岩石-钢纤维混凝土复合层动态抗压强度计算模型

陈猛; 田矣涵; 崔秀文; 张通

doi:10.11779/CJGE20230686

岩石-钢纤维混凝土复合层动态抗压强度计算模型 English Version

东北大学资源与土木工程学院, 辽宁沈阳 110819

基金项目:

国家自然科学基金项目 52178382

国家自然科学基金项目 52308395

博士后创新人才支持计划项目 BX20230063

中国博士后科学基金面上项目 2023M730526

中央高校基本科研业务专项资金项目 N2201023

中央高校基本科研业务专项资金项目 N2301023

辽宁省博士科研启动基金计划项目 2023-BS-058

详细信息

作者简介:
陈猛(1981—)，男，博士，教授，主要从事混凝土及岩石动态力学性能方面的研究。E-mail: chenmeng@mail.neu.edu.cn

通讯作者:
张通, E-mail: zhangtong@mail.neu.edu.cn

中图分类号: TU45
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出版历程
- 收稿日期: 2023-07-19
- 网络出版日期: 2024-04-25
- 刊出日期: 2024-09-30

Dynamic compressive strength model for rock-steel fiber-reinforced concrete composite layer

School of Resources and Civil Engineering, Northeastern University, Shenyang 110819, China

摘要

摘要: 为了研究冲击荷载下岩石-钢纤维混凝土（R-SFRC）复合层的抗压强度模型，利用分离式霍普金森压杆对花岗岩、混凝土和R-SFRC复合层进行动态冲击压缩试验，并通过回归试验结果得到R-SFRC复合层的对数型、幂函数型和强度-应变率依赖机制型3种强度模型，同时考虑R-SFRC复合层界面相互作用，基于Mohr-Coulomb强度准则建立复合层动态抗压强度计算模型。结果表明，R-SFRC复合层动态抗压强度随应变率及钢纤维掺量增大而增大；3种回归模型拟合复合层动态抗压强度试验结果的相关系数范围为0.918~0.999，其中依赖机制型模型与试验结果的相关性最大；基于Mohr-Coulomb强度准则的3种模型得到的复合层抗压强度计算值相对试验值的误差范围为-9.23%~3.16%，对数型模型的误差最大值较小。R-SFRC复合层动态抗压强度计算模型可为混凝土支护隧道围岩设计提供理论基础。
- 岩石 /
- 钢纤维混凝土 /
- 动态抗压强度 /
- 应变率 /
- Mohr-Coulomb强度准则 /
- 强度预测模型
Abstract: In order to study the compressive strength model for rock-steel fiber-reinforced concrete (R-SFRC) composite layer under impact loading, the dynamic impact compression tests on the granite, concrete and R-SFRC composite layer are carried out by using the separated Hopkinson pressure bar to obtain the dynamic compressive strengths of different materials. With the regression fitting of the test results, three types of strength models for the R-SFRC composite layer called logarithmic, power function and strength-strain rate dependent mechanism are obtained, and the dynamic compressive strength models for the R-SFRC composite layer are established based on the Mohr-Coulomb strength criterion considering the interface interaction of the R-SFRC composite layer. The results show that the dynamic compressive strength of the R-SFRC composite layer increases with the increase of the strain rate and steel fiber content, and the range of the correlation coefficient of three regression models is 0.918~0.999, and the R² of the dependent mechanism model is the largest. The error range of the theoretical value of the dynamic compressive strength calculated based on the Mohr-Coulomb strength criterion relative to the test value is -9.23%~3.16%, and the maximum error value of the logarithmic model is the smallest. The computational model for the dynamic compressive strength of the R-SFRC composite layer can provide a theoretical basis for the design of the surrounding rock of concrete-supported tunnels.
- rock /
- steel fiber-reinforced concrete /
- dynamic compressive strength /
- strain rate /
- Mohr-Coulomb strength criterion /
- strength prediction model

