Gardner, A.R. Quereshi, Internal vibration and the lateral pressure exerted by fresh concrete, Can. J. Civil Eng. 6 (1979) 592–600. [2] N.J. Gardner, Pressure of concrete on formwork – a review, ACI J. 82 (5) (1985) 744–753. [3] A. Santilli, I. Puente, A. López, Rates of placement discussion for the validation of experimental models of fresh concrete lateral pressure in walls, Constr. Build. Mater. 25 (2011) 227–238. [4] A. Santilli, I. Puente, A. Lopez, Rate of placement discussion for the validation of experimental models of fresh concrete lateral pressure in columns, Constr. Build. Mater. 24 (2010) 934–945. [5] I. Puente, A. Santilli, A. Lopez, Lateral pressure over formwork on large dimension concrete blocks, Eng. Struct. 32 (2010) 195–206. [6] M. Arslan, Effects of drainer formworks on concrete lateral pressure, Constr. Build. Mater. 16 (2002) 253–259. [7] M. Arslan, O. Sß imsßek, S. Subasßı, Effects of formwork surface materials on concrete lateral pressure, Constr. Build. Mater. 19 (2005) 319–325. [8] M.K. Hurd, Formwork for Concrete, seventh ed., American Concrete Institute, Farmington Hills, Michigan, 2005.
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[9] M.K. Hurd, Lateral pressures for formwork design, Concr. Int. 29 (06) (2007) 31–33. [10] C. Kopczynski, Formwork Efficiencies, Concr. Int. 30 (06) (2008) 41–43. [11] G. Ovarlez, N. Roussel, A physical model for the prediction of lateral stress exerted by self-compacting concrete on formwork, Mater. Struct. 39 (2006) 269–279. [12] T. Proske, C.A. Graubner, Formwork pressure of concrete with high workability, Adv. Constr. Mater. (2007) 463–470. [13] Y. Vanhovea, C. Djelala, G. Schwendenmanna, P. Brissetb, Study of self consolidating concretes stability during their placement, Constr. Build. Mater. 35 (2012) 101–108. [14] A. Santilli, I. Puente, M. Tanco, A factorial design study to determine the significant parameters of fresh concrete lateral pressure and initial rate of pressure decay, Constr. Build. Mater. 25 (2011) 1946–1955.
[15] A.F. Omran, Y.M. Elaguab, K.H. Khayat, Effect of placement characteristics on SCC lateral pressure variations, Constr. Build. Mater. 66 (2014) 507–514. [16] ACI Committee 347R-04. Guide to Formwork for Concrete, American Concrete Institute, 2004. [17] CIRIA Report 108. Concrete pressure on formwork, Construction Industry Research and Information Association, 1985. [18] China Academy of Building Research, GB50666-2011 Code for the Construction of Concrete Structures, China Building Industry Press, 2011. [19] TZ210-2005. Technical Guide for Construction of Railway Concrete Engineering, Economic Planning Research Institute of Ministry of Railway, 2005.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
An experimental study on the lateral pressure of fresh concrete in formwork Wenxue Zhang, Jian Huang, Zengyin Li, Chun Huang ⇑ College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China
h i g h l i g h t s Four specifications to calculate lateral pressure are compared to obtain differences. The effects of factors on lateral pressure are tested and analyzed in experiments. A modification to the lateral pressure formula denoted in GB50666-2011 was proposed.
a r t i c l e
i n f o
Article history: Received 2 July 2015 Received in revised form 19 December 2015 Accepted 17 February 2016 Available online 21 March 2016 Keywords: Concrete Formwork Lateral pressure Concrete slump Vibration Casting speed
a b s t r a c t Most of the accidents related to concrete formwork are triggered by improper construction operations and the unsound lateral pressure estimations detailed in concrete formwork specifications. In this study a series of experiments was conducted to reveal the effect of different factors on lateral pressure. The results show that concrete slump, casting speed, and vibration mode can greatly influence the pressure; and the data obtained in the experiments differ greatly from the values yielded by different specifications. A modification is proposed to the GB50666 specification in order to improve the accuracy and reliability of pressure estimations. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Formwork is very critical to a building constructed by cast-inplace reinforced concrete and it comprises a high proportion of the total cost of concrete engineering. Extensive research has been conducted on the lateral pressure of concrete formwork recently. However, the components and mechanics of the lateral pressure in fresh concrete formwork have not been thoroughly understood. This can potentially cause design complications, poor construction quality, and accidents. Therefore, it is necessary to investigate the factors affecting the lateral pressure of fresh-concrete vertical formwork. Gardner and Quereshi [1] argued that the use of vibration to fluidize concrete can destroy the shear strength and eliminate the friction in formwork. Once concrete is completely fluidized, it behaves as a fluid because the lateral pressure is equal to the hydrostatic pressure produced by a fluid with the density of concrete. Gardner [2] stated that, as depth and time increase, concrete ⇑ Corresponding author. E-mail addresses: [email protected] (W. Zhang), [email protected] (C. Huang). http://dx.doi.org/10.1016/j.conbuildmat.2016.02.067 0950-0618/Ó 2016 Elsevier Ltd. All rights reserved.
