Bond Behavior between Concrete and Self-Expansion Polymer Material under Normal Pressures

Li, Xinxin; Wang, Fuming; Fang, Hongyuan; Zheng, Dan; Fu, Yingchun

doi:https://doi.org/10.1155/2021/6675102

Advances in Civil Engineering

On this page

Abstract Introduction Conclusions Abbreviations Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2021 | Article ID 6675102 | https://doi.org/10.1155/2021/6675102

Bond Behavior between Concrete and Self-Expansion Polymer Material under Normal Pressures

Xinxin Li,^1,2Fuming Wang,^1,3Hongyuan Fang ,^1,3Dan Zheng,²and Yingchun Fu²

Academic Editor: Qiang Tang

Received16 Nov 2020

Revised10 Feb 2021

Accepted27 Feb 2021

Published24 Mar 2021

Abstract

Self-expansion polymer grouting technology is a new rapid trenchless method for repairing leakage and subsidence of underground concrete structures. The bond between polymer and concrete is critical to determine the ultimate conditions of repaired concrete. In this paper, a series of direct shear tests were performed to investigate the influence of normal pressure on the shear bond properties between self-expansion polymer and concrete with different polymer density and concrete strength. Results indicate that failure modes and bond strength are greatly influenced by the normal pressure for specimens with a lower polymer density. For a given normal pressure, the bond strength linearly increases with the increasing polymer density. As the polymer density increased up to 0.43 g/cm³, the increased ratio decreases with the polymer density. Moreover, the displacement at the peak point reduces with an increase in polymer density. Finally, a finite element model is proposed to evaluate the bond strength for specimen failure in concrete and verified with the test results.

1. Introduction

A polyurethane polymer material with the characteristics of self-expansion [1], lightweight [2], early strength [3], high tensile strength [4], and excellent water resistance [5] has been successfully and effectively used to repair underground structures such as tunnels, road foundations, dams, and concrete pipelines [6, 7]. As shown in Figure 1, for a buried concrete drainage pipeline, when the polymer is injected into the outside wall of the pipe by grouting apparatus, the volume of polymer expands quickly and fills the voids and cracks between the pipe wall and soil. Then, the pipelines are lifted by the hardened polymer in 15 minutes [8]. Finally, the leakage, subsidence, and disengagement of the buried defective concrete pipelines have been restored. Based on the full-scale field tests and numerical analysis, Fang et al. [2] and Wang et al. [5] found that the self-expansion polymer grouting can improve the stress distribution and deformation of bottom hollow defective pipelines effectively. However, under the influence of vertical traffic loading or seismic loading, the pipeline-polymer interface may be subject to shear stress. Therefore, it is critical to study the shear bond performance of the self-expansion polymer and concrete for accurately evaluating the response of polymer reinforced underground concrete structures under external loading [9].

Existing studies found that the bond performance between concrete and polymer adhesive material such as epoxy is influenced by many factors [10–12]. Ivano and Andrea [13] observed that the bond quality between epoxy and concrete is greatly improved with larger interfacial roughness, and sandblasting is an effective way to increase the surface roughness of concrete. For a given surface roughness of the concrete substrate, Zhang et al. [14] pointed out that the bond resistance is increased by incrementing the strength of materials between the interfaces. Ouyang and Wan [15] and Zhou et al. [16] revealed that the bond capacity is greatly decreased and the failure model shifts from concrete to the epoxy-concrete interface as the interface is subject to moisture invasion. Yuan et al. [9, 17] discovered that the shear bond strength decreased with a larger size of the coarse aggregate. As to the self-expansion polyurethane polymer material, the chemical reaction involves a substantial increase in volume and exerts huge compressive stress on the concrete interface. Shi [8] found that the expansion pressure and polymer strength are extremely improved with a higher polymer density. For polymer with designed densities of 0.29, 0.35, 0.48, 0.53, 0.67, 0.79, and 0.84 g/cm³, the corresponding maximum expansion pressure is 0.36, 1.22, 1.97, 2.72, 3.10, 4.38, and 4.83 MPa, respectively. Therefore, during the self-expanding diffusion process of polymer, a higher grouting volume results in a larger expansion force at the polymer-concrete interface. Moreover, the soil cover depth and traffic load above the pipelines also exert different compressive stress around the bond region. The existence of normal stress around the bond region exerts a great influence on the shear bond strength [18, 19]. Therefore, to accurately evaluate the overall performance of polymer-repaired pipelines, the effect of normal stress on the shear bond performance between the self-expansion polymer and concrete should be considered. However, researches about this topic are limited.