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图 1 SHPB试验装置示意图

Figure 1. Schematic diagram of SHPB testing apparatus

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图 2 SHPB试验波形图

Figure 2. Strain waves of SHPB tests

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图 3 SHPB试验应力平衡波形图

Figure 3. Validation of stress equilibrium during the SHPB test

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图 4 不同应变率下复合层试件的破坏形态

Figure 4. Failure modes of composite layer specimens at different strain rates

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图 5 动态抗压强度随应变率变化曲线

Figure 5. Variation of dynamic compressive strength with strain rate

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图 6 R-SFRC复合层的对数型模型拟合曲线

Figure 6. Fitting curves of logarithmic model for R-SFRC composite layer

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图 7 R-SFRC复合层的幂函数型模型拟合曲线

Figure 7. Fitting curves of power functional model for R-SFRC composite layer

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图 8 R-SFRC复合层的强度-应变率依赖机制型模型拟合曲线

Figure 8. Fitting curves of strength-strain rate dependent mechanism model for R-SFRC composite layer

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图 9 R-SFRC复合层界面处单元体应力分析图

Figure 9. Stress analysis of element at interface of R-SFRC composite layer

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表 1 花岗岩的物理及力学性能

Table 1 Physical and mechanical properties of granite

密度/ (kg·m^-3)	弹性模量/ GPa	单轴抗压强度/MPa	泊松比	内摩擦角/(°)
3000	67.41	187.1	0.207	53

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表 2 钢纤维的物理及力学性能

Table 2 Physical and mechanical properties of steel fiber

长度/ mm	直径/ mm	密度/ (kg·m^-3)	抗拉强度/ MPa	弹性模量/ GPa
35	0.3	7850	1150	220

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表 3 混凝土配合比

Table 3 Mixture proportions of concrete 单位: kg/m³

材料类型	水泥	水	细骨料	粗骨料	减水剂	钢纤维
FC0	418	182	611	1239	4.18	0
FC4	418	182	611	1239	4.18	40
FC6	418	182	611	1239	4.18	60
FC8	418	182	611	1239	4.18	80
注：FC4，FC6和FC8分别表示钢纤维掺量为40，60，80 kg/m³的钢纤维混凝土。

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表 4 回归模型中R-SFRC复合层的参数拟合值

Table 4 Fitting values of parameters of R-SFRC composite layer using regression models

复合层类型	对数型			幂函数型		依赖机制型
复合层类型	k₁	${b_1}$	${R^2}$	k₂	${R^2}$	k₄	${\dot \varepsilon _{\text{s}}}$	$n$	${R^2}$
R-FC0	1.132	-0.608	0.996	0.356	0.991	0.833	61.348	2.731	0.999
R-FC4	0.998	-0.207	0.963	0.362	0.980	3.873	364.699	1.198	0.998
R-FC6	1.001	-0.172	0.942	0.382	0.918	3.623	298.722	1.196	0.971
R-FC8	1.100	-0.456	0.979	0.378	0.977	1.584	108.280	1.392	0.993

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表 5 回归模型中混凝土的参数拟合值

Table 5 Fitting values of parameters of concrete using regression models

材料类型	对数型			幂函数型		依赖机制型
材料类型	${k_{{\text{1C}}}}$	${b_{1{\text{C}}}}$	${R^2}$	${k_{{\text{2C}}}}$	${R^2}$	${k_{{\text{4C}}}}$	${\dot \varepsilon _{{\text{sC}}}}$	${n_{\text{C}}}$	${R^2}$
FC0	0.842	-0.357	0.941	0.287	0.961	0.476	81.603	4.923	0.988
FC4	0.940	-0.448	0.957	0.309	0.961	0.494	64.627	5.211	0.980
FC6	1.031	-0.516	0.947	0.334	0.966	0.725	68.548	3.012	0.972
FC8	1.038	-0.530	0.987	0.333	0.989	0.784	71.679	2.734	0.998