develops internal shear strength and friction, causing the pressure to increase with depth at a lower rate than hydrostatic pressure. He also demonstrated that, for depths greater than 2 m, the magnitude of lateral pressure decreases near the base of a form. Santilli et al. [3,4] and Puente et al. [5] determined that, for low placement rates, a very low correlation coefficient exists between the concrete yield stress resulting from the slump cone and the maximum pressure reductions resulting from the hydrostatic cone. This relationship is even stronger for high placement rates. Arslan [6] and Arslan et al. [7] studied the influence of surface materials on lateral pressure and concluded that lateral pressure in concrete can be decreased by almost 40% by implementing a drainer system or a liner on the surfaces of formwork. Hurd [8] provided detailed suggestions concerning formwork design calculations. His work shows that lateral pressure overestimations increase the costs of formwork, which comprise about 60% of the costs of concrete structures [9]. This finding is confirmed by Kopczynski [10]. Studies concerning the lateral pressure of self-compacting concrete (SCC) formwork [11–14] have indicated that the pressure envelopes of SCC are similar to hydrostatic pressure. However, Omran et al. [15] reached a different conclusion—that the lateral pressure of SCC is obviously
W. Zhang et al. / Construction and Building Materials 111 (2016) 450–460
less than the hydrostatic pressure produced by a fluid with the density of concrete. The design standards of concrete formwork in different countries are based on industry standards [16–19] that are constrained by the economics of concrete construction and the requirements of concrete engineering quality and construction safety. Although formwork has been designed with more and more concern for safety recently, a number of accidents caused by the collapse of concrete formwork still occur. In order to provide a better reference for concrete formwork design, a series of experiments was conducted in this study to reveal the effects of critical factors on the lateral pressure values by comparing four standards: the ACI Committee 347 [16], CIRIA Report 108 [17], GB50666-2011 (China) [18] and TZ210-2005 (China) [19]. The critical factors include the concrete slump, rate of placement, initial setting time, environmental temperature, and vibration mode. On the basis of the experimental results, we propose some modifications to the GB50666 specification in order to improve the accuracy and reliability of pressure estimation through a regression analysis.
In this section, four specifications are selected as the standards to calculate pressure values using Eqs. (1)–(7). We analyze the effects of the rate of placement, concrete slump, initial setting time and environmental temperature on the lateral pressure values estimated using different specifications. (1) GB50666-2011 hhCode for the construction of concrete structuresii [18]. According to Appendix A.0.4 of the GB50666-2011 specification, when the concrete has a slump of no more than 180 mm and a normal internal vibration with a placement rate of less than 10 m/h, the smaller of the values yielded by Eqs. (1) and (2) should be selected as the lateral pressure value. 1
F ¼ 0:28Dc t 0 bR2
ð1Þ
F ¼ Dc h
ð2Þ
For concrete with a slump greater than 180 mm and a rate of placement greater than 10 m/h, the lateral pressure of the formwork can be calculated using Eq. (2). In Eqs. (1) and (2), Dc represents the weight density of the concrete (kN/ m3); and t0 indicates the initial setting time of the concrete—if there are no measured data, the initial setting time can be calculated from t0 = 200/(T + 15), where T is the environmental temperature in °C. The parameter b is the correction factor for the concrete slump (k): b = 0.85 when 50 mm < k 6 90 mm, b = 0.9 when 90 mm < k 6 130 mm, and b = 1.0 when 130 mm < k 6 180 mm; R represents the rate of placement (m/h), and h represents the depth of the concrete from the top of the placement to the point of consideration in the formwork. (2) TZ210-2005 Technical guide for construction of railway concrete engineering [19]. For new-site large-volume concrete and common concrete projects, the formwork lateral pressure can be calculated using Eq. (3), where R represents the placement rate (m/h).
F¼
72R P 19 R þ 1:6
the concrete and the concrete’s temperature. Furthermore, the concrete slump-correction is not considered in TZ210. (3) ACI Committee 347R-04, Guide to formwork for concrete [16]. For concrete with a slump of no more than 175 mm, and placed using normal internal vibration to a depth of no more than 1.2 m, the formwork lateral pressure can be calculated by using Eq. (4).
785R P max ¼ C w C c 7:2 þ T þ 18:7
ð3Þ
TZ210 primarily considers the influence of the rate of placement while neglecting the effects of the initial setting time of
ð4Þ
Eq. (4) can also be applied to calculate the pressure value of columns ranging from 30 Cw (kPa) to qgh and for walls with a rate of placement less than 2.1 m/h and a placement height less than 4.2 m. For walls with a placement rate that is less than 2.1 m/h and a placement height that is greater than 4.2 m, or all walls with a placement rate that ranges from 2.1 to 4.5 m/h, the pressure value can be calculated by using Eq. (5).
1156 224R P max ¼ C w C c 7:2 þ þ T þ 18:7 T þ 18:7
2. Comparison of the estimated formwork lateral pressure values using different specifications
451
ð5Þ
The minimum is 30 Cw (kPa) and the maximum is qgh; Pmax represents the maximum lateral pressure (kPa); R is the rate of placement (m/h); T is the temperature (°C) of the concrete during placement; Cw, Cc, and Dc indicate the unit weight coefficient, the chemistry coefficient, and the weight density of the concrete (kN/m3), respectively. (4) CIRIA Report No. 108 [17]. The maximum concrete pressure of a formwork is less than Dch and can be calculated by using Eq. (6).
pffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffi P max ¼ Dc C 1 R þ C 2 K H C 1 R
ð6Þ
pffiffiffi In Eq. (6), if C 1 R > H then the fluid pressure (Dch) equals the design pressure. The coefficient C1 depends on the size and shape of the formwork; for walls, C1 is set at 1, and for columns C1 is set at 1.5. The coefficient C2 depends on the constituent materials of the concrete; for ordinary Portland concrete (OPC) without a retardant, C2 is set at 0.3 and it is set at 0.45 for OPC with a retardant. H represents the height of the vertical formwork (in meters), and K is the temperature coefficient yielded by Eq. (7).
