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Development of a horizontal shifting mechanistic-empirical prediction model for concrete block pavement
Construction and Building Materials 118 (2016) 245–255
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Development of a horizontal shifting mechanistic-empirical prediction model for concrete block pavement Wuguang Lin a, SungWoo Ryu b,⇑, Han Hao a, Yoon-Ho Cho c a
College of Transport and Communications, Shanghai Maritime Univ., 1550 Haigang Ave., Shanghai, PR China Korea Expressway Corporation Research Institute, 208-96, Dongbu-daero 922beon-gil, Dongtan-myeon, Hwaseong-si, Gyeonggi-do, Republic of Korea c Dept. of Civil and Environmental Engineering, Chung-Ang Univ., 84 Heukseok-Ro, Dongjak-Gu, Seoul, Republic of Korea b
h i g h l i g h t s A horizontal shifting prediction model for concrete block pavements was developed considering block shapes and laying patterns. The SDM concept was proposed to explain the relationships between the individual movements and overall pattern movements of a block. The cumulative horizontal shifting values decreased as the SDM value increased. The results also showed that the horizontal interlocking effect also
increased as the shape factor value increased.
a r t i c l e
i n f o
Article history: Received 2 December 2015 Received in revised form 13 April 2016 Accepted 26 April 2016 Available online 14 May 2016 Keywords: Concrete block pavement Horizontal shifting Mechanistic-empirical prediction model Block shapes Construction patterns
a b s t r a c t Few studies have been conducted on horizontal shifting prediction models that consider block shapes and laying patterns for block pavements. To develop a prediction model, a combination of different block shapes and laying patterns was evaluated by computer modeling and laboratory tests. The relationship between the force and displacement was recorded via a photogrammetric method using a friction tester. In order to quantify the recorded video results, rigid body analysis was performed. The results of laboratory experiments and the rigid body analysis offered a good match. A displacement vector was used to express the movement of the block with time, according to the start and end position information of each block. Also, a concept of Specific D-Moment (SDM) was proposed to describe the relationship between the movement of the individual blocks and the entire movement. A horizontal shifting mechanisticempirical prediction model of concrete block pavement is proposed based on regression analysis of the existing performance data. According to the prediction model, higher SDM values give lower cumulative amounts of horizontal shifting due to traffic. Ó 2016 Published by Elsevier Ltd.
1. Introduction The surface of a block pavement is different from that of typical pavements. It is built by using individual blocks, with different laying patterns, to form a discrete surface layer. Thus, blocks act with joint sand as structural surfacing rather than merely providing a wearing course [1]. The main distress of block pavement can be divided into horizontal shifting, breakage of blocks, faulting, and rutting. Yasuhisa et al. [2] evaluated the condition of 48 block pavements applied on roads and reported that the ratio of horizontal shifting distress occurrence was as high as 52%. Damage to block pavement (horizontal and vertical displacements) can ⇑ Corresponding author. E-mail addresses: [email protected] (W. Lin), [email protected] (S. Ryu), [email protected] (H. Hao), [email protected] (Y.-H. Cho). http://dx.doi.org/10.1016/j.conbuildmat.2016.04.124 0950-0618/Ó 2016 Published by Elsevier Ltd.
frequently be observed. They are mainly the result of poor quality construction and overloading of the block pavement. Hence, the concrete industry is attempting to improve the performance of block pavement by minimizing displacement by, for example, developing advanced block forms. New block shapes with horizontally interlocking features are intended to ensure the increased bearing capacity and deformation resistance of block pavements [3]. To determine the reason for the damage caused by horizontal torsion, Knapton [4] divided block interaction into three types: rotational, vertical, and horizontal. A block’s rotation is constrained by the curb installed at the end of pavement. Vertical interlocking occurs due to the joint sealing compound in the joint. Horizontal interlocking varies depending on the block shape and laying pattern. The surface of the block pavement consists of a discontinuous layer that is resistant to external loads via the interlocking, which
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Table 1 Experimental variables to evaluate horizontal shifting characteristics of concrete block pavement. A (Rec.)
Stretcher Basket weave Herringbone
Center Corner Center Corner Center Corner
p p p p p p
B (Foot.) p p
C (Uni) p p p p p p
D (Das.) p p p p p p
Table 3 Material properties for the rigid body analysis model. Category
Material property
E (Key.) p p
Block Steel plate
Modulus (Pa)
Poisson’s ratio
Friction coefficient
3.1E09 2.0E11
0.15 0.25
0.60 0.45
1. Video camera 2. Tripod 3. Main frame 1
4. Load cell 5. Load frame 6. Control PC
2
6
Table 2 Shape factors calculation results for different block shapes used in the study.
Surface area mm2 Side area mm2 L mm h mm Shape factora a
A (Rec.)
B (Foot.)
C (Uni)
D (Das.)
E (Key.)
4232 9936 276 36 2.34
2899 6204 172 36 2.41
4321 10,692 297 36 2.53
4041 10,620 295 36 2.62
3676 9396 261 36 2.56
4
3 5
Shape factor = side area/surface area.
Fig. 2. Friction test equipment.
is why horizontal torsion can be a function of block shape and the laying pattern. Shackel and Lim [1] demonstrated that a shaped block had better interlocking action than a rectangular block with respect to horizontal interlocking between blocks. And they reported that the herringbone pattern can distribute loads efficiently. Yaginuma et al. [5] generalized block shapes by considering the ratio of the total side area to the top area, in order to identify the appropriate sizes of blocks for use in roads. They claimed that as the area ratio increased, the load transfer efficiency between blocks also increased. Horizontal interlocking is primarily
achieved through the use of laying patterns that disperse the forces from braking, turning, and accelerating vehicles [6]. However, based on previous studies by Panda and Ghosh [7] and Soutsos et al. [8], a laying pattern has little effect on the performance of block pavement. Ascher et al. [3] stated that the horizontal shifting of block pavement was a function of joint width. Upon reviewing previous research on the horizontal shifting of block pavement, it was found that few studies were conducted on
Fig. 1. Loading condition and boundary condition of the rigid body analysis model.
W. Lin et al. / Construction and Building Materials 118 (2016) 245–255
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horizontal shifting prediction models that consider the block shape and laying pattern. Moreover, contradictory study results were reported. In this study, after developing a horizontal shifting mechanistic-empirical prediction model of block pavement using existing performance data, a combination of different block shapes and laying patterns was evaluated by computer modeling and laboratory tests.