This paper aims to present an experimental investigation to quantify the normal pressure on the shear bond behavior between self-expansion polymer and concrete. The effects of polymer density, the magnitude of normal pressure, and the strength of concrete on the failure mode, bond parameters, and shear bond stress-slip curves are analyzed. Then, a shear bond strength model for specimen failure in concrete is proposed.

2. Experimental Program

2.1. Specimens

Concrete with dimensions of 100 × 100 × 50 mm was adopted as the substrate for the direct shear tests. The concrete substrates were cured for 28 days in the standard curing room at a constant temperature and relative humidity of 20°C and 90%. All concrete was cast in one batch, and the surface roughness of different strength of concrete was measured by the sand filling method with five specimens. The average surface roughness of different strength of concrete is shown in Table 1. When the concrete substrate was horizontally placed in a special steel model with inner dimensions of 100 × 100 × 100 mm, a bicomponent liquid polyurethane polymer material with a temperature of 95°C was pumped into the steel model by grouting system. The polymer was then expanding and hardening rapidly in the model and squeezed the air out of the model through the air vent. About 60 minutes later, all specimens were demolded. As depicted in Figure 2, composite cubic specimens with half concrete and half polymer were formed. Thus, the bond section area A was 0.01 m². After that, all the specimens were stored in the laboratory until testing.

2.2. Materials

Concrete with three designed compressive strengths was used to fabricate the composite specimens during the test. Coarse aggregate with a maximum size of 20 mm, P.O 42.5 ordinary Portland cement, medium sand, and tap water were selected as the concrete mixture. The mixture proportions and mechanical properties of concrete are listed in Table 1. Polyurethane polymer materials with six different densities of 0.23, 0.36, 0.43 0.54, 0.69, and 0.92 g/cm³ were designed. The density of the polymer was determined by the amount of polymer grouted in a steel mold. The average compressive strengths and elastic modulus of each density of polymer are listed in Table 2.

2.3. Testing Apparatus and Procedure

Polymer-concrete interfacial bond tests were performed on a retrofitted direct shear test apparatus. As illustrated in Figure 3, two steel boxes with internal dimensions of 100 × 100 × 50 mm were fastened on the horizontal pistons to apply horizontal shear stress, and a load cell with an accuracy of 0.01 kN was connected between the horizontal piston and left part of the lower shear box to measure the shear load P. Besides, two linear voltage displacement transducers (LVDTs) were attached on the bottom shear box to monitor the horizontal displacement between polymer and concrete. Thus, the average slip s between polymer and concrete can be calculated as s = (s₁ + s₂)/2, where s₁ and s₂ are the measured slip value of the two LVDTs. Steel support was fixed between the bottom part of the lower shear box and the guide plate to bear the vertical force of the device, and a row of rollers was placed between the guide plate and the base of the test machine to reduce the friction between them. During the test, the concrete part of the specimen was first placed in the lower shear box.

After the required normal pressures were applied to the polymer by the vertical piston, the shear force was applied at a rate of 0.01 mm/s. Specimens were classified into three groups to examine the effect of the polymer density, normal pressure, and concrete strength on bond behavior. In group I, specimens with designed polymer densities of 0.23, 0.36, 0.43, 0.54, 0.69, and 0.92 g/cm³ (P23, P36, P43, P54, P69, and P92) were prepared to examine the influence of the polymer density. In group II, specimens with normal pressures of 0, 0.1, 0.3, 0.5, 1.0, and 2.0 MPa were tested to study the normal pressure effect. In group III, specimens with designed compressive strength of 25, 30, and 45 MPa (C25, C30, C45) were tested to evaluate the effect of the strength of concrete. Therefore, C30P23 represents a specimen with designed concrete compressive strength of 30 MPa and a polymer density of 0.23 g/cm³. The combinations of normal pressures, polymer density, and concrete strength are shown in Table 2.

3. Testing Results and Discussions

3.1. Failure Modes

For FRP strengthened structures, the bonding system is comprised of three types of materials (concrete, epoxy, and FRP) and two interfaces [20–22]. During the test, FRP and epoxy failures can be observed for specimens with poor FRP quality or poor surface preparation, whereas failure in concrete is the dominant failure models for specimens with good bond quality [23].