K¼
2 36 T þ 16
ð7Þ
In order to compare these pressure values calculated according to the four specifications, a real project was used to analyze the effects of the environmental temperature, concrete slump, initial setting time, and pouring speed on the lateral pressure values of concrete formwork. The concrete, which is mixed in a mixing plant, has a strength grade of C40 with a retardant. The weight density value of the concrete equals 3
Dc ¼ 25 kN=m and H = h = 9 m. The detailed results of the analysis are described in the following sections. 2.1. Placement rate The effects of different rates of placement (R) on the lateral pressure of formwork were analyzed under the conditions of an initial setting time of six hours, a 120 mm concrete slump, and a temperature of 20 °C. The correction factor of the concrete slump (b) is equal to 0.9 according to GB50666, and the unit weight coefficient (Cw) according to ACI347 is equal to 1.1. The chemistry coefficient (Cc) according to ACI347 is equal to 1.2. The coefficient
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dependent on the size and the shape of the formwork (C1) is equal to 1.5 according to CIRIA.108, and the coefficient dependent on the constituent materials of the concrete (C2) is equal to 0.45. The temperature coefficient (K) is 1.0. The formwork lateral pressure values, calculated by using different equations with different rates of placement, are shown in Fig. 1. The figure shows the following. (1) The lateral pressure values of formwork calculated using different specifications are different. The differences vary according to the different rates of placement. The biggest difference observed among the pressure values is a magnitude of 3.75 within the same placement rate. The values calculated using the standard TZ210 specification are significantly smaller than the values obtained using the other three specifications; this can potentially cause safety risks. (2) Although the placement rate is considered in all four of the specifications, the effect on the pressure value is different. The value calculated using the ACI347 specification is the highest when the placement rate is 6 m/h. The values calculated using the specifications ACI347 and GB50666 are around 181.4 kPa and 73.2 kPa within the calculated placement rate range, respectively. The pressure value obtained using the TZ210 specification is about 37.8 kPa and is the least affected by the rate of placement. (3) For a placement rate less than 3.0 m/h, the value calculated using the CIRIA.108 specification is larger than the value obtained using the other three specifications. Thus, this set of guidelines may yield a more conservative estimate. When the rate of placement is relatively high, the largest value is obtained using the ACI347 specification. Thus, the estimates yielded by this set of guidelines are too conservative. These results are consistent with the results obtained by Santilli et al. [3,4] and Puente et al. [5]. 2.2. Concrete slump The effects of different concrete slump values on the formwork lateral pressure were analyzed under the conditions of an initial setting time of six hours, a rate of placement of 2 m/h, and an environmental temperature of 20 °C. The unit weight coefficient (Cw) and the chemistry coefficient (Cc) according to ACI347 are 1.1 and 1.2. The coefficient dependent on the size and shape of the formwork (C1) according to CIRIA.108 is 1.5, the coefficient dependent on the constituent materials of the concrete (C2) is 0.45 and the temperature coefficient (K) is 1.0. The formwork
lateral pressure values, calculated with different concrete slump values, are shown in Fig. 2. (1) Only the formula specified by GB50666 takes into account the influence of the concrete slump on the lateral pressure. For the same concrete slump, the values yielded by the various formulas are significantly different. The value calculated using the TZ210 specification is the lowest, and the value calculated using the CIRIA.108 specification is the highest. The highest value is almost three times greater than the lowest value. (2) Although the formula given in GB50666 allows for the influence of the concrete slump, the values calculated by using the CIRIA.108 specification are almost twice as high as those calculated by using the GB50666 specification. Thus, using the CIRIA.108 specification can result in an unnecessary waste of resources. 2.3. Initial setting time The effects of different initial setting times on the framework lateral pressure were analyzed under the conditions of a concrete slump of 120 mm, a casting speed of 2 m/h, and an environmental temperature of 20 °C. The correction factor of the concrete slump (b) according to GB50666 is 0.9. The unit weight coefficient (Cw) and the chemistry coefficient (Cc) according to ACI347 are 1.1 and 1.2, respectively. The coefficient dependent on the size and shape of the formwork (C1) according to CIRIA.108 is 1.5; the coefficient dependent on the constituent materials of the concrete (C2) is 0.45 and the temperature coefficient (K) is 1.0. The lateral pressure values of formwork, calculated by using different formulas and with different initial setting times, are shown in Fig. 3. Of the four specification guidelines, only the GB50666 specification considers the effects of the initial setting time on formwork lateral pressure. The lateral pressure of formwork rises as the initial setting time of the concrete increases; it is a linear relationship. 2.4. Environmental temperature The effects of the environmental temperature on the lateral pressure during concrete pouring were analyzed with a concrete slump of 120 mm, a casting speed of 2 m/h, and an initial setting time of six hours. The correction factor of the concrete slump (b) according to GB50666 is equal to 0.9. The unit weight coefficient (Cw) and the chemistry coefficient (Cc) of ACI347 are equal to 1.1 120
225
GB50666
100
TZ210 ACI347
175
Lateral pressure (kPa)
Lateral pressure (kPa)
200
CIRIA.108
150 125 100 75 50
80 60 40 20
GB50666 ACI347
25 0
TZ210 CIRIA.108
0 0.5
2.0
4.0
6.0
Rate of placement (m/h) Fig. 1. Relationship between the placement rate and lateral pressure.