2. Research program 2.1. Factorial design
Fig. 3. (a) Rigid body analysis result vs. (b) laboratory test result (case of rectangular – herringbone).
Investigations of horizontal interlocking behavior of block pavements were conducted by lab experiment and rigid body analysis. The variables of block shape, laying pattern, and loading location are summarized in Table 1. The lab experiment was conducted by using a friction tester for different block shapes. Rectangular, Uni, and Dasuri block were used for different shapes, while the stretcher, basket-weave, and herringbone were used as laying pattern. In the rigid body analysis, a footprint and keystone block with a stretcher pattern were added. Dimension of blocks used in the study are shown in Table 2. To generalize the block dimensions,
(a) Corner loading condition
(b) Center loading condition Fig. 4. Individual block displacement vectors with the stretcher pattern, for different block shapes under corner and center loading (1) Rectangular block; (2) Uni-block; (3) Dasuri block.
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(a) Corner loading condition
(b) Center loading condition Fig. 5. Individual block displacement vectors with basket-wave pattern, for different block shapes under corner and center loading (1) Rectangular block; (2) Uni-block; (3) Dasuri block.
a shape factor proposed by Yaginuma et al. [5] was used. The shape factor is the area ratio of the total side area to the surface area and the range in this study was set at 2.3–2.6. 2.2. Rigid body analysis ABAQUS 6.10 [9] was used to conduct the rigid body analysis for evaluating the horizontal interlocking behavior of block pavement. 3D solid elements were used in the analysis model. The real size of blocks is usually too heavy and large to be tested in a laboratory, so it is difficult to handle the dynamic effects of block movement. Therefore, the sizes of the blocks used in the study were smaller than those of real blocks. The typical dimension of a block used in Korea is 200 mm 100 mm 80 mm. The dimension of block used in this study is 92 mm 46 mm 36 mm. Thirty-six blocks were arranged in a fixed steel plate (368 mm 736 mm) with various patterns. The loading condition of the model is shown in Fig. 1 (a). Corner and center loadings were applied to investigate the effect of rotation and horizontal movement of the block pavement. The aim of the corner loading was to investigate the horizontal interlocking between blocks when rotation and horizontal movement occurred simultaneously, while the center loading was to evaluate the horizontal interlocking effect when the rotation was minimized. The side of the whole pattern was setup as a free con-
dition. The boundary condition of the model was setup as shown in Fig. 1(b). The steel plate supporting the blocks was fixed in all directions. A general contact was applied between the elements. And also, the contact was considered for the interface between blocks and a steel plate. The maximum displacement of the directly loading block was set at 50 mm. In addition, material properties, including the friction coefficients, are presented in Table 3. The values suggested by Phuong [10] were used for the friction coefficients between blocks, and between the blocks and the steel plate. To evaluate the loaddisplacement behavior of individual blocks as well as the overall pavement, meshes in each block were set differently depending on the block shape. 2.3. Laboratory experiments The lab experiment setup for evaluating the laying pattern is shown in Fig. 2. The friction tester consisted of a main frame, a load cell and frame, an actuator of the horizontal load, and a loading controller with data storage. Blocks were laid on the surface of the main frame and a horizontal force with a loading rate of 20 mm/min was applied. This tester loading capability was a maximum of 1.96 kN (the weight of 200 kg). The displacement control range is 0–400 mm.
W. Lin et al. / Construction and Building Materials 118 (2016) 245–255
The size of the blocks used in the lab test was the same as for the rigid body analysis (92 mm 46 mm 36 mm). The test specimens were made of gypsum DIASTONE MR-150 with a water/ cement ratio of 0.22, and the average weight of one specimen was 280 g. The relationship between applying force and displacement could be recorded automatically by a control PC. A video camera was setup upon the whole pattern to monitor the displacement pathway by real time. The sides were unconstrained. 3. Results analysis 3.1. Displacement vector field To compare and analyze the results of the friction experiment and rigid body analysis, the displacement vector field was used. A displacement vector expresses the position of a final point in space in terms of a displacement from an initial point. Assuming an object A is located at point P at time t1, after the force was applied, the location of A has changed from point P to Q at time t2. On the basis of reference point O, the location vectors of P (x1, !
!
y1) and Q (x2, y2) can be expressed as r 1 and r2 . Here, the displace!
r. The movement between ment vector PQ from location P to Q is D~ two points can be represented using Eq. (1) as follows.
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jD~ rj ¼ Dr ¼ ðx2 x1 Þ2 þ ðy2 y1 Þ2
249
ð1Þ
Fig. 3 shows the displacement comparison results between rigid body analysis and lab experiment video image for the case of rectangular block in herringbone pattern with center loading. The rigid body analysis and lab experiment video image were matched well for displacements up to 50 mm. Figs. 4–6 show the results of the displacement vector field for different combinations of block shapes, laying patterns, and loading conditions. Overall, the rigid body analysis results were wellmatched with the lab test results, which indicated that the method used in the study can be used as a suitable analysis tool for predicting and understanding the horizontal interlocking behavior of pavement blocks.
3.2. Specific D-Moment concept The concept of Dynamic Displacement Moment (D-Moment) was applied to explain the behavior of the individual blocks and whole pattern by horizontal loading, The D-Moment concept was first introduced by Phuong et al. [11] and started from the application of the force-moment concept. A moment is represented by the product of force and the distance to the specific point, thereby
Fig. 6. Individual block displacement vectors with herringbone pattern for different block shapes under corner and center loading: (1) Rectangular block; (2) Uni-block; (3) Dasuri block.
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expressing the rotational force of objects. However, instead of using a single force and a displacement at a fixed point, the DMoment was computed by the local displacement and the moving position of each block as showed in Eq. (2). D-Moment can express load-displacement behavior of an individual block over time. Then the load-displacement behavior of the overall pattern can be expressed by the sum of individual blocks’ displacement. However, since D-Moment is calculated based on the behavior of individual blocks, the block’s rotation and movement should occur simultaneously. That is, when a block is rotated without movement or when a block is moved without rotation, D-Moment is calculated as ‘‘0”, which cannot explain the behavior.