Figure 4 shows the failure modes between self-expansion polyurethane polymer and concrete with different polymer density and normal pressure. Under no normal stress, the failure mainly occurs in the polymer-concrete interface (Model A) for specimens with low polymer density. As shown in Figure 4(a), it can be observed that most of the polymers that penetrated into the voids of the concrete soundly adhere to the polymer part of the specimen and a thin layer of cement paste has been sheared off. When the density of polymer increases up to 0.43 g/cm³, the interfacial shear cracks propagate in the concrete substrate (Model B) rather than along the interface, and more concrete will be adhered off with the increasing of polymer density. Moreover, a certain amount of aggregates can be observed in the concrete matrix. This indicates that the roughness of the failure surface is increased with the increasing of polymer density, which results in a larger friction resistance between polymer and concrete.

(a)

(b)

(c)

When normal pressure is applied, as presented in Figure 4(b), for specimens with a polymer density of 0.23 g/cm³, the failure model is changed into a new pattern, in which the debonding primarily occurs in the polymer and a thin polymer layer above the interface is sheared off (Model C). Besides, with the increment of normal pressure, more polyurethane polymer material will be sheared off. As illustrated in Figure 4(c), for specimens with a polymer density of 0.36 g/cm³, the failure model is not changed with the increase of normal pressure, and the failure surface roughness is reduced with a higher normal pressure. When polymer density increased up to 0.43 g/cm³, the failure mode is less influenced by normal pressure, and the dominant failure is Model B.

3.2. Ultimate Bond Strength

Figure 5 shows the relationship between polymer density and shear bond resistance of specimens under different normal pressure. It can be found from Figures 5(a) and 5(b) that, for a given normal pressure, the ultimate bond strength τ_u almost linearly increases with the increasing of polymer density. As the polymer density increased up to 0.43 g/cm³, the increased ratio decreased with the increase of polymer density. Thus, the relationship between τ_u and polymer density under different normal pressure can be represented by two straight lines. When no normal pressure is applied, for the comparison specimens C30P23, the increasing percentage of the average bond strength with polymer density of 0.36 to 0.43 0.54, 0.69, and 0.92 g/cm³ is 67, 133, 130, 202, and 253%, respectively. Thus, the bond resistance is highly sensitive to the density of the polymer, and the failure modes discussed in the above section can be used to judge the bond quality of concrete and polymer.

(a)

(b)

(c)

(d)

(e)

From Figures 5(a) and 5(b), it can also be found that the ultimate bond strength increases significantly as normal pressures increase for a given polymer density. As the normal pressure increased up to 2.0 MPa, compared with the specimens of C30P23, C30P36, C30P43, C30P54, C30P69, and C30P92 under no normal pressure, the bond strength increased about 166, 162, 115, 140, 80, and 79%, respectively. The test results further manifest that the effect of normal pressure on the bond resistance decreases with increasing polymer density. Moreover, it can be seen from Figures 5(c)–5(e) that, for a given polymer density and normal pressure, the bond strength is decreased with a lower strength of concrete.

When the polymer was injected into the steel model, the chemical reaction between the two-component liquid polyurethane materials results in a substantial increase in volume, and a certain amount of foaming polymer has been squeezed into the pores, voids, and cracks of the concrete grouting surface by the self-expansion force. Thus, as shown in Figure 6, the voids in the concrete are fulfilled by the polymer, the polymer-concrete interface is contacted soundly, and no cracks are observed between the interfaces even though the scanning electron microscope specimens are suffering cutting process. Therefore, the bond resistance of concrete polymer can be considered composed by chemical adhesion generated by the chemical reaction of polymer on concrete and the mechanical interlocking of the polymer keys provided by the penetration of polymer into the pores and cracks of the concrete interface. Previous studies demonstrated that the strength and expansion force of polyurethane polymer are extremely improved with a higher polymer density [8]. Hence, with the increasing of polymer density, more polymers can be squeezed into the indentations of the concrete grouting surface and result in a larger chemical adhesion and mechanical interlocking between the interfaces. Moreover, as listed in Table 2, the polymer compressive strength is significantly increased with the density. Therefore, the bond strength rises with the increase of polymer density. When normal pressure is applied to the polymer material, the interface between concrete and polymer has been compacted, and the mechanical interlocking of the polymer is pretightened and strengthened. Moreover, the friction resistance generated by the wedging action of polymer and concrete particles at the polymer and concrete interface as slip begins to increase with the normal pressure. Therefore, the normal pressures exert a positive influence on the bond behavior.

