超高性能混凝土板冲切与弯曲性能研究

樊健生; 王哲; 杨松; 陈钒; 丁然

doi:10.6052/j.issn.1000-4750.2020.06.0349

超高性能混凝土板冲切与弯曲性能研究

doi: 10.6052/j.issn.1000-4750.2020.06.0349

樊健生^{1, 2, ,},
王哲^1,,
杨松^3,,
陈钒^4,,
丁然^{1, 2,}

1.
清华大学土木工程系，北京 100084
2.
清华大学土木工程安全与耐久教育部重点实验室，北京 100084
3.
清华大学水利水电工程系，北京 100084
4.
中电建路桥集团有限公司，北京 100048

基金项目: 国家自然科学基金项目(51890903)；国家重点研发计划项目(2018YFC0705400)

详细信息

作者简介:
王　哲(1992−)，男，天津人，博士生，主要从事组合结构研究(E-mail: wang305856596@163.com)

杨　松(1980−)，男，贵州人，博士生，主要从事工程结构研究(E-mail: yangsong277@126.com)

陈　钒(1972−)，男，江西人，教授级高工，博士，主要从事隧道工程稳定性研究(E-mail: 737123124@qq.com)

丁　然(1988−)，男，安徽人，助理研究员，博士，主要从事新材料结构和组合结构研究工作(E-mail: dingran@mail.tsinghua.edu.cn)

通讯作者:
樊健生(1975−)，男，山东人，教授，博士，博导，主要从事组合结构教学与研究(E-mail: fanjsh@tsinghua.edu.cn)

中图分类号: U443.31
计量
- 文章访问数: 632
- HTML全文浏览量: 243
- PDF下载量: 120
- 被引次数: 0
出版历程
- 收稿日期: 2020-06-06
- 修回日期: 2020-09-14
- 网络出版日期: 2021-04-27
- 刊出日期: 2021-04-14

RESEARCH ON PUNCHING SHEAR AND BENDING BEHAVIOR OF ULTRA-HIGH PERFORMANCE CONCRETE SLABS

FAN Jian-sheng^{1, 2
, ,},
WANG Zhe^1
,,
YANG Song^3
,,
CHEN Fan^4
,,
DING Ran^{1, 2
,}

1.
Department of Civil Engineering, Tsinghua University, Beijing 100084, China
2.
Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry, Tsinghua University, Beijing 100084, China
3.
Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China
4.
Power China Road Bridge Group Co., Ltd., Beijing 100048, China

摘要

摘要: 超高性能混凝土(Ultra-high performance concrete，简称UHPC)桥面板具有良好的应用前景。桥面板在车轮荷载作用下存在冲切和弯曲问题，以此为背景设计了系列UHPC板件试验，主要研究板的厚度、保护层厚度、配筋率及加载区域面积等参数对试验板抗冲切及抗弯性能的影响，分析了不同试件的破坏模式、挠度、应变分布以及整体延性等，并提出UHPC板抗冲切极限承载力计算方法。试验结果表明：UHPC板的破坏模式包括冲切破坏、弯曲破坏和二者混合的冲弯破坏；相比于C50混凝土板，UHPC板的刚度、抗冲切承载力及位移延性有显著提高；随着板厚增大、保护层厚度减小、加载区域增大，UHPC板的抗冲切承载力提高。经过试验数据验证，抗冲切及抗弯承载力的计算值与试验值吻合良好。
- 桥梁工程 /
- 冲切性能 /
- 弯曲性能 /
- 静力试验 /
- 超高性能混凝土板 /
- 计算方法
Abstract: Ultra-high performance concrete (UHPC) bridge deck has good prospects for engineering application. In order to study the punching shear and bending behavior of bridge deck under wheel loading, a series of UHPC slab tests were designed. The effects of slab thickness, cover thickness, reinforcement ratio and loading area on the punching shear and bending behavior of the slabs were studied. The failure modes, the deflection, the strain distribution and the ductility of different specimens were analyzed. And the calculation methods of punching shear capacities of UHPC slabs were proposed. The test results show that the failure mode includes punching shear, flexure and mixed punching-flexure mode. The stiffness, the punching capacity, the ductility and the energy absorption capacity of the UHPC slabs are much higher, compared with the C50 concrete slab. And the punching shear capacity of UHPC slabs increases with the increase of slab thickness, with the decrease of cover thickness and with the increase of loading area. Verified by the test data, the calculated values of punching shear and bending bearing capacity are in a good agreement with the test values.
- bridge engineering /
- punching shear behavior /
- bending behavior /
- static test /
- ultra-high performance concrete /
- calculation method