D-Moment ¼
n X
jRi di j
ð2Þ
i¼1
where Ri : displacement from the original position to a temporary position (mm) di : vertical distance from the loading position to the motion extensive line of block central point (mm). The load-displacement relationships for the various block shapes and laying patterns for each loading condition are shown in Fig. 7. The legend used in the figures is shown in the order of block shape, laying pattern, and loading condition. R, U, and D represent the rectangular block, Uni block, and Dasuri block, respectively, while S, B, and H in the middle position represent stretcher, basket-weave, and herringbone, respectively. S and C in the last position represent the side and center loading locations, respectively. The difference in the maximum loading according to the combination of block shape and laying pattern is clearly
(a)
(b) Fig. 7. Relationship between horizontal force and displacement: (a) Corner loading condition; (b) Center loading condition.
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(a)
(b) Fig. 8. Relationship between SDM and shape factor (a) Corner loading condition; (b) Center loading condition.
revealed. Overall, the horizontal displacement resistance of the Dasuri block was the largest followed by those of the Uni block and rectangular block, regardless of loading conditions. With regard to the patterns, the herringbone showed the best performance. The changes in applied load with displacements showed that horizontal loading was reduced after a certain displacement, implying that the interlocking effect is weakened since the block structure becomes unstable. Overall, the experiment result showed that the displacement where the block structure became unstable was 20 mm or longer, despite a number of differences depending on conditions. Based on the above results, an arbitrary DMoment was calculated at a location of 20 mm displacement and this was defined as the specific D-Moment (SDM), which was investigated according to block shapes and laying patterns. The relationship between shape factor (area ratio) and SDM was analyzed with respect to the stretcher bond pattern only, which is shown in Fig. 8. Fig. 8(a) shows the relationship between SDM and the shape factor (area ratio) when loading was applied at the
corner. It also shows a high coefficient of determination as 0.76. Fig. 8(b) shows the relationship between SDM and the shape factor when loading was applied at the center and the square of its correlation coefficient is 0.68. The SDM values were changed by different loading conditions within the shape factor range of 2.4–2.7. For the corner loading, the range of SDM is 0.01–0.05. However, when loading was applied at the center, the range of the SDM value became 0.02–0.08. Comparison results for the SDMs with the two loading applications are shown in Fig. 9. The maximum value of SDM with respect to the application patterns showed that the herringbone bond (or pattern) had the highest SDM followed by the stretcher bond and basket-weave bond. This result also indicated that the herringbone bond should be used to increase the horizontal interlocking effect between blocks. For the stretcher bond, the SDM in the keystone block (block E, Table 2) was the highest while the SDM of the Dasuri block (block D) was the highest with the other patterns. That is, the horizontal interlocking effect was good when a
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(a)
(b) Fig. 9. SDM for block shapes at the 20 mm displacement location by block pattern. (a) Corner loading condition; (b) Center loading condition.
keystone block (block E) was used with the stretcher bond, while the Dasuri block (block D) was desirable when the basket-weave and herringbone patterns were used. In summary, an optimal pattern can be theoretically determined for various block shapes prior to block installation if the SDM is calculated using the rigid body analysis method.
4. Horizontal shifting prediction model of concrete block pavement To create a horizontal shifting prediction model for concrete block pavement, a regression analysis was conducted using the performance data presented in previous literature. Fig. 10 shows the re-created results based on traffic performance data by Mampearachchi and Senadeera [6]. Three types of blocks were applied at traffic sites and horizontal movement was measured at 10 joints located at a wheel pass. The mean measured value was used to calculate the horizontal shifting of block types according to traffic vol-
ume. Two loading application methods were used in the lab experiments and a 3D rigid body analysis process was used. However, to evaluate the horizontal shifting prediction model for concrete block pavement, SDM values calculated by the center loading condition were used in order to minimize the rotational effect occurring during loading application. The horizontal shifting behavior showed that there were no significant differences between the SDMs with traffic volumes up to 13,000 vehicles. However, for greater cumulative volumes, the absolute horizontal displacement decreased as the SDM values increased. The horizontal shifting model of concrete block pavements versus cumulative traffic volume can be expressed by Eq. (3), via a power function. Since blocks cannot accumulate behaviors simply due to movement in the right and left directions under the applied traffic loading, absolute values should be used to evaluate the behavior in order to display the characteristics with regard to cumulative traffic volumes.
Vabs ¼ a Nb
ð3Þ
W. Lin et al. / Construction and Building Materials 118 (2016) 245–255
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Fig. 10. Horizontal shifting behavior versus cumulative traffic volume [6].
Table 4 Horizontal shifting model coefficient based on performance data. SDM
a
b
0 0.05 0.06
0.09 0.11 0.19
0.36 0.34 0.27
where, Vabs : absolute value of horizontal behavior (mm) N: traffic volume (veh/day) A, b: model coefficients Since not enough performance data on the horizontal shifting of concrete pavement pavements was available, derivations of model coefficients from regression analysis have been quite limited. Using the limited performance data, regression coefficients were obtained as shown in Table 4, in which the a and b coefficients are the regression coefficients of the real horizontal shifting results measured by Mampearachchi and Senadeera [6]. Using the regression coefficients, a horizontal shifting estimation equation related to cumulative traffic volume and SDM was created. To determine the coefficients a and b for each SDM, four cases (Cases 1–4) were divided and a regression analysis was conducted for the four cases. In Case 1, a linear regression analysis was performed using the a and b coefficient values shown in Table 4; in Cases 2 and 3, a regression analysis was conducted using exponential functions (unlike Case 1). Finally, in Case 4, a linear regression analysis was used for coefficient a, and for coefficient b an exponential function analysis was used. SDM was calculated by applying the shape factor calculated for a block type that is used on construction sites to the regression equation presented in Fig. 8 (b). The measured performance data were compared with the model calculation results, which are shown in Fig. 11. The relationships between SDM and the coefficients a and b derived from each case in the horizontal shifting prediction model are summarized in Table 5. To derive results that were closest to the performance data, the root-mean-square deviation (RMSD) was calculated and compared for different cases. The results show that Case 1 had the lowest error whereas Case 2 had the highest error.
In this study, it was found that the model coefficient determination should be analyzed via regressions based on the RMSD calculation results, and the horizontal shifting prediction model of concrete block pavement can be modified from Eq. (3) to Eq. (4). But this model should be applied only when an SDM value is within the range of 0–0.07. To minimize the effect of rotational behavior, SDM values calculated under the center loading condition were used in a regression analysis to determine the model coefficients a and b.