3.3. Slip at the Peak Bond Strength

The slip at the peak bond point s₀ is plotted in Figure 7. It can be found that s₀ is a decreasing function of polymer density. However, for a given polymer density, s₀ increases with increasing the increment of normal pressure, and the increasing percentage becomes less pronounced for specimens with larger polymer density. Figure 6 also shows that the strength of concrete has a slight influence on the slip s₀.

3.4. Shear Bond Stress-Slip Curves between Polymer and Concrete

The relationship between shear bond stress and average horizontal displacement for specimens is illustrated in Figure 8. For specimens under no normal stress, each curve is composed of ascending and descending branches. The bond stress in the ascending branch increases significantly as the polymer density increases. When the chemical adhesion and mechanical interlocking between the interfaces have been overcome, the bond stress drops rapidly, and the specimen is sheared into two pieces along with the interface. Figure 9 gives the normalized bond stress-slip relationship for specimens under different polymer density, where it can be observed that the relations between τ/τ_u and s/s₀ can be represented by two straight lines. As the polymer density increases, the ascending branch nearly keeps unchanged, while the descending branch decreases more dramatically with a lower polymer density. The test results further manifested that the ascending branch can be defined by τ_u and s₀, and the descending branch is mainly influenced by normal pressure and polymer density.

(a)

(b)

As normal pressure is applied, the polymer-concrete interface has been compacted and the friction action between the interfaces becomes an important part of the bond resistance. As illustrated in Figure 10, ascending and descending branches are closely related to normal pressure. For a given polymer density, the bond stress in the ascending branch increases more dramatically while decreasing more slowly in the descending branch with increasing normal pressure. As described in Figure 11, when the density of the polymer is in the range of 0.23∼0.43 g/cm³, the increase in normal pressure leads to the normalized ascending branch changes from straight to concave, and the descending branch decreases even more slowly with a lower polymer density. As the polymer density larger than 0.43 g/cm³, the effect of normal pressure on the shape of the ascending curves becomes less pronounced.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(a)

(b)

(c)

3.5. FE Model for Polymer-Concrete Interface

As illustrated in Figure 4, when no normal pressure is applied, for specimens with polymer density larger than 0.43 g/cm³, the failure location in concrete is consistent with epoxy-concrete under good bond conditions. To study the shear failure mechanism at the polymer-concrete interface with a good bond condition, a 2D FE model of the specimen was established employing the ABAQUS software. As presented in Figure 12, the specimen was divided into the polymer layer, adhesive layer, and concrete layer with depths of 50 mm, 0 cm, and 50 mm, respectively. Owing to the interfacial failure that takes place in concrete, the polymer is treated as a linear elastic material in the FE model, and its elastic modulus varies with the density. The polymer and concrete are connected with the sharing nodes and keep intact during the failure process. The Concrete Damaged Plasticity (CDP) model proposed by Lee and Fenves [24] was applied to model the concrete, and the detailed parameters are listed in Table 3. The vertical and horizontal direction of concrete is restrained along with the lower shear box to simulate the restraints of the shear box. The shear load is applied on the left surface of the polymer in a displacement-controlled manner. The predicted shear bond strength of specimens under different polymer density is presented in Figure 13. It shows that the predicted results agree with the test value, especially for polymer density larger than 0.43 g/cm³. For specimens with a polymer density lower than 0.43 g/cm³, failure occurs in the interface. Therefore, the predicted value is larger than the test results.