0
20
40
60
80
100
120
140
160
Slump (mm) Fig. 2. Relationship between the concrete slump and lateral pressure.
Lateral pressure (kPa)
W. Zhang et al. / Construction and Building Materials 111 (2016) 450–460
453
120
3. Lateral pressure experimental session
100
This experiment consisted of 16 specimens. Ten of the specimens had dimensions of 60 cm 120 cm; two had dimensions of 30 cm 120 cm; one of them was 15 cm 120 cm; and the last three had dimensions of 60 cm 60 cm. All of the specimens were 300 cm in height. C30 concrete was used for the experiment; its main ingredients included JINYU brand P.O42.5 cement, river sand, and graded crushed stone. Due to the material supply, formwork processing, and garbage treatment characteristics, Beijing’s Yun Meng Bridge, which was under construction at the time, was selected as the site of the experiment.
80 60 40 20 0
3
GB50666
TZ210
ACI347
CIRIA.108
5
7
9
11
Initial setting time (h) Fig. 3. Relationships between the initial setting time and lateral pressure.
and 1.2, respectively. The coefficient dependent on the size and shape of the formwork (C1) according to CIRIA.108 is equal to 1.5 and the coefficient dependent on the constituent materials of the concrete (C2) is equal to 0.45. The formwork lateral pressure values, calculated using the different formulas for different environmental temperatures, are shown in Fig. 4. (1) At the same environmental temperature, there are significant differences among the lateral pressure values of concrete formwork. The minimum value is obtained from the TZ210 specifications. At low environmental temperatures, the pressure values yielded by the various formulas vary significantly. This may result in accidents during construction. (2) The GB50666 and TZ210 specifications do not take into account the influence of environmental temperature on lateral pressure directly, but both the ACI347 and CIRIA.108 specifications do take into account the temperature effects. However, the formwork lateral pressure values that are obtained using the ACI347 and CIRIA.108 specifications can vary significantly when the environmental temperature decreases, and the obtained values drop at different rates. When the environmental temperature increases from 5 °C to 30 °C, the values obtained using ACI347 decrease by 47% while the values obtained using CIRIA.108 decline by 61%.
3.1. Formwork design and measuring point arrangements The formwork required sufficient strength and stiffness to avoid large template deformation, which would affect the accuracy of the test results. In accordance with our preliminary calculations, 6 mm thick steel plate was used as the formwork’s faceplate and 8 mm 60 mm steel plate was used for stiffening ribs at every 300 mm both vertically and horizontally. The edge rib was L63 8 mm angle steel; M20 high-strength bolts, spaced 150 mm apart, were used for connecting the formwork. The layouts of the pressure measure cells are shown in Fig. 5. From the bottom of the formwork to a height of 200 cm, pressure measure cells were located at a regular distance of 50 cm. A single cell was used for a side 60 cm wide and a side 30 cm wide. Two cells were used for a side 120 cm long. No cell was used with a side 15 cm wide. To analyze the influence of the edges of the 30 cm 120 cm specimens on the lateral pressure, tests were conducted on both sides. The detailed information about the specimens is listed in Table 1. 3.2. Data acquisition system In order to ensure the reliability of the data, two kinds of pressure measure cell (made by the DANDONG experimental instrument factory and JINMA Hi Tech Co. Ltd.) were simultaneously utilized in this experiment. In Fig. 5, ‘J’ and ‘D’ represent JINMA and DANDONG cells, respectively. The main performance index of these two kinds of cells is as follows. (1) The range, resolution, nonlinear error, repeatability error, and hysteresis error of the JINMA JM-5006X double membrane intelligent string type digital pressure cell are 0.6 MPa, 60.2% F.S., 61.2% F.S., 61.0% F.S., and 61.0% F.S., respectively. (2) The range, resolution, nonlinear error, repeatability error, and hysteresis error of the DANDONG DY-110 single membrane pressure cell are 0.4 MPa, 60.3% F.S., 62.0% F.S., 60.5% F.S., and 61.0% F.S., respectively. 3.3. Experimental process
Fig. 4. Relationship between the environmental temperature and lateral pressure.
A slump experiment was conducted on each specimen before casting and the pertinent data were recorded in detail. Once the concrete had been poured to a height of 0.5 m, the changes in the lateral pressure, environmental temperature, casting time, and other parameter values were recorded. The initial setting time of the concrete was recorded at the same time. The experiment required approximately 35 m3 of concrete and took 36 days to complete. Some of the steps in the experiment are shown in Fig. 6. To accurately simulate the real construction environment, the whole experiment was conducted in an outdoor environment.
