基于分形理论的RTPF混凝土冲击压缩性能

doi:10.12068/j.issn.1005-3026.2025.20230214

摘要/Abstract

摘要：

为探寻回收轮胎聚合物纤维（RTPF）混凝土的冲击压缩性能与破碎后碎块尺寸分布规律的关系，利用直径100 mm的分离式霍普金森压杆对不同RTPF体积分数（0，0.05%，0.1%，0.2%和0.4%）的混凝土进行冲击压缩试验.结果表明：应变率在38.2~122.2 s^-1时，不同掺量RTPF混凝土的分形维数范围为1.422~2.401；分形维数随应变率增加而增大，具有应变率效应；分形维数随RTPF掺量增加呈现先减小后增大的趋势，RTPF体积分数为0.1%时混凝土的分形维数最小；不同应变率下RTPF混凝土的动态抗压强度及耗散能均随分形维数的增加而增大；相同分形维数下，RTPF体积分数为0.1%时纤维与基体协同作用效果最佳，混凝土的动态抗压强度和耗散能提升幅度最大.利用分形理论建立RTPF混凝土的宏观损伤与冲击压缩性能的关系，可以确定混凝土中RTPF的最优掺量.

关键词: 纤维混凝土, 回收轮胎聚合物纤维, 分离式霍普金森压杆, 分形维数, 冲击压缩

Abstract:

In order to explore the relationship between the dynamic compressive performance of recycled tire polymer fiber （RTPF） reinforced concrete and the distribution rule of fragment size， the impact compression tests of concrete incorporating different volume fractions of RTPF （0， 0.05%， 0.1%， 0.2% and 0.4%） were conducted using a split Hopkinson pressure bar with a diameter of 100 mm. The results indicate that the fractal dimension of concrete with different RTPF contents ranges from 1.422 to 2.401 under the strain rates of 38.2～122.2 s^-1. The fractal dimension increases with the increase of strain rate， which has typical strain rate effect. The fractal dimension first decreases and then increases with the increase of RTPF content， and the fractal dimension of concrete reinforced with 0.1% RTPF is the lowest. The dynamic compressive strength and dissipated energy of RTPF reinforced concrete all increase with the increase of fractal dimension regardless of the strain rates. At the same fractal dimension， the fiber‑matrix synergistic effect is the optimum under RTPF volume fraction of 0.1%， which provides the superior enhancement in the dynamic compressive strength and dissipative energy of concrete. The relationship between the macroscopic damage and dynamic compressive properties of RTPF reinforced concrete can be established using fractal theory to obtain the optimal content of RTPF for concrete.

Key words: fiber reinforced concrete, recycled tire polymer fiber （RTPF）, split Hopkinson pressure bar （SHPB）, fractal dimension, impact compression

中图分类号:

TU 528.572

陈猛, 于航, 王瑜婷, 张通. 基于分形理论的RTPF混凝土冲击压缩性能[J]. 东北大学学报（自然科学版）, 2025, 46(1): 127-133.

Meng CHEN, Hang YU, Yu-ting WANG, Tong ZHANG. Impact Compressive Properties of RTPF Reinforced Concrete Based on Fractal Theory[J]. Journal of Northeastern University(Natural Science), 2025, 46(1): 127-133.

图/表 14

图1 RTPF形貌（a）—实物图；（b）—显微镜图；（c）—扫描电镜图.

Fig.1 Morphology of RTPF

表1 RTPF物理及力学性能

Table 1 Physical and mechanical properties of RTPF

长度/mm	直径/ $μ m$	密度/（kg·m^-3）	弹性模量/GPa
8.7±4.1	21.1±2.5	1 160	3.21

表1 RTPF物理及力学性能

Table 1 Physical and mechanical properties of RTPF

长度/mm	直径/ $μ m$	密度/（kg·m^-3）	弹性模量/GPa
8.7±4.1	21.1±2.5	1 160	3.21

表2 RTPF混凝土配合比 (reinforced concrete kg/m3)

Table 2 Proportions of mixture of RTPF

试件编号	水泥	粗骨料	细骨料	水	减水剂	RTPF
R0	472	1 144	616	218	2.36	0
R0.05	472	1 144	616	218	2.36	0.6
R0.1	472	1 144	616	218	2.36	1.2
R0.2	472	1 144	616	218	2.36	2.4
R0.4	472	1 144	616	218	2.36	4.8

图2 SHPB试验装置

Fig.2 SHPB testing device

图3 混凝土破坏界面扫描电镜图

Fig.3 Scanning electron microscope of failure interface in concrete

图4 不同掺量RTPF混凝土试件破碎块度分布（a）—R0；（b）—R0.05；（c）—R0.1；（d）—R0.2；（e）—R0.4.

Fig.4 Fragment size distributions of concrete specimens reinforced by different RTPF contents

图5 不同掺量RTPF混凝土的ln [M（x）/M]-lnx（a）—R0；（b）—R0.05；（c）—R0.1；（d）—R0.2；（e）—R0.4.

Fig.5 The ln [M（x）/M]-lnx curves of concrete reinforced by different RTPF contents

图6 RTPF混凝土分形维数随应变率的变化关系

Fig.6 Variations of fractal dimension of RTPF reinforced concrete with strain rate

图7 不同应变率下混凝土分形维数随RTPF掺量的变化关系

Fig.7 Variations of fractal dimension of concrete with RTPF content under different strain rates

图8 RTPF混凝土动态抗压强度与分形维数的变化关系

Fig.8 Variations of dynamic compressive strength of RTPF reinforced concrete with fractal dimension

表4 动态抗压强度拟合方程 (strength)

Table 4 Fitting equation for dynamic compressive

试件编号	拟合方程	R²
R0	f=19.42D_b+23.42	0.992
R0.05	f=15.10D_b+39.08	0.948
R0.1	f=20.24D_b+33.50	0.923
R0.2	f=16.52D_b+29.97	0.986
R0.4	f=13.34D_b+28.07	0.957

图9 RTPF混凝土耗散能与分形维数的变化关系

Fig.9 Variations of dissipated energy of RTPF reinforced concrete with fractal dimension

表5 耗散能拟合方程

Table 5 Fitting equation for dissipated energy

试件编号	拟合方程	R²
R0	W_A =373.13D_b-377.12	0.957
R0.05	W_A =317.95D_b-198.73	0.995
R0.1	W_A =321.44D_b-129.26	0.999
R0.2	W_A =399.40D_b-396.75	0.973
R0.4	W_A =392.01D_b-540.42	0.959

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