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Analysis of Friction Effect on Recycled Concrete Ends Using Base Force Element Method
DOI: 10.12677/IJM.2021.104020, PDF, HTML, XML, 下载: 190  浏览: 363  国家自然科学基金支持

Abstract: In this paper, a two-dimensional random aggregate mesoscopic model of recycled concrete is de-veloped using the base force element method, which employs Delaunay triangular dissection aligned with the interface, and the constitutive relation of multi-line damage evolution is used for each phase material in the model, and the Kupfer criterion is applied as the basis for determining damage in the biaxial compression zone. The friction between the recycled concrete specimens and the loading plate was considered using the zero-thickness interface element, and the influence of end friction on the peak strength and failure mode of the recycled concrete specimen was discussed. The numerical results are compared well with experimental results. It is proven that the model established in this paper can simulate the macroscopic mechanical behavior of recycled concrete specimens. In addition, the numerical results show that: End friction significantly affects the peak strength and damage mode of recycled concrete, and the degree of influence increases as the aspect ratio decreases; the influence range of end friction is limited, and the farther away from the end, the smaller the influence is.

1. 引言

2. 细观模型简介

2.1. 随机骨料生成及网格划分

Figure 1. Schematic diagram of random aggregate distribution and meshing of recycled aggregate concrete

2.2. 基面力单元法的单元刚度矩阵

${K}^{IJ}=\frac{E}{2A\left(1+\nu \right)}\left[\frac{2\nu }{1-2\nu }{m}^{I}\otimes {m}^{J}+{m}^{IJ}U+{m}^{J}\otimes {m}^{I}\right],\left(I,J=1,2,3\right)$ (1)

${m}^{I}={m}_{\alpha }^{I}{P}_{\alpha }=\frac{1}{2}\left({L}_{IJ}{n}^{IJ}+{L}_{IK}{n}^{IK}\right)$ (2)

Figure 2. A triangular element

2.3. 零厚度界面单元 [8] 基本原理

Figure 3. A zero-thickness interface element

$\left\{\sigma \right\}=\left\{\begin{array}{l}{\tau }_{s}\\ {\sigma }_{n}\end{array}\right\}=\left[\lambda \right]\left\{\Delta \delta \right\}$ (3)

$\left\{\Delta \delta \right\}=\left\{\begin{array}{c}\Delta u\\ \Delta v\end{array}\right\},\left[\lambda \right]=\left[\begin{array}{cc}{\lambda }_{s}& 0\\ 0& {\lambda }_{n}\end{array}\right]$ (4)

${\left[k\right]}^{e}=\frac{l}{6}\left[\begin{array}{cccccccc}2{\lambda }_{s}& 0& {\lambda }_{s}& 0& -{\lambda }_{s}& 0& -2{\lambda }_{s}& 0\\ 0& 2{\lambda }_{n}& 0& {\lambda }_{n}& 0& -{\lambda }_{n}& 0& -2{\lambda }_{n}\\ {\lambda }_{s}& 0& 2{\lambda }_{s}& 0& -2{\lambda }_{s}& 0& -{\lambda }_{s}& 0\\ 0& {\lambda }_{n}& 0& 2{\lambda }_{n}& 0& -2{\lambda }_{n}& 0& -{\lambda }_{n}\\ -{\lambda }_{s}& 0& -2{\lambda }_{s}& 0& 2{\lambda }_{s}& 0& {\lambda }_{s}& 0\\ 0& -{\lambda }_{n}& 0& -2{\lambda }_{n}& 0& 2{\lambda }_{n}& 0& {\lambda }_{n}\\ -2{\lambda }_{s}& 0& -{\lambda }_{s}& 0& {\lambda }_{s}& 0& 2{\lambda }_{s}& 0\\ 0& -2{\lambda }_{n}& 0& -{\lambda }_{n}& 0& {\lambda }_{n}& 0& 2{\lambda }_{n}\end{array}\right]$ (5)