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values of the formwork at the same height on the long walls were averaged. Then the maximum formwork lateral pressure values during the pouring of the concrete were determined. The relationships between the lateral pressure values and the placement heights of typical specimens are shown in Fig. 7. The data regarding the 16 specimens are shown in Table 1 and Fig. 8. In Table 1 ‘position’ represents the place, measured vertically from the bottom surface, where the lateral pressure reached a maximum; and ‘placement height’ indicates the corresponding height of the pouring concrete. For example, 0.5(2.5) means that the lateral pressure reached a maximum 0.5 m from the bottom surface and the corresponding height of the pouring concrete was 2.5 m. (1) The maximum values of the formwork lateral pressure did not necessarily occur at the bottom of the formwork but at some elevation above the base of the formwork. The impact of the lateral pressure values on formwork increased as the pouring height rises; this resulted in the outward deformation of formwork. In addition, the shear strength of the poured concrete increased, due to vibration and setting. The increased shear strength allowed the concrete to support vertical loads. (2) The formwork lateral pressure values increase as the pouring height rises. However, once the pouring height reaches a certain value, the growth of lateral pressure values stops and the values even diminish as the pouring height continues to increase. (3) The average of the maximum values of the formwork lateral pressure on the short sides of specimens 1–12 was 31.1 kPa. The average of the maximum values of the formwork lateral pressure on the long sides of specimens 1–12 was 30.1 kPa. Four of the average formwork lateral pressure values that were recorded on the long sides were greater than those recorded on the short sides. Thus, the shape of the formwork structures did not significantly influence the lateral pressure values of the concrete. These results are consistent with those reported by Santilli et al. [14]. (4) Table 1 lists the data for the concrete slump, rate of placement, and vibration mode; these factors significantly influence formwork lateral pressure. Therefore, a detailed analysis of the concrete slump, rate of placement, and vibration mode is conducted in the following section. 4. Analysis of the experimental results 4.1. Comparison of the calculated and measured formwork lateral pressure values
Fig. 5. Pressure test point arrangements.
The formwork lateral pressure values (Fc) calculated using the formulas detailed in the GB50666-2011, TZ210-2005, CIRIA.108, and ACI347 specifications are compared with the measured formwork lateral pressure values (Ft). The results are shown in Fig. 9; the absolute error and the relative error are calculated as Ea ¼ F c F t and Er ¼ EFat 100%, respectively. Fig. 9 shows the following.
3.4. Estimated formwork lateral pressure values First, the data obtained from the experiment were processed. For the specimens with dimensions of 60 cm 60 cm 300 cm, the average formwork lateral pressure at the same height was calculated. For the specimens with dimensions of 60 cm 120 cm 300 cm and 30 cm 120 cm 300 cm, the lateral pressure values of the formwork at the same height on the long and short walls were averaged separately. For the specimens with dimensions of 15 cm 120 cm 300 cm, only the lateral pressure
(1) The values of the relative errors calculated using the GB50666 specification range from 11% to +78%; the average relative error is 21%. The absolute error values of SP.4, SP.7, and SP.8 are 4.5 kPa, 2.5 kPa, and 0.8 kPa, respectively. The probability that the obtained value is less than the corresponding measured value is 23%. (2) The values of the relative errors calculated using the TZ210 specification range from 38% to +76%; the average relative error is 0.8%. The calculated values of seven of the
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W. Zhang et al. / Construction and Building Materials 111 (2016) 450–460 Table 1 Specimen parameters and maximum lateral pressure values. Specimen number
Size (m) (L * W * H)
Slump (mm)
Placement rate (m/h)
Temperature (°C)
Vibration mode
1 2 3 4 5 6 7 8 9 10 11 12 13 14
0.6 1.2 3 0.6 1.2 3 0.6 1.2 3 0.6 1.2 3 0.6 1.2 3 0.6 1.2 3 0.6 1.2 3 0.6 1.2 3 0.6 1.2 3 0.6 1.2 3 0.3 1.2 3 0.3 1.2 3 0.15 1.2 3 0.6 0.6 3
155 203 240 210 154 154 155 86 157 150 157 159 160 159
1.29 1.29 1.33 0.93 1.16 1.16 0.45 0.80 1.45 1.16 1.97 3.30 6.38 1.5
13 24 17 19 24 16 21 20 22 16 18 8 20 17
15
0.6 0.6 3
159
2.36
9
16
0.6 0.6 3
160
5.17
20
1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 1 vibration/0.5 m 2 full vibrations in the end 1 vibration/1 m Final full vibration No vibration during pouring Final full vibration
specimens are less than the corresponding measured values. The probability that the obtained value is less than the corresponding measured value is 54%. (3) The values of the relative errors calculated using the ACI347 specification range from 0% to +47%; the average relative error is 25%. Thus, these results are conservative. (4) The relative errors of the values calculated using the CIRIA.108 specification range from +5% to +116%; the average relative error is 58%. Thus, these results are overlyconservative. (5) The results demonstrate that numerous factors affect the lateral pressure values of formwork and significant differences exist between the measured and calculated values regardless of the specification used. The values calculated by using the CIRIA.108 specification are significantly larger than the corresponding measured values. Thus, the use of the CIRIA.108 specification may result in an unnecessary waste of resources. In addition, there is a very high probability that a value calculated using the TZ210 specification is less than the corresponding measured value. Thus, the TZ210 specification is not adequately conservative. 4.2. Fractional analysis of the experimental data 4.2.1. Regression analysis Since the experiment was conducted in an outdoor environment, several factors—such as the temperature, sunshine, and wind speed—may have influenced the results. In order to study the individual effects of the main factors on the formwork lateral pressure, some of the variables were normalized by multi-parameter fitting. First, on the basis of an analysis of the environment, the parameters that may possibly have affected the results were determined. Then, the nlinfit function of Matlab and Eq. (8) were used to subject the data to nonlinear least-squares fitting. The rate of placement, environmental temperature, and concrete slump were normalized and grouped according to Eq. (8). Thus, while the variables of one parameter were studied, the other two parameters were adjusted to certain values using Eq. (8) so that the influence of a single particular parameter could be analyzed. The sectional area (x1), formwork length (x2), rate of placement (x3), environmental temperature (x4), and concrete slump (x5) were
Long side
Short side
Measured value (kPa)
Position (placement height)
Measured value (kPa)
Position (placement height)
27.0 26.0 37.5 41.5 30.5 21.5 27.5 28.5 38.2 27.2 24.8 31.3 33.0 36.2 54.7 47.7 52.9 17.1 43.7
0.5 (2.5) 1.0 (3.0) 0.5 (3.0) 0.5 (3.0) 0.5 (3.0) 1.0 (2.5) 0.5 (2.0) 0.5 (2.0) 0.5 (2.5) 0.5 (2.0) 1.0 (3.0) 0 (1.5) 0 (3.0)
25.0 32.0 42.1 37.0 32.0 24.0 26.0 30.0 39.0 28.1 24.1 34.0
0.5 1.0 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
(2.5) (3.0) (3.0) (2.5) (3.0) (2.0) (2.0) (2.5) (2.0) (2.0) (2.0) (1.5)
0.5 (2.5) 0 (second full vibration) 0.5 (3.0) 0 (full vibration) 0 (1.5) 0.5 (full vibration)
considered during the multi-parameter fitting. Because the vibration modes of SP.14 and SP.16 were different from those of the other specimens, the related data were not included in the analysis. The determination coefficient (Rs) was 0.92. So the regression equation, or Eq. (8), was capable of predicting the formwork lateral pressure values precisely.