4. Conclusions

A total of 105 composite specimens have been prepared and tested to evaluate the effect of normal pressure on the shear bond behavior of concrete and self-expansion polyurethane polymer under different polymer density and concrete strength. The conclusions can be drawn as follows:(1)The failure mode is mainly related to the magnitude of polymer density and normal pressure. For specimens with a lower polymer density, the failure mode changes with the increase of normal pressure. As the normal pressure rises to 0.36 g/cm³, the influence of normal pressure on the failure mode is negligible.(2)Polymer density, normal pressure, and concrete strength all positively affect the bond capacity. For a given normal pressure, the relationship between shear strength and polymer density can be repressed by two straight lines, and the increment in the bond strength gradually decreases for a higher polymer density.(3)When no normal pressure is applied, with increasing polymer density, the bond stress increases rapidly to the peak point and then drops sharply on the descending branch. The normalized bond-slip curves can be represented by two straight lines. When normal pressure is applied, the bond stress increases dramatically to the peak point and then drops sharply to the residual strength with a higher polymer density.(4)The finite element model proposed in this study can be used to predict the shear bond strength between self-expansion polymer and concrete failure in concrete mode.

Abbreviations

E_c:	Elastic modulus of concrete
f_c:	Compressive strength of concrete
f_p:	Compressive strength of polymer density
υ_c:	Poisson’s ratio of concrete
P:	Shear load
s:	Average slip between the interfaces
s₀:	Slip at peak bond strength
s₁:	Slip at lower shear box
s₂:	Slip at lower shear box
A:	Cross-sectional area of the bond region
τ:	Bond strength
τ_u:	Ultimate bond strength
p:	Normal pressure.

Data Availability

All data used to support the findings of this study are included within the article, and the data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This study was supported by the National Key Research and Development Program of China (2017YFC1501204), the National Natural Science Foundation of China (51978630; 51809025), the Program for Science and Technology Innovation Talents in Universities of Henan Province (19HASTIT043), the Outstanding Young Talent Research Fund of Zhengzhou University (1621323001), the Department of Education’s Production-Study-Research Combined Innovation Funding-“Blue Fire Plan (Huizhou)” (CXZJHZ01742), the Chongqing Natural Science Foundation of China (cstc2020jcyj-msxmX0852), and the Chongqing Youth Science and Technology Talent Training Program (CSTC2014KJRC-QNRC30001).