2.4. 损伤本构模型和强度准则

$\sigma ={E}_{0}\left(1-D\right)\epsilon$ (6)

$E={E}_{0}\left(1-D\right)$ (7)

${D}_{t}=\left\{\begin{array}{ccc}0& & \epsilon \le {\epsilon }_{t0}\\ 1-\frac{{\epsilon }_{t0}}{\epsilon }+\frac{\epsilon -{\epsilon }_{t0}}{{\eta }_{t}{\epsilon }_{t0}-{\epsilon }_{t0}}\frac{{\epsilon }_{t0}}{\epsilon }\left(1-\alpha \right)& & {\epsilon }_{t0}<\epsilon \le {\eta }_{t}{\epsilon }_{t0}\\ 1-\frac{\alpha }{{\xi }_{t}-{\eta }_{t}}\frac{\epsilon -{\eta }_{t}{\epsilon }_{t0}}{\epsilon }+\frac{\alpha {\epsilon }_{t0}}{\epsilon }& & {\eta }_{t}{\epsilon }_{t0}<\epsilon \le {\xi }_{t}{\epsilon }_{t0}\\ 1& & \epsilon >{\xi }_{t}{\epsilon }_{t0}\end{array}$ (8)

${D}_{c}=\left\{\begin{array}{ccc}1-\frac{\beta }{\lambda }& & \epsilon \le \lambda {\epsilon }_{c0}\\ 1-\frac{1-\beta }{1-\lambda }\frac{\epsilon -\lambda {\epsilon }_{co}}{\epsilon }-\beta \frac{{\epsilon }_{co}}{\epsilon }& & \lambda {\epsilon }_{c0}<\epsilon \le {\epsilon }_{c0}\\ 1-\frac{1-\gamma }{1-{\eta }_{c}}\frac{\epsilon -{\epsilon }_{co}}{\epsilon }-\frac{{\epsilon }_{co}}{\epsilon }& & {\epsilon }_{c0}<\epsilon \le {\eta }_{c}{\epsilon }_{c0}\\ 1-\frac{\gamma {\epsilon }_{c0}}{\epsilon }& & {\eta }_{c}{\epsilon }_{c0}<\epsilon \le {\xi }_{c}{\epsilon }_{c0}\\ 1& & \epsilon >{\xi }_{c}{\epsilon }_{c0}\end{array}$ (9)

Table 1. Mechanical parameters of each phase material of recycled concrete

${\sigma }_{c}=\frac{1+3.65\alpha }{{\left(1+\alpha \right)}^{2}}{f}_{c}$ (10)

3. 模拟方案

Figure 4. Numerical calculation model

4. 计算结果与分析

4.1. 端部摩擦对再生混凝土试件峰值强度的影响

Table 2. Peak strength of recycled concrete specimen

Figure 5. Peak strength of specimens with different slenderness under different end conditions

Table 3. Comparison between the simulation results and test result

4.2. 端部摩擦对再生混凝土试件破坏模式的影响

4.3. 结果分析

(a) 100 mm × 100 mm (b) 100 mm × 150 mm (c) 100 mm × 200 mm

Figure 6. The final failure mode of the specimens without considering the end friction

(a) 100 mm × 100 mm (b) 100 mm × 150 mm (c) 100 mm × 200 mm

Figure 7. The final failure mode of the specimens considering the end friction

Figure 8. Biaxial compression zones of specimens

5. 结论

1) 在基面力单元法中引入零厚度界面单元可较好的用于模拟再生混凝土试件与垫板之间的摩擦，且模拟结果与试验结果一致，证明了本文模型的可靠性。

2) 考虑试件与加载垫板之间的端部摩擦时，再生混凝土试件的高宽比对峰值强度的影响较不考虑端部摩擦时更明显。

3) 端部摩擦会显著影响再生混凝土试件的峰值强度和破坏模式，并且随着高宽比减小，影响程度增大。

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