Vabs ¼ ð0:08 þ 1:26 SDMÞ Nð0:371:15SDMÞ
ð4Þ
where Vabs : absolute value of horizontal shifting (mm) N: traffic volume (veh/day) SDM: Specific D-moment (mm mm) To validate the horizontal shifting model of the concrete block pavement mentioned above, conditions under various patterns with rectangular, Uni, and Dasuri blocks, which are the most widely used blocks, were applied to this model. Fig. 12 shows the horizontal shifting results versus the cumulative traffic volume and patterns. The stretcher bond and basket-weave bonds with rectangular and Uni blocks were found to be the worst at resisting the horizontal displacement, while the herringbone bond in rectangular blocks was found to be the least vulnerable bond to horizontal displacement resistance followed by the basket-weave bond in Dasuri blocks, stretcher bond in Dasuri blocks, and herringbone bond in Uni blocks. The horizontal interlocking effect was increased as the value of the shape factor increased. For block patterns, the herringbone bond was the most stable condition, followed by the basketweave bond and the stretcher bond. Based on the analysis results, the design of the block pavement surface course should not simply consider the block shape or laying pattern only. Therefore, it is reasonably accepted that, for the design of the concrete block pavement surface course, horizontal shifting should be calculated using the SDM value, which represents the overall shapes and patterns. Fig. 13 shows the horizontal shifting results for the observed SDM values and cumulative traffic volumes. As shown in the figure, with the SDM increased, the resistance of horizontal shifting
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Case 1
Case 2
Case 3
Case 4
Fig. 11. Comparison between results of performance measurements and calculations using the model.
Table 5 Regression equations of coefficients for horizontal shifting model and RMSD.
Case Case Case Case
1 2 3 4
Regression equation of coefficient a
Regression equation of coefficient b
RMSD
a = 0.08 + 1.26SDM a = 0.09 + 6.4e6 exp(150.92SDM) a = 0.08 exp(12.12SDM) a = 0.08 + 1.26SDM
b = 0.37–1.15SDM b = 0.385 0.008 exp(40.681SDM) b = 0.385 0.008 exp(40.681SDM) b = 0.385 0.008 exp(40.681SDM)
0.72 1.32 0.95 0.80
against traffic volume improved. Constructability varies depending on block patterns and shapes. For example, irregular shaped blocks can require more cutting at the pavement finishing job than other simple shaped blocks. Thus, if simple shaped blocks are installed according to some specific patterns, high performance and easy construction can be achieved simultaneously.
5. Conclusion This study investigated performance estimation models with regard to horizontal displacement for the main types of damage to block pavement. Various combinations of block shapes and construction patterns were evaluated through a finite element analysis and lab experiments. In the experiments in the laboratory, the relationship between force and displacement was recorded for various block shapes and construction patterns via a photogrammetric method using a friction tester, and the recorded images were quan-
tified and compared with the rigid body analysis results. The comparison of the results obtained from theory and experiment showed that both trends and sizes were matched, which enabled the development of a horizontal behavior analysis model for blocks based on block shapes and laying patterns. To express the movements of a block over time, displacement vectors were employed using location information from the start and finish points of individual blocks. The SDM concept was proposed to explain the relationships between the individual movements and overall pattern movements of a block. Since a regression equation between the SDM and shape factor was derived, horizontal interlocking performance can be predicted even if a new block shape appears. The horizontal shifting prediction model of concrete block pavement was analyzed using a regression analysis with performance data previously presented. By applying the developed horizontal shifting prediction model, the results showed that as the SDM value increased, the cumulative horizontal shifting values
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Absolute horizontal displacement (mm)
10 R-S R-B R-H U-S U-B U-H D-S D-B D-H
8
6
4
2
0 0
50x103
100x103
150x103
200x103
250x103
300x103
Vehicle passes Fig. 12. Horizontal shifting behavior versus cumulative traffic volume by different surface structure.
Fig. 13. Horizontal shifting behavior versus cumulative traffic volume by SDM.
decreased. The results also showed that as the shape factor value increased, the horizontal interlocking effect also increased. Regarding laying patterns, the herringbone bond showed the best performance, followed by the basket-weave and stretcher bonds. Acknowledgment This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2014R1A2A2A01007697). References [1] B. Shackel, D.O.O. Lim, Mechanism of block interlock, in: Proc. 7th Int. Conf. on Concrete Block Paving, 2003. Sun City, South Africa. [2] K. Yasuhisa, Y. Ando, S. Omoto, K. Yaginuma, K. Toriiminami, Study on block shifting of interlocking block pavement, in: Proc. 8th Int. Conf. on Concrete Block Paving, 2006, pp. 447–456. San Francisco, CA, USA. [3] D. Ascher, T. Lerch, M. Oeser, F. Wellner, 3D-FEM simulation of concrete block pavements, in: Proc. 8th Int. Conf. on Concrete Block Paving, 2006, pp. 457– 465. San Francisco, CA, USA.
[4] J. Knapton, Concrete block pavement design in the UK, in: Proc. 2nd Int. Conf. on Concrete Block Paving, 1984, pp. 129–138. Delft/April. [5] H. Yaginuma, M. Tanaka, A. Kasahara, S. Yazawa, Development of a standard for block dimensions for use under Japanese conditions, in: Proceedings of the 7th Int. Conf. on Concrete Block Paving, 2003. Sun City, South Africa, ISBN Number: 0-958-46091-4. [6] W.K. Mampearachchi, A. Senadeera, Determination of the most effective cement concrete block laying pattern and shape for road pavement based on field performance, J. Mater. Civil. Eng. (ASCE) 26 (2) (2014). [7] B.C. Panda, A.K. Ghosh, Structural behavior of concrete block paving. II: concrete blocks, J. Transp. Eng. (ASCE) 128 (2) (2002). [8] M.N. Soutsos, K.K. Tang, H.A. Khalid, S.G. Millard, The effect of construction pattern and unit interlock on the structural behaviour of block pavements, Constr. Build. Mater. 25 (2011) 3832–3840. [9] ABAQUS Inc, ABAQUS/CAE User’s Manual, Version 6.10, 2006. [10] N.P. Phuong, Evaluation method for interlocking efficiency by laying pattern of concrete block pavement (Master Thesis), Chung-Ang University, Seoul, Korea, 2012. [11] N.P. Phuong, W.G. Lin, D.G. Park, H.W. Kim, Y.H. Cho, Evaluation methodology for laying pattern of interlocking concrete block pavements using a displacement-moment concept, J. Transp. Eng. (ASCE) 140 (2) (2013) 04013008.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Development of a horizontal shifting mechanistic-empirical prediction model for concrete block pavement Wuguang Lin a, SungWoo Ryu b,⇑, Han Hao a, Yoon-Ho Cho c a
College of Transport and Communications, Shanghai Maritime Univ., 1550 Haigang Ave., Shanghai, PR China Korea Expressway Corporation Research Institute, 208-96, Dongbu-daero 922beon-gil, Dongtan-myeon, Hwaseong-si, Gyeonggi-do, Republic of Korea c Dept. of Civil and Environmental Engineering, Chung-Ang Univ., 84 Heukseok-Ro, Dongjak-Gu, Seoul, Republic of Korea b
h i g h l i g h t s A horizontal shifting prediction model for concrete block pavements was developed considering block shapes and laying patterns. The SDM concept was proposed to explain the relationships between the individual movements and overall pattern movements of a block. The cumulative horizontal shifting values decreased as the SDM value increased. The results also showed that the horizontal interlocking effect also
increased as the shape factor value increased.