References

M. Li, H. Fang, M. Du, C. Zhang, Z. Su, and F. Wang, “The behavior of polymer-bentonite interface under shear stress,” Construction and Building Materials, vol. 248, p. 118680, 2020.
View at: Publisher Site | Google Scholar
H. Fang, B. Li, F. Wang, Y. Wang, and C. Cui, “The mechanical behaviour of drainage pipeline under traffic load before and after polymer grouting trenchless repairing,” Tunnelling and Underground Space Technology, vol. 74, pp. 185–194, 2018.
View at: Publisher Site | Google Scholar
J. Xu, H. Hu, Y. Zhong, R. Wang, and B. Wang, “Numerical analysis on underground pipe settlement and vacancy repairing with polymer injection,” Chinese Journal of Underground Space and Engineering, vol. 13, no. 5, pp. 1165–1172, 2017.
View at: Google Scholar
B. Li, H. Fang, H. He, K. Yang, C. Chen, and F. Wang, “Numerical simulation and full-scale test on dynamic response of corroded concrete pipelines under Multi-field coupling,” Construction and Building Materials, vol. 200, pp. 368–386, 2019.
View at: Publisher Site | Google Scholar
R. Wang, F. Wang, J. Xu, Y. Zhong, and S. Li, “Full-scale experimental study of the dynamic performance of buried drainage pipes under polymer grouting trenchless rehabilitation,” Ocean Engineering, vol. 181, pp. 121–133, 2019.
View at: Publisher Site | Google Scholar
C. Guo and F. Wang, “Mechanism study on the construction of ultra-thin anti-seepage wall by polymer injection,” Journal of Materials in Civil Engineering, vol. 24, no. 9, pp. 1183–1192, 2012.
View at: Google Scholar
M. Shi, F. Wang, and J. Luo, “Compressive strength of polymer grouting material at different temperatures,” Journal of Wuhan University of Technology-Mater. Sci. Ed., vol. 25, no. 6, pp. 962–965, 2010.
View at: Publisher Site | Google Scholar
M. Shi, Research on Polymer Grouting Material Properties and Directional Fracturing Grouting Mechanical for Dykes and Dams, Dalian University of Technology, Dalian, China, 2011.
H. Fang, P. Tan, X. Du, B. Li, K. Yang, and Y. Zhang, “Mechanical response of buried HDPE double-wall corrugated pipe under traffic-sewage coupling load,” Tunnelling and Underground Space Technology, vol. 108, p. 103664, 2021.
View at: Publisher Site | Google Scholar
M. Heshmati, R. Haghani, and M. Al-Emrani, “Environmental durability of adhesively bonded FRP/steel joints in civil engineering applications: state of the art,” Composites Part B: Engineering, vol. 81, pp. 259–275, 2015.
View at: Publisher Site | Google Scholar
J. Shi, H. Zhu, Z. Wu, R. Seracino, and G. Wu, “Bond behavior between basalt fiber-reinforced polymer sheet and concrete substrate under the coupled effects of freeze-thaw cycling and sustained load,” Journal of Composites for Construction, vol. 17, no. 4, pp. 530–542, 2013.
View at: Publisher Site | Google Scholar
X. L. Zhao, Y. Bai, R. Al-Mahaidi, and S. Rizkalla, “Effect of dynamic loading and environmental conditions on the bond between CFRP and steel: state-of-the-art review,” J. Compos. Constr., vol. 18, no. 3, Article ID 0000419, 2014.
View at: Publisher Site | Google Scholar
I. Iovinella, A. Prota, and C. Mazzotti, “Influence of surface roughness on the bond of FRP laminates to concrete,” Construction and Building Materials, vol. 40, pp. 533–542, 2013.
View at: Publisher Site | Google Scholar
P. Zhang, G. Wu, H. Zhu, D. Meng, and Z. Wu, “Mechanical performance of the wet-bond interface between FRP plates and cast-inplace concrete,” Journal of Composites for Construction, vol. 18, no. 6, Article ID 04014016, 2014.
View at: Publisher Site | Google Scholar
Z. Ouyang and B. Wan, “Modeling of moisture diffusion in FRP strengthened concrete specimens,” Journal of Composites for Construction, vol. 12, no. 4, pp. 425–434, 2008.
View at: Publisher Site | Google Scholar
A. Zhou, O. Büyüköztürk, and D. Lau, “Debonding of concrete-epoxy interface under the coupled effect of moisture and sustained load,” Cement and Concrete Composites, vol. 80, pp. 287–297, 2017.
View at: Publisher Site | Google Scholar
C. Yuan, W. Chen, T. M. Pham, and H. Hao, “Effect of aggregate size on bond behaviour between basalt fibre reinforced polymer sheets and concrete,” Composites Part B: Engineering, vol. 158, pp. 459–474, 2019.
View at: Publisher Site | Google Scholar
F. Xu, Z. M. Wu, J. J. Zheng, Y. Hu, and Q. B. Li, “Bond behavior of plain round bars in concrete under complex lateral pressures,” ACI Structural Journal, vol. 111, no. 1, pp. 15–25, 2014.
View at: Google Scholar
X. Li, Z. Wu, J. Zheng, and W. Dong, “Effect of loading rate on the bond behavior of plain round bars in concrete under lateral pressure,” Construction and Building Materials, vol. 94, no. 30, pp. 826–836, 2015.
View at: Publisher Site | Google Scholar
X. Z. Lu, J. G. Teng, L. P. Ye, and J. J. Jiang, “Bond-slip models for FRP sheets/plates bonded to concrete,” Engineering Structures, vol. 27, no. 6, pp. 920–937, 2005.
View at: Publisher Site | Google Scholar
F. C. An, W. Liu, and B. Fu, “A predictive 2D finite element model for modelling FRP-to-concrete bond behavior,” Composite Structures, vol. 226, Article ID 111189, 2019.
View at: Publisher Site | Google Scholar
Y. Tao and J. F. Chen, “Concrete damage plasticity model for modeling FRP-to-concrete bond behavior,” Journal of Composites for Construction, vol. 19, Article ID 04014026, 2015.
View at: Publisher Site | Google Scholar
F.-C. An, F.-Y. Zhang, and C.-C. Hou, “Influence of mechanical properties of concrete on the failure behaviour of FRP-to-concrete interface,” Construction and Building Materials, vol. 264, p. 120572, 2020.
View at: Publisher Site | Google Scholar
J. Lee and G. L. Fenves, “Plastic-damage model for cyclic loading of concrete structures,” Journal of Engineering Mechanics, vol. 124, no. 8, pp. 892–900, 1998.
View at: Publisher Site | Google Scholar

Copyright

Copyright © 2021 Xinxin Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation

Download other formats

Order printed copies