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表 6 R-SFRC复合层的动态抗压强度计算值与试验值对比

Table 6 Comparison of calculated and tested values of dynamic compressive strength of R-SFRC composite layer

复合层类型	应变率/s^-1	${f_{\text{e}}}$ /MPa	${f_{{\text{RC1}}}}$ /MPa	${f_{{\text{RC2}}}}$ /MPa	${f_{{\text{RC3}}}}$ /MPa	${x_1}$ /%	${x_2}$ /%	${x_3}$ /%
R-FC0	38.3	82.5±1.1	75.1	75.0	81.0	-8.93	-9.09	-1.87
	55.4	94.2±3.0	89.5	88.2	85.5	-5.02	-6.33	-9.23
	72.1	105.6±2.5	98.5	97.7	96.0	-6.77	-7.48	-9.08
	97.2	114.6±6.4	105.9	106.3	107.4	-7.62	-7.27	-6.31
	111.5	118.4±4.0	110.3	111.7	112.3	-6.87	-5.65	-5.17
R-FC4	33.9	88.8±4.3	82.8	83.4	83.9	-6.76	-6.03	-5.50
	57.6	99.2±3.0	97.6	96.7	94.4	-1.59	-2.54	-4.83
	73.5	109.9±5.8	105.9	104.9	106.9	-3.66	-4.52	-2.76
	94.1	119.3±5.9	115.9	115.9	118.0	-2.86	-2.85	-1.13
	115.9	129.6±4.6	121.9	123.1	120.8	-5.91	-5.03	-6.80
R-FC6	34.5	99.2±3.5	91.0	92.1	91.3	-8.28	-7.20	-8.01
	58.1	109.7±4.9	106.3	105.4	103.5	-3.13	-3.88	-5.67
	72.6	114.2±4.9	117.8	116.8	117.1	3.16	2.31	2.51
	93.8	129.8±5.3	128.3	128.2	128.6	-1.16	-1.19	-0.95
	116.3	135.6±5.4	133.8	134.7	133.2	-1.33	-0.68	-1.78
R-FC8	38.5	100.7±0.6	94.4	95.3	95.2	-6.26	-5.38	-5.51
	53.7	112.7±2.7	109.2	108.3	113.3	-3.12	-3.92	0.56
	76.5	121.5±4.0	119.7	118.6	119.3	-1.50	-2.40	-1.78
	93.0	135.2±6.4	131.6	131.5	132.6	-2.67	-2.75	-1.91
	114.4	140.7±5.7	138.9	140.0	139.0	-1.31	-0.49	-1.24
注： ${f_{\text{e}}}$ 为R-SFRC复合层的动态抗压强度试验值； ${f_{{\text{RC1}}}}$ ， ${f_{{\text{RC2}}}}$ 和 ${f_{{\text{RC3}}}}$ 分别为基于Mohr-Coulomb强度准则建立的对数型、幂函数型和强度-应变率依赖机制型模型的R-SFRC复合层动态抗压强度计算值。 ${x_i}$ 为 ${f_{{\text{RC}}i}}$ 的误差， ${x_i} = ({f_{{\text{RC}}i}} - {f_{\text{e}}}) \times 100\% /{f_{\text{e}}}$ ， $i$ =1，2，3。

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参考文献(23)