a r t i c l e
i n f o
Article history: Received 2 December 2015 Received in revised form 13 April 2016 Accepted 26 April 2016 Available online 14 May 2016 Keywords: Concrete block pavement Horizontal shifting Mechanistic-empirical prediction model Block shapes Construction patterns
a b s t r a c t Few studies have been conducted on horizontal shifting prediction models that consider block shapes and laying patterns for block pavements. To develop a prediction model, a combination of different block shapes and laying patterns was evaluated by computer modeling and laboratory tests. The relationship between the force and displacement was recorded via a photogrammetric method using a friction tester. In order to quantify the recorded video results, rigid body analysis was performed. The results of laboratory experiments and the rigid body analysis offered a good match. A displacement vector was used to express the movement of the block with time, according to the start and end position information of each block. Also, a concept of Specific D-Moment (SDM) was proposed to describe the relationship between the movement of the individual blocks and the entire movement. A horizontal shifting mechanisticempirical prediction model of concrete block pavement is proposed based on regression analysis of the existing performance data. According to the prediction model, higher SDM values give lower cumulative amounts of horizontal shifting due to traffic. Ó 2016 Published by Elsevier Ltd.
1. Introduction The surface of a block pavement is different from that of typical pavements. It is built by using individual blocks, with different laying patterns, to form a discrete surface layer. Thus, blocks act with joint sand as structural surfacing rather than merely providing a wearing course [1]. The main distress of block pavement can be divided into horizontal shifting, breakage of blocks, faulting, and rutting. Yasuhisa et al. [2] evaluated the condition of 48 block pavements applied on roads and reported that the ratio of horizontal shifting distress occurrence was as high as 52%. Damage to block pavement (horizontal and vertical displacements) can ⇑ Corresponding author. E-mail addresses: [email protected] (W. Lin), [email protected] (S. Ryu), [email protected] (H. Hao), [email protected] (Y.-H. Cho). http://dx.doi.org/10.1016/j.conbuildmat.2016.04.124 0950-0618/Ó 2016 Published by Elsevier Ltd.
frequently be observed. They are mainly the result of poor quality construction and overloading of the block pavement. Hence, the concrete industry is attempting to improve the performance of block pavement by minimizing displacement by, for example, developing advanced block forms. New block shapes with horizontally interlocking features are intended to ensure the increased bearing capacity and deformation resistance of block pavements [3]. To determine the reason for the damage caused by horizontal torsion, Knapton [4] divided block interaction into three types: rotational, vertical, and horizontal. A block’s rotation is constrained by the curb installed at the end of pavement. Vertical interlocking occurs due to the joint sealing compound in the joint. Horizontal interlocking varies depending on the block shape and laying pattern. The surface of the block pavement consists of a discontinuous layer that is resistant to external loads via the interlocking, which
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Table 1 Experimental variables to evaluate horizontal shifting characteristics of concrete block pavement. A (Rec.)
Stretcher Basket weave Herringbone
Center Corner Center Corner Center Corner
p p p p p p
B (Foot.) p p
C (Uni) p p p p p p
D (Das.) p p p p p p
Table 3 Material properties for the rigid body analysis model. Category
Material property
E (Key.) p p
Block Steel plate
Modulus (Pa)
Poisson’s ratio
Friction coefficient
3.1E09 2.0E11
0.15 0.25
0.60 0.45
1. Video camera 2. Tripod 3. Main frame 1
4. Load cell 5. Load frame 6. Control PC
2
6
Table 2 Shape factors calculation results for different block shapes used in the study.
Surface area mm2 Side area mm2 L mm h mm Shape factora a
A (Rec.)
B (Foot.)
C (Uni)
D (Das.)
E (Key.)
4232 9936 276 36 2.34
2899 6204 172 36 2.41
4321 10,692 297 36 2.53
4041 10,620 295 36 2.62
3676 9396 261 36 2.56
4
3 5
Shape factor = side area/surface area.
Fig. 2. Friction test equipment.
is why horizontal torsion can be a function of block shape and the laying pattern. Shackel and Lim [1] demonstrated that a shaped block had better interlocking action than a rectangular block with respect to horizontal interlocking between blocks. And they reported that the herringbone pattern can distribute loads efficiently. Yaginuma et al. [5] generalized block shapes by considering the ratio of the total side area to the top area, in order to identify the appropriate sizes of blocks for use in roads. They claimed that as the area ratio increased, the load transfer efficiency between blocks also increased. Horizontal interlocking is primarily
achieved through the use of laying patterns that disperse the forces from braking, turning, and accelerating vehicles [6]. However, based on previous studies by Panda and Ghosh [7] and Soutsos et al. [8], a laying pattern has little effect on the performance of block pavement. Ascher et al. [3] stated that the horizontal shifting of block pavement was a function of joint width. Upon reviewing previous research on the horizontal shifting of block pavement, it was found that few studies were conducted on
Fig. 1. Loading condition and boundary condition of the rigid body analysis model.
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horizontal shifting prediction models that consider the block shape and laying pattern. Moreover, contradictory study results were reported. In this study, after developing a horizontal shifting mechanistic-empirical prediction model of block pavement using existing performance data, a combination of different block shapes and laying patterns was evaluated by computer modeling and laboratory tests.