F ¼ 86:3 þ 36:8x0:39 x0:024 x0:06 x0:19 1 2 3 4 1:71 0:87 sinð5:2 þ 6:1x0:51 Þ 5
ð8Þ
As is shown in Table 1, the influence of the sectional dimensions on the formwork lateral pressure was negligible. Thus, the effects of the sectional dimensions were ignored when grouping the experimental data. Since the effects of the concrete slump, rate of placement, and environmental temperature were the primary consideration during the analysis, the specimens were divided into three experimental groups. 4.2.2. Influence of the concrete slump The concrete slumps of SP.8, SP.9, SP.12, SP.4, and SP.3 were equal to 86 mm, 157 mm, 159 mm, 210 mm, and 240 mm, respectively. The rate of placement and environmental temperature values of these five specimens were revised using Eq. (8). The temperature values and the rate of placement values were changed to 20 °C and 1.20 m/h in order to obtain the corrected lateral pressure values of the formwork. The corrected results are shown in Table 2, and the effects of the concrete slump on the formwork lateral pressure values are shown in Fig. 10. The results indicate that the concrete slump significantly influences the formwork lateral pressure in that the formwork lateral pressure rises as the concrete slump increases, under the same conditions; the relationship is linear. The determination coefficient of the linear regression function is Rs = 0.93; this can be used to characterize the relationship between the lateral pressure and the concrete slump. 4.2.3. Influence of the rate of placement The placement rates of SP.7, SP.8, SP.4, SP.10, SP.2, SP.3, and SP.9 were 0.45 m/h, 0.80 m/h, 0.93 m/h, 1.16 m/h, 1.29 m/h, 1.33 m/h, and 1.45 m/h, respectively. The concrete slump and environmental temperature of these seven specimens were revised using Eq. (8).
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(a) Formwork assembly
(b) Test site Fig. 8. Maximum lateral pressure of all specimens at different test points.
(c) Specimens Fig. 6. Experimental process.
Fig. 7. Relationships between the lateral pressure values of typical specimens and the placement height.
The environmental temperature and concrete slump values were corrected to 20 °C and 150 mm in order to obtain the corrected formwork lateral pressure values. The corrected results are listed
in Table 3, and the influence of the rate of placement on the formwork lateral pressure is shown in Fig. 11. The results indicate that the formwork lateral pressure increases as the placement rate increases, under the same conditions, and that the formwork lateral pressure values exhibit an exponential relationship with the placement rate. The determination coefficient of the exponential function is equal to Rs = 0.99; this can be used to characterize the relationship between the lateral pressure and the rate of placement. 4.2.4. Influence of the environmental temperature The environmental temperatures of SP.10, SP.4, SP.8, SP.7, and SP.2 were 16 °C, 19 °C, 20 °C, 21 °C, and 24 °C, respectively. The concrete slump and placement rate values of these five specimens were revised using Eq. (8). The rate of placement and concrete slump values were corrected to 1.20 m/h and 150 mm, respectively, in order to obtain the corrected formwork lateral pressure values. The corrected results are shown in Table 4, and the influence of the environmental temperature on the formwork lateral pressure is shown in Fig. 12. The results indicate that the environmental temperature influenced the formwork lateral pressure significantly less than the concrete slump and placement rate. These results are consistent with those reported by Santilli et al. [14]. The environmental temperature does not directly influence the formwork lateral pressure, but it affects the initial setting time of the concrete. According to Omran et al. [15], environmental temperature does not influence the rate of lateral pressure variation. As the temperature increases, however, both the initial setting time and the concrete slump are affected. 4.2.5. Influence of the vibration mode In order to analyze the maximum formwork lateral pressure values, which were influenced by the vibration method during the concrete casting, the vibration modes of SP.14, SP.15, and SP.16 were changed during the process of the experiment. Specimen 14 was vibrated once after each 50-cm increment of concrete
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Fig. 10. Influence of the concrete slump on the lateral pressure.