[1]	郭东明, 闫鹏洋, 凡龙飞, 等. 喷层混凝土-围岩组合体波动特性及动力特性研究[J]. 振动与冲击, 2018, 37(24): 85-91, 136. GUO Dongming, YAN Pengyang, FAN Longfei, et al. A study on the stress wave characteristics and dynamic mechanical property of the sprayed concrete-surrounding rock combined body[J]. Journal of Vibration and Shock, 2018, 37(24): 85-91, 136. (in Chinese)
[2]	JIANG Q, YANG Y, YAN F, et al. Deformation and failure behaviours of rock-concrete interfaces with natural morphology under shear testing[J]. Construction and Building Materials, 2021, 293: 123468. doi: 10.1016/j.conbuildmat.2021.123468
[3]	MOUZANNAR H, BOST M, LEROUX M, et al. Experimental study of the shear strength of bonded concrete–rock interfaces: surface morphology and scale effect[J]. Rock Mechanics and Rock Engineering, 2017, 50(10): 2601-2625. doi: 10.1007/s00603-017-1259-2
[4]	CHANG X, LU J Y, WANG S Y, et al. Mechanical performances of rock-concrete bi-material disks under diametrical compression[J]. International Journal of Rock Mechanics and Mining Sciences, 2018, 104: 71-77. doi: 10.1016/j.ijrmms.2018.02.008
[5]	ZHU J B, BAO W Y, PENG Q, et al. Influence of substrate properties and interfacial roughness on static and dynamic tensile behaviour of rock-shotcrete interface from macro and micro views[J]. International Journal of Rock Mechanics and Mining Sciences, 2020, 132: 104350. doi: 10.1016/j.ijrmms.2020.104350
[6]	ZHAO B Y, LIU Y, LIU D Y, et al. Research on the influence of contact surface constraint on mechanical properties of rock-concrete composite specimens under compressive loads[J]. Frontiers of Structural and Civil Engineering, 2020, 14(2): 322-330. doi: 10.1007/s11709-019-0594-7
[7]	陈猛, 王浩, 齐迈, 等. 岩石–钢纤维混凝土复合层动态压缩性能试验研究[J]. 岩石力学与工程学报, 2020, 39(6): 1222-1230. CHEN Meng, WANG Hao, QI Mai, et al. Experimental study on dynamic compressive properties of composite layers of rock and steel fiber reinforced concrete[J]. Chinese Journal of Rock Mechanics and Engineering, 2020, 39(06): 1222-1230. (in Chinese)
[8]	赵坚, 李海波. 莫尔-库仑和霍克-布朗强度准则用于评估脆性岩石动态强度的适用性[J]. 岩石力学与工程学报, 2003, 22(2): 171-176. doi: 10.3321/j.issn:1000-6915.2003.02.001 ZHAO Jian, LI Haibo. Estimating the dynamic strength of rock using Mohr-coulomb and hoek-brown criteria[J]. Chinese Journal of Rock Mechanics and Engineering, 2003, 22(2): 171-176. (in Chinese) doi: 10.3321/j.issn:1000-6915.2003.02.001
[9]	宫凤强, 司雪峰, 李夕兵, 等. 基于应变率效应的岩石动态Mohr-Coulomb准则和Hoek-Brown准则研究[J]. 中国有色金属学报, 2016, 26(8): 1763-1773. GONG Fengqiang, SI Xuefeng, LI Xibing, et al. Rock dynamic Mohr-Coulomb and Hock-Brown criteria based on strain rate effect[J]. The Chinese Journal of Nonferrous Metals, 2016, 26(8): 1763-1773. (in Chinese)
[10]	宫凤强, 陆道辉, 李夕兵, 等. 不同应变率下砂岩动态强度准则的试验研究[J]. 岩土力学, 2013, 34(9): 2433-2441. GONG Fengqiang, LU Daohui, LI Xibing, et al. Experimental research of sandstone dynamic strength criterion under different strain rates[J]. Rock and Soil Mechanics, 2013, 34(9): 2433-2441. (in Chinese)
[11]	钱七虎, 戚承志. 岩石、岩体的动力强度与动力破坏准则[J]. 同济大学学报(自然科学版), 2008, 36(12): 1599-1605. doi: 10.3321/j.issn:0253-374X.2008.12.001 QIAN Qihu, QI Chengzhi. Dynamic strength and dynamic fracture criteria of rock and rock mass[J]. Journal of Tongji University (Natural Science), 2008, 36(12): 1599-1605. (in Chinese) doi: 10.3321/j.issn:0253-374X.2008.12.001