2. Research program 2.1. Factorial design
Fig. 3. (a) Rigid body analysis result vs. (b) laboratory test result (case of rectangular – herringbone).
Investigations of horizontal interlocking behavior of block pavements were conducted by lab experiment and rigid body analysis. The variables of block shape, laying pattern, and loading location are summarized in Table 1. The lab experiment was conducted by using a friction tester for different block shapes. Rectangular, Uni, and Dasuri block were used for different shapes, while the stretcher, basket-weave, and herringbone were used as laying pattern. In the rigid body analysis, a footprint and keystone block with a stretcher pattern were added. Dimension of blocks used in the study are shown in Table 2. To generalize the block dimensions,
(a) Corner loading condition
(b) Center loading condition Fig. 4. Individual block displacement vectors with the stretcher pattern, for different block shapes under corner and center loading (1) Rectangular block; (2) Uni-block; (3) Dasuri block.
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(a) Corner loading condition
(b) Center loading condition Fig. 5. Individual block displacement vectors with basket-wave pattern, for different block shapes under corner and center loading (1) Rectangular block; (2) Uni-block; (3) Dasuri block.
a shape factor proposed by Yaginuma et al. [5] was used. The shape factor is the area ratio of the total side area to the surface area and the range in this study was set at 2.3–2.6. 2.2. Rigid body analysis ABAQUS 6.10 [9] was used to conduct the rigid body analysis for evaluating the horizontal interlocking behavior of block pavement. 3D solid elements were used in the analysis model. The real size of blocks is usually too heavy and large to be tested in a laboratory, so it is difficult to handle the dynamic effects of block movement. Therefore, the sizes of the blocks used in the study were smaller than those of real blocks. The typical dimension of a block used in Korea is 200 mm 100 mm 80 mm. The dimension of block used in this study is 92 mm 46 mm 36 mm. Thirty-six blocks were arranged in a fixed steel plate (368 mm 736 mm) with various patterns. The loading condition of the model is shown in Fig. 1 (a). Corner and center loadings were applied to investigate the effect of rotation and horizontal movement of the block pavement. The aim of the corner loading was to investigate the horizontal interlocking between blocks when rotation and horizontal movement occurred simultaneously, while the center loading was to evaluate the horizontal interlocking effect when the rotation was minimized. The side of the whole pattern was setup as a free con-
dition. The boundary condition of the model was setup as shown in Fig. 1(b). The steel plate supporting the blocks was fixed in all directions. A general contact was applied between the elements. And also, the contact was considered for the interface between blocks and a steel plate. The maximum displacement of the directly loading block was set at 50 mm. In addition, material properties, including the friction coefficients, are presented in Table 3. The values suggested by Phuong [10] were used for the friction coefficients between blocks, and between the blocks and the steel plate. To evaluate the loaddisplacement behavior of individual blocks as well as the overall pavement, meshes in each block were set differently depending on the block shape. 2.3. Laboratory experiments The lab experiment setup for evaluating the laying pattern is shown in Fig. 2. The friction tester consisted of a main frame, a load cell and frame, an actuator of the horizontal load, and a loading controller with data storage. Blocks were laid on the surface of the main frame and a horizontal force with a loading rate of 20 mm/min was applied. This tester loading capability was a maximum of 1.96 kN (the weight of 200 kg). The displacement control range is 0–400 mm.
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The size of the blocks used in the lab test was the same as for the rigid body analysis (92 mm 46 mm 36 mm). The test specimens were made of gypsum DIASTONE MR-150 with a water/ cement ratio of 0.22, and the average weight of one specimen was 280 g. The relationship between applying force and displacement could be recorded automatically by a control PC. A video camera was setup upon the whole pattern to monitor the displacement pathway by real time. The sides were unconstrained. 3. Results analysis 3.1. Displacement vector field To compare and analyze the results of the friction experiment and rigid body analysis, the displacement vector field was used. A displacement vector expresses the position of a final point in space in terms of a displacement from an initial point. Assuming an object A is located at point P at time t1, after the force was applied, the location of A has changed from point P to Q at time t2. On the basis of reference point O, the location vectors of P (x1, !
!
y1) and Q (x2, y2) can be expressed as r 1 and r2 . Here, the displace!
r. The movement between ment vector PQ from location P to Q is D~ two points can be represented using Eq. (1) as follows.
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jD~ rj ¼ Dr ¼ ðx2 x1 Þ2 þ ðy2 y1 Þ2
249
ð1Þ
Fig. 3 shows the displacement comparison results between rigid body analysis and lab experiment video image for the case of rectangular block in herringbone pattern with center loading. The rigid body analysis and lab experiment video image were matched well for displacements up to 50 mm. Figs. 4–6 show the results of the displacement vector field for different combinations of block shapes, laying patterns, and loading conditions. Overall, the rigid body analysis results were wellmatched with the lab test results, which indicated that the method used in the study can be used as a suitable analysis tool for predicting and understanding the horizontal interlocking behavior of pavement blocks.
3.2. Specific D-Moment concept The concept of Dynamic Displacement Moment (D-Moment) was applied to explain the behavior of the individual blocks and whole pattern by horizontal loading, The D-Moment concept was first introduced by Phuong et al. [11] and started from the application of the force-moment concept. A moment is represented by the product of force and the distance to the specific point, thereby
Fig. 6. Individual block displacement vectors with herringbone pattern for different block shapes under corner and center loading: (1) Rectangular block; (2) Uni-block; (3) Dasuri block.
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expressing the rotational force of objects. However, instead of using a single force and a displacement at a fixed point, the DMoment was computed by the local displacement and the moving position of each block as showed in Eq. (2). D-Moment can express load-displacement behavior of an individual block over time. Then the load-displacement behavior of the overall pattern can be expressed by the sum of individual blocks’ displacement. However, since D-Moment is calculated based on the behavior of individual blocks, the block’s rotation and movement should occur simultaneously. That is, when a block is rotated without movement or when a block is moved without rotation, D-Moment is calculated as ‘‘0”, which cannot explain the behavior.