Table 3 Influence of the casting speed on the lateral pressure. Specimen number
Placement rate (m/h)
Measured data (kPa)
Correction coefficient
Corrected result (kPa)
7 8 4 10 2 3 9
0.45 0.80 0.93 1.16 1.29 1.33 1.45
27.5 30.0 37.0 28.1 32.0 42.0 39.4
0.93 0.96 0.79 1.07 0.95 0.73 0.78
25.6 28.7 29.2 30.0 30.4 30.5 30.8
Fig. 9. Comparison of the measured values and the values calculated using the GB50666, ACI347, CIRIA.108 and TZ210 specifications. Fig. 11. Influence of the casting speed on the lateral pressure. Table 2 Influence of the concrete slump on the lateral pressure. Specimen number
Slump (mm)
Measured data (kPa)
Correction coefficient
Corrected result (kPa)
8 9 12 4 3
86 157 159 210 240
30.0 39.4 34.3 37.0 42.0
1.08 0.98 1.17 1.03 0.99
32.4 37.8 38.0 38.8 41.6
was poured. Once the pouring process was complete, a vibrating rod was inserted in the bottom of the specimen and vibrated twice from the bottom to the top. Specimen 15 was vibrated once after every 100-cm increment of concrete was poured. Once the pouring process was complete, a vibrating rod was inserted in the bottom of the specimen and vibrated once from the bottom to the top.
Table 4 Influence of the environmental temperature on the lateral pressure. Specimen number
Temperature (°C)
Measured data (kPa)
Correction coefficient
Corrected result (kPa)
10 4 8 7 2
16 19 20 21 24
28.1 37.0 30.0 27.5 26.0
0.99 0.80 1.01 1.08 1.20
27.7 29.6 29.2 29.7 31.1
Specimen 16 was not vibrated during the pouring process. Once the pouring process was completed, a vibrating rod was inserted in the bottom of the specimen and vibrated from the bottom to the top. The lateral pressure values recorded at the 0-cm and 50cm measurement points of these three specimens are shown in Fig. 13, which shows the following.
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with the measured values, a modification of the formwork lateral pressure calculation formula given in the GB50666 specification is proposed. First, the relationship between the maximum formwork lateral pressure and the rate of placement (R) is revised with regard to the casting speed items in the GB50666 formula. Next, the relationship between the maximum formwork lateral pressure and the slump (k) is revised in order to include in the formula the influence of the concrete slump. Then, the modified formula to calculate the formwork lateral pressure is obtained. 5.1. Revision of the placement rate In accordance with Fig. 11, the relationship between the lateral pressure and the placement rate can be expressed as Eq. (9). 1
Fig. 12. Influence of the environmental temperature on the lateral pressure.
F ¼ 30R4
ð9Þ
The determination coefficient of the fitting function (Rs) is 0.99; this function can be applied to characterize the relationship between the lateral pressure and the rate of placement. The values of the absolute errors, calculated using Eq. (9), are listed in Table 5. In order to ensure that the calculated values are larger than the measured values, when the placement rate is less than 10 m/h Eq. (9) is modified to: 1
F ¼ 31R4
ð10Þ
The effects of the concrete’s weight density and the initial setting time are also considered. When the weight density of the concrete (Dc) is equal to 24 kN/m3 and the temperature is 20 °C, the initial setting time can be expressed as t0 ¼ 200=ðT þ 15Þ ¼ 5:71. Thus, Eq. (11) can be obtained by substituting Dc and t0 into Eq. (10). 1
F ¼ 0:23Dc t 0 R4
ð11Þ
5.2. Revision of the concrete slump correction factor Fig. 13. Influence of the vibration mode on the lateral pressure.
(1) The vibration depth significantly influences the maximum formwork lateral pressure. The maximum formwork lateral pressure of SP.15, which was vibrated once after each 100cm increment of concrete was poured, is 47.4% higher than that of SP.14, which was vibrated once after each 50-cm increment of concrete was poured. (2) The maximum formwork lateral pressure of SP.14 increases by 89.3% after the first vibration by the vibrating rod from the bottom to the top, then it increases by 92.6% after the second vibration by the vibrating rod from the bottom to the top. The maximum formwork lateral pressure of SP.15 increases by 29.0% after vibration by the vibrating rod from the bottom to the top. (3) The maximum values of the formwork lateral pressure of SP.14, SP.15, and SP.16—after the vibration by the vibrating rod from the bottom to the top—are different.
5. Formula modifications The results and analysis demonstrate that the concrete slump and rate of placement can significantly influence the maximum formwork lateral pressure and that the influence of the environmental temperature on the maximum formwork lateral pressure is relatively minor. Existing specifications may yield highly inaccurate formwork lateral pressure values. As the parameters in the experiment were consistent with the parameters in the GB50666 specification and the calculated values were in good agreement
In accordance with Fig. 10, the relationship between the lateral pressure and the concrete slump can be expressed as Eq. (12).