[12]	GONG F Q, SI X F, LI X B, et al. Dynamic triaxial compression tests on sandstone at high strain rates and low confining pressures with split Hopkinson pressure bar[J]. International Journal of Rock Mechanics and Mining Sciences, 2019, 113: 211-219. doi: 10.1016/j.ijrmms.2018.12.005
[13]	SI X F, GONG F Q, LI X B, et al. Dynamic Mohr–Coulomb and Hoek–Brown strength criteria of sandstone at high strain rates[J]. International Journal of Rock Mechanics and Mining Sciences, 2019, 115: 48-59. doi: 10.1016/j.ijrmms.2018.12.013
[14]	FU Q, XU W R, HE J Q, et al. Dynamic strength criteria for basalt fibre-reinforced coral aggregate concrete[J]. Composites Communications, 2021, 28: 100983. doi: 10.1016/j.coco.2021.100983
[15]	LU D C, WANG G S, DU X L, et al. A nonlinear dynamic uniaxial strength criterion that considers the ultimate dynamic strength of concrete[J]. International Journal of Impact Engineering, 2017, 103: 124-137. doi: 10.1016/j.ijimpeng.2017.01.011
[16]	ZHAO B Y, LIU Y, HUANG T Z, et al. Experimental study on strength and deformation characteristics of rock–concrete composite specimens under compressive condition[J]. Geotechnical and Geological Engineering, 2019, 37(4): 2693-2706. doi: 10.1007/s10706-018-00787-9
[17]	陈猛, 崔秀文, 颜鑫, 等. 岩石-钢纤维混凝土复合层抗压强度预测模型[J]. 岩土力学, 2021, 42(3): 638-646. CHEN Meng, CUI Xiuwen, YAN Xin, et al. Prediction model for compressive strength of rock-steel fiber reinforced concrete composite layer[J]. Rock and Soil Mechanics, 2021, 42(3): 638-646. (in Chinese)
[18]	ZHANG X H, CHIU Y W, HAO H, et al. Dynamic compressive properties of Kalgoorlie basalt rock[J]. International Journal of Rock Mechanics and Mining Sciences, 2020, 135: 104512. doi: 10.1016/j.ijrmms.2020.104512
[19]	袁良柱, 苗春贺, 单俊芳, 等. 冲击下混凝土试样应变率效应和惯性效应探讨[J]. 爆炸与冲击, 2022, 42(1): 1-13. YUAN Liangzhu, MIAO Chunhe, SHAN Junfang, et al. On strain-rate and inertia effects of concrete samples under impact[J]. Explosion and shock waves, 2022, 42(1): 1-13. (in Chinese)
[20]	FENG S W, ZHOU Y, WANG Y, et al. Experimental research on the dynamic mechanical properties and damage characteristics of lightweight foamed concrete under impact loading[J]. International Journal of Impact Engineering, 2020, 140: 103558. doi: 10.1016/j.ijimpeng.2020.103558
[21]	王健, 李二兵, 谭跃虎, 等. 层状盐岩及泥岩夹层动态力学特性对比试验研究[J]. 岩石力学与工程学报, 2017, 36(12): 3002-3011. WANG Jian, LI Erbing, TAN Yuehu, et al. Comparative experimental study on dynamic mechanical properties of bedded salt rock and mudstone interbed[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(12): 3002-3011. (in Chinese)
[22]	LI X Z, QI C Z. A micro-macro dynamic compressive-shear fracture model under static confining pressure in brittle rocks[J]. International Journal of Impact Engineering, 2018, 122: 109-118. doi: 10.1016/j.ijimpeng.2018.07.010
[23]	ZHAO J, LI H B, WU M B, et al. Dynamic uniaxial compression tests on a granite[J]. International Journal of Rock Mechanics and Mining Sciences, 1999, 36(2): 273-277. doi: 10.1016/S0148-9062(99)00008-X