D-Moment ¼
n X
jRi di j
ð2Þ
i¼1
where Ri : displacement from the original position to a temporary position (mm) di : vertical distance from the loading position to the motion extensive line of block central point (mm). The load-displacement relationships for the various block shapes and laying patterns for each loading condition are shown in Fig. 7. The legend used in the figures is shown in the order of block shape, laying pattern, and loading condition. R, U, and D represent the rectangular block, Uni block, and Dasuri block, respectively, while S, B, and H in the middle position represent stretcher, basket-weave, and herringbone, respectively. S and C in the last position represent the side and center loading locations, respectively. The difference in the maximum loading according to the combination of block shape and laying pattern is clearly
(a)
(b) Fig. 7. Relationship between horizontal force and displacement: (a) Corner loading condition; (b) Center loading condition.
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(a)
(b) Fig. 8. Relationship between SDM and shape factor (a) Corner loading condition; (b) Center loading condition.
revealed. Overall, the horizontal displacement resistance of the Dasuri block was the largest followed by those of the Uni block and rectangular block, regardless of loading conditions. With regard to the patterns, the herringbone showed the best performance. The changes in applied load with displacements showed that horizontal loading was reduced after a certain displacement, implying that the interlocking effect is weakened since the block structure becomes unstable. Overall, the experiment result showed that the displacement where the block structure became unstable was 20 mm or longer, despite a number of differences depending on conditions. Based on the above results, an arbitrary DMoment was calculated at a location of 20 mm displacement and this was defined as the specific D-Moment (SDM), which was investigated according to block shapes and laying patterns. The relationship between shape factor (area ratio) and SDM was analyzed with respect to the stretcher bond pattern only, which is shown in Fig. 8. Fig. 8(a) shows the relationship between SDM and the shape factor (area ratio) when loading was applied at the
corner. It also shows a high coefficient of determination as 0.76. Fig. 8(b) shows the relationship between SDM and the shape factor when loading was applied at the center and the square of its correlation coefficient is 0.68. The SDM values were changed by different loading conditions within the shape factor range of 2.4–2.7. For the corner loading, the range of SDM is 0.01–0.05. However, when loading was applied at the center, the range of the SDM value became 0.02–0.08. Comparison results for the SDMs with the two loading applications are shown in Fig. 9. The maximum value of SDM with respect to the application patterns showed that the herringbone bond (or pattern) had the highest SDM followed by the stretcher bond and basket-weave bond. This result also indicated that the herringbone bond should be used to increase the horizontal interlocking effect between blocks. For the stretcher bond, the SDM in the keystone block (block E, Table 2) was the highest while the SDM of the Dasuri block (block D) was the highest with the other patterns. That is, the horizontal interlocking effect was good when a
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(a)
(b) Fig. 9. SDM for block shapes at the 20 mm displacement location by block pattern. (a) Corner loading condition; (b) Center loading condition.
keystone block (block E) was used with the stretcher bond, while the Dasuri block (block D) was desirable when the basket-weave and herringbone patterns were used. In summary, an optimal pattern can be theoretically determined for various block shapes prior to block installation if the SDM is calculated using the rigid body analysis method.
4. Horizontal shifting prediction model of concrete block pavement To create a horizontal shifting prediction model for concrete block pavement, a regression analysis was conducted using the performance data presented in previous literature. Fig. 10 shows the re-created results based on traffic performance data by Mampearachchi and Senadeera [6]. Three types of blocks were applied at traffic sites and horizontal movement was measured at 10 joints located at a wheel pass. The mean measured value was used to calculate the horizontal shifting of block types according to traffic vol-
ume. Two loading application methods were used in the lab experiments and a 3D rigid body analysis process was used. However, to evaluate the horizontal shifting prediction model for concrete block pavement, SDM values calculated by the center loading condition were used in order to minimize the rotational effect occurring during loading application. The horizontal shifting behavior showed that there were no significant differences between the SDMs with traffic volumes up to 13,000 vehicles. However, for greater cumulative volumes, the absolute horizontal displacement decreased as the SDM values increased. The horizontal shifting model of concrete block pavements versus cumulative traffic volume can be expressed by Eq. (3), via a power function. Since blocks cannot accumulate behaviors simply due to movement in the right and left directions under the applied traffic loading, absolute values should be used to evaluate the behavior in order to display the characteristics with regard to cumulative traffic volumes.
Vabs ¼ a Nb
ð3Þ
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Fig. 10. Horizontal shifting behavior versus cumulative traffic volume [6].
Table 4 Horizontal shifting model coefficient based on performance data. SDM
a
b
0 0.05 0.06
0.09 0.11 0.19
0.36 0.34 0.27
where, Vabs : absolute value of horizontal behavior (mm) N: traffic volume (veh/day) A, b: model coefficients Since not enough performance data on the horizontal shifting of concrete pavement pavements was available, derivations of model coefficients from regression analysis have been quite limited. Using the limited performance data, regression coefficients were obtained as shown in Table 4, in which the a and b coefficients are the regression coefficients of the real horizontal shifting results measured by Mampearachchi and Senadeera [6]. Using the regression coefficients, a horizontal shifting estimation equation related to cumulative traffic volume and SDM was created. To determine the coefficients a and b for each SDM, four cases (Cases 1–4) were divided and a regression analysis was conducted for the four cases. In Case 1, a linear regression analysis was performed using the a and b coefficient values shown in Table 4; in Cases 2 and 3, a regression analysis was conducted using exponential functions (unlike Case 1). Finally, in Case 4, a linear regression analysis was used for coefficient a, and for coefficient b an exponential function analysis was used. SDM was calculated by applying the shape factor calculated for a block type that is used on construction sites to the regression equation presented in Fig. 8 (b). The measured performance data were compared with the model calculation results, which are shown in Fig. 11. The relationships between SDM and the coefficients a and b derived from each case in the horizontal shifting prediction model are summarized in Table 5. To derive results that were closest to the performance data, the root-mean-square deviation (RMSD) was calculated and compared for different cases. The results show that Case 1 had the lowest error whereas Case 2 had the highest error.
In this study, it was found that the model coefficient determination should be analyzed via regressions based on the RMSD calculation results, and the horizontal shifting prediction model of concrete block pavement can be modified from Eq. (3) to Eq. (4). But this model should be applied only when an SDM value is within the range of 0–0.07. To minimize the effect of rotational behavior, SDM values calculated under the center loading condition were used in a regression analysis to determine the model coefficients a and b.