F ¼ 0:055k þ 28:32
ð12Þ
The determination coefficient of the fitting function (Rs) is 0.93; this function can be used to characterize the relationship between the lateral pressure and the concrete slump. The absolute errors of the values, calculated using Eq. (12), are listed in Table 6. In order to ensure that the calculated values are larger than the measured values, Eq. (12) is modified to F ¼ 0:055k þ 28:32 þ DF; from the data in Table 6, DF is found to be 0.92. In order to allow for the effects of the concrete slump, the following Eq. (13) is upgraded by introducing the concrete slump correction factor bðkÞ into Eq. (11). Thus, the lateral pressure formula can be expressed as: 1
F ¼ 0:23Dc bðkÞt 0 R4
ð13Þ
Table 5 Influence of the casting speed on Ff and Ft (kPa). Specimen number
Measured value Ft
Calculated value Ff
Error Ft Ff
7 8 4 10 2 3 9
25.59 28.67 29.21 29.99 30.36 30.46 30.76
26.63 28.61 29.15 29.97 30.37 30.48 30.82
1.0189 0.3002 0.2520 1.1475 1.6153 1.7543 2.1590
W. Zhang et al. / Construction and Building Materials 111 (2016) 450–460 Table 6 Influence of the concrete slump on Ff and Ft (kPa). Specimen number
Measured value Ft
Calculated value Ff
Error Ft Ff
8 9 12 4 3
32.35 37.78 38.01 38.83 41.6
33.06 36.98 37.09 39.91 41.56
0.72 0.79 0.92 1.08 0.04
459
A further analysis of the results indicates that the placement rates of SP.4, SP.7, and SP.8 are 0.93 m/h, 0.45 m/h, and 0.8 m/h, respectively. Thus, there may be safety risks if the formwork is designed using the GB50666 specification when the placement rate is relatively low. (2) The average relative error of the values yielded by the modified formula Eq. (15) is 21%. The average relative error of the values yielded by the ACI347 specification is 25%, and the average relative error of the values yielded by the CIRIA.108 specification is 58.3%. Thus, both of these guidelines yield higher average errors than the modified formula proposed in this paper. 6. Conclusions The results in this study lead to the following conclusions.
Fig. 14. Comparison of the absolute error values of the modified and original formulas.
Here, Dc = 24 kN/m3; T = 20 °C; t 0 ¼ 200=ðT þ 15Þ ¼ 5:71; and R = 1.2 m/h. bðkÞ was solved by the use of two Eqs. (12) and (13).
bðkÞ ¼ 1:75 103 k þ 0:93
ð14Þ
In this way, the formula given in the GB50666 specification is modified on the basis of the experimental data. For R 6 10 m/h and 50 mm 6 k 6 240 mm, the modified formula for the formwork lateral pressure can be expressed as Eq. (15); the smaller value should be adopted as the design value.
(
1
F ¼ 0:23Dc bt0 R4
ð15Þ
F ¼ Dc H
Here, Dc represents the weight density of the concrete (kN/m3); t0 represents the initial setting time of the concrete; R represents the rate of placement (m/h); and b represents the concrete slump correction factor (b = 1.10 when 50 mm < k 6 90 mm, b = 1.25 when 90 mm < k 6 180 mm, and b = 1.40 when 180 mm < k 6 240 mm).
1
(F ¼ 0:23Dc bt0 R4 ) is more capable of effectively ensuring formwork engineering security and yielding accurate formwork lateral pressure values. (4) The vibration mode and depth have significant effects on the maximum formwork lateral pressure. Increasing the depth of vibration and/or repeating vibration greatly increase the formwork lateral pressure and should be avoided. (5) The concrete slump and the placement rate significantly affect the maximum lateral pressure. However, in previous research the influence of environmental temperature has not been thoroughly studied and remains unclear, especially in the cases when the casting process is completed before the initial setting of the concrete starts. The effects of environmental temperature should be investigated further.
Acknowledgement The research is supported and funded by the grants Natural Science Foundation of China: 51378034 and 5150081022.
5.3. Comparison of the modified and original formulas Due to the formula modifications, the specification coefficient changed from 0.28 to 0.23, the applicable range of the concrete slump increased from 50–180 mm to 50–240 mm, the corresponding concrete slump correction factor was revised, and the partial 1
(1) The values of the relative errors yielded by the TZ210 specification are small, but the probability of a value yielded by the TZ210 specification being less than the corresponding measured value is very high. (2) The experimental results demonstrate that the ACI347 and CIRIA.108 specifications are conservative. (3) The formula given in the GB50666 specification is modified in such a way that the applicable range of the concrete slump is extended, and the corresponding concrete slump adjustment factor is revised. Compared to the formula given in the GB50666 specification, the modified formula
1
coefficient of the placement rate changed from R2 to R4 . The formwork lateral pressure values calculated using the modified formula Eq. (15) and the formulas detailed in the GB506662011, CIRIA.108, and ACI347 specifications were compared with the measured lateral pressure values of the specimens. The relative errors are shown in Fig. 14. This figure shows the following. (1) All of the SP.4, SP.7, and SP.8 values yielded by the GB50666 specification are smaller than the corresponding measured values, but all of the values yielded by the modified formula are no less than the corresponding measured values.
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[15] A.F. Omran, Y.M. Elaguab, K.H. Khayat, Effect of placement characteristics on SCC lateral pressure variations, Constr. Build. Mater. 66 (2014) 507–514. [16] ACI Committee 347R-04. Guide to Formwork for Concrete, American Concrete Institute, 2004. [17] CIRIA Report 108. Concrete pressure on formwork, Construction Industry Research and Information Association, 1985. [18] China Academy of Building Research, GB50666-2011 Code for the Construction of Concrete Structures, China Building Industry Press, 2011. [19] TZ210-2005. Technical Guide for Construction of Railway Concrete Engineering, Economic Planning Research Institute of Ministry of Railway, 2005.