Vabs ¼ ð0:08 þ 1:26 SDMÞ Nð0:371:15SDMÞ
ð4Þ
where Vabs : absolute value of horizontal shifting (mm) N: traffic volume (veh/day) SDM: Specific D-moment (mm mm) To validate the horizontal shifting model of the concrete block pavement mentioned above, conditions under various patterns with rectangular, Uni, and Dasuri blocks, which are the most widely used blocks, were applied to this model. Fig. 12 shows the horizontal shifting results versus the cumulative traffic volume and patterns. The stretcher bond and basket-weave bonds with rectangular and Uni blocks were found to be the worst at resisting the horizontal displacement, while the herringbone bond in rectangular blocks was found to be the least vulnerable bond to horizontal displacement resistance followed by the basket-weave bond in Dasuri blocks, stretcher bond in Dasuri blocks, and herringbone bond in Uni blocks. The horizontal interlocking effect was increased as the value of the shape factor increased. For block patterns, the herringbone bond was the most stable condition, followed by the basketweave bond and the stretcher bond. Based on the analysis results, the design of the block pavement surface course should not simply consider the block shape or laying pattern only. Therefore, it is reasonably accepted that, for the design of the concrete block pavement surface course, horizontal shifting should be calculated using the SDM value, which represents the overall shapes and patterns. Fig. 13 shows the horizontal shifting results for the observed SDM values and cumulative traffic volumes. As shown in the figure, with the SDM increased, the resistance of horizontal shifting
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Case 1
Case 2
Case 3
Case 4
Fig. 11. Comparison between results of performance measurements and calculations using the model.
Table 5 Regression equations of coefficients for horizontal shifting model and RMSD.
Case Case Case Case
1 2 3 4
Regression equation of coefficient a
Regression equation of coefficient b
RMSD
a = 0.08 + 1.26SDM a = 0.09 + 6.4e6 exp(150.92SDM) a = 0.08 exp(12.12SDM) a = 0.08 + 1.26SDM
b = 0.37–1.15SDM b = 0.385 0.008 exp(40.681SDM) b = 0.385 0.008 exp(40.681SDM) b = 0.385 0.008 exp(40.681SDM)
0.72 1.32 0.95 0.80
against traffic volume improved. Constructability varies depending on block patterns and shapes. For example, irregular shaped blocks can require more cutting at the pavement finishing job than other simple shaped blocks. Thus, if simple shaped blocks are installed according to some specific patterns, high performance and easy construction can be achieved simultaneously.
5. Conclusion This study investigated performance estimation models with regard to horizontal displacement for the main types of damage to block pavement. Various combinations of block shapes and construction patterns were evaluated through a finite element analysis and lab experiments. In the experiments in the laboratory, the relationship between force and displacement was recorded for various block shapes and construction patterns via a photogrammetric method using a friction tester, and the recorded images were quan-
tified and compared with the rigid body analysis results. The comparison of the results obtained from theory and experiment showed that both trends and sizes were matched, which enabled the development of a horizontal behavior analysis model for blocks based on block shapes and laying patterns. To express the movements of a block over time, displacement vectors were employed using location information from the start and finish points of individual blocks. The SDM concept was proposed to explain the relationships between the individual movements and overall pattern movements of a block. Since a regression equation between the SDM and shape factor was derived, horizontal interlocking performance can be predicted even if a new block shape appears. The horizontal shifting prediction model of concrete block pavement was analyzed using a regression analysis with performance data previously presented. By applying the developed horizontal shifting prediction model, the results showed that as the SDM value increased, the cumulative horizontal shifting values
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Absolute horizontal displacement (mm)
10 R-S R-B R-H U-S U-B U-H D-S D-B D-H
8
6
4
2
0 0
50x103
100x103
150x103
200x103
250x103
300x103
Vehicle passes Fig. 12. Horizontal shifting behavior versus cumulative traffic volume by different surface structure.
Fig. 13. Horizontal shifting behavior versus cumulative traffic volume by SDM.
decreased. The results also showed that as the shape factor value increased, the horizontal interlocking effect also increased. Regarding laying patterns, the herringbone bond showed the best performance, followed by the basket-weave and stretcher bonds. Acknowledgment This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2014R1A2A2A01007697). References [1] B. Shackel, D.O.O. Lim, Mechanism of block interlock, in: Proc. 7th Int. Conf. on Concrete Block Paving, 2003. Sun City, South Africa. [2] K. Yasuhisa, Y. Ando, S. Omoto, K. Yaginuma, K. Toriiminami, Study on block shifting of interlocking block pavement, in: Proc. 8th Int. Conf. on Concrete Block Paving, 2006, pp. 447–456. San Francisco, CA, USA. [3] D. Ascher, T. Lerch, M. Oeser, F. Wellner, 3D-FEM simulation of concrete block pavements, in: Proc. 8th Int. Conf. on Concrete Block Paving, 2006, pp. 457– 465. San Francisco, CA, USA.
[4] J. Knapton, Concrete block pavement design in the UK, in: Proc. 2nd Int. Conf. on Concrete Block Paving, 1984, pp. 129–138. Delft/April. [5] H. Yaginuma, M. Tanaka, A. Kasahara, S. Yazawa, Development of a standard for block dimensions for use under Japanese conditions, in: Proceedings of the 7th Int. Conf. on Concrete Block Paving, 2003. Sun City, South Africa, ISBN Number: 0-958-46091-4. [6] W.K. Mampearachchi, A. Senadeera, Determination of the most effective cement concrete block laying pattern and shape for road pavement based on field performance, J. Mater. Civil. Eng. (ASCE) 26 (2) (2014). [7] B.C. Panda, A.K. Ghosh, Structural behavior of concrete block paving. II: concrete blocks, J. Transp. Eng. (ASCE) 128 (2) (2002). [8] M.N. Soutsos, K.K. Tang, H.A. Khalid, S.G. Millard, The effect of construction pattern and unit interlock on the structural behaviour of block pavements, Constr. Build. Mater. 25 (2011) 3832–3840. [9] ABAQUS Inc, ABAQUS/CAE User’s Manual, Version 6.10, 2006. [10] N.P. Phuong, Evaluation method for interlocking efficiency by laying pattern of concrete block pavement (Master Thesis), Chung-Ang University, Seoul, Korea, 2012. [11] N.P. Phuong, W.G. Lin, D.G. Park, H.W. Kim, Y.H. Cho, Evaluation methodology for laying pattern of interlocking concrete block pavements using a displacement-moment concept, J. Transp. Eng. (ASCE) 140 (2) (2013) 04013008.