HTML全文

图 1 实际组合桥面系示意图

Figure 1. Composite deck system

下载: 全尺寸图片幻灯片

图 2 试验板设计

Figure 2. Test specimen design

下载: 全尺寸图片幻灯片

图 3 加载示意图

Figure 3. Test setup

下载: 全尺寸图片幻灯片

图 4 测点布置图　/mm

Figure 4. Arrangement of measurement devices

下载: 全尺寸图片幻灯片

图 5 试验板冲切破坏

Figure 5. Punching shear failure pattern

下载: 全尺寸图片幻灯片

图 6 试验板弯曲破坏

Figure 6. Bending failure pattern

下载: 全尺寸图片幻灯片

图 7 试验板冲弯破坏

Figure 7. Punching & bending failure pattern

下载: 全尺寸图片幻灯片

图 8 荷载-挠度曲线

Figure 8. Load-deflection curves

下载: 全尺寸图片幻灯片

图 9 跨中变形模式

Figure 9. Deflection at mid span

下载: 全尺寸图片幻灯片

图 10 板顶应变分布

Figure 10. Strain distribution on top surface of slabs

下载: 全尺寸图片幻灯片

图 11 钢筋应变分布

Figure 11. Strain distribution on reinforcement

下载: 全尺寸图片幻灯片

图 12 冲切破坏机制

Figure 12. Punching shear failure mechanism

下载: 全尺寸图片幻灯片

图 13 理论承载力与试验承载力对比

Figure 13. Comparison between theoretical and experimental bearing capacity

下载: 全尺寸图片幻灯片

图 14 抗弯承载力计算流程

Figure 14. Calculating procedure of flexural capacity

下载: 全尺寸图片幻灯片

图 15 钢筋及钢板本构关系

Figure 15. Constitutive relation of rebar and steel plate

下载: 全尺寸图片幻灯片

表 1 试件基本参数

Table 1. Details of tested slabs

序号	试件编号	混凝土材料	跨高比	板厚 h/mm	加载区域边长a/mm	保护层厚度c/mm	冲跨比	纵向配筋	横向配筋
1	OS-1	UHPC	11.5	52	40	10	7.8	12@50	8@50
2	OS-2	UHPC	15.0	40	40	10	11.7	12@50	8@50
3	OS-3	UHPC	10.0	60	40	10	6.4	12@50	8@50
4	OS-4	UHPC	12.0	50	40	6	7.4	12@50	8@50
5	OS-5	UHPC	12.0	50	40	15	9.7	12@50	8@50
6	OS-6	UHPC	9.5	63	40	6	5.5	12@50	8@50
7	OS-7	UHPC	9.8	61	40	20	8.0	12@50	8@50
8	OS-8	UHPC	12.0	50	40	10	7.8	8@100	8@100
9	OS-9	UHPC	11.3	53	40	10	7.2	8@200	8@200
10	OS-10	UHPC	11.3	53	70	10	7.2	12@50	8@50
11	OS-11	UHPC	11.3	53	100	10	6.8	12@50	8@50
12	OS-12	普通混凝土	11.5	52	40	10	7.8	12@50	8@50

下载: 导出CSV

表 2 UHPC配合比

Table 2. Mix proportions of UHPC

组分	用量/(kg/m³)
水泥	870
硅灰	180
超细矿粉	240
细砂	1000
平直钢纤维	195
减水剂	27.27
水	199

下载: 导出CSV

表 3 材料力学性能

Table 3. Material properties

材料	指标	数值
C50	f_c/MPa	38.0
	f_t /MPa	3.2
	E_c/MPa	34 500
UHPC	f_c/MPa	149.0
	f_t /MPa	7.9
	f_tu /MPa	9.0
	E_c /MPa	45 400
8 mm钢筋	f_y /MPa	456.8
	f_u /MPa	682.9
	E_rs /MPa	206 000
12 mm钢筋	f_y /MPa	488.6
	f_u /MPa	626.7
	E_rs /MPa	206 000
注：f_c为混凝土轴心抗压强度；f_t为混凝土轴心抗拉初裂强度；f_tu为混凝土轴心抗拉极限强度；E_c为混凝土弹性模量；f_y为钢筋屈服强度；f_u为钢筋极限强度；E_rs为钢筋弹性模量。

下载: 导出CSV

表 4 试验板延性

Table 4. Ductility of slabs

试件编号	P_u /kN	Δ_u /mm	S_u /(N·m)	Δ_u/Δ_y
OS-1	162.7	15.55	1853.6	1.87
OS-2	102.9	17.94	1258.7	1.57
OS-3	179.4	7.13	783.5	1.29
OS-4	148.5	8.73	811.6	1.34
OS-5	147.5	15.16	1648.7	1.90
OS-6	213.7	5.54	715.9	1.26
OS-7	176.9	9.54	1077.4	1.38
OS-8	99.2	11.51	888.9	2.25
OS-9	86.7	8.35	539.7	1.96
OS-10	214.2	18.40	2923.6	1.93
OS-11	236.5	13.06	2123.0	1.60
OS-12	68.7	5.80	234.1	1.21
注：P_u为试件极限承载力；Δ_u为极限承载力对应的位移；S_u为试件达到极限承载力时吸收的能量；Δ_u/Δ_y为位移延性系数。

下载: 导出CSV

表 5 抗冲切及抗弯承载力计算

Table 5. Calculation of punching shear and flexural capacity

试件编号	试验值P_u /kN	抗冲切承载力计算值P_pun /kN	P_pun/P_u	抗弯承载力计算值P_flex /kN	P_flex/P_u	预测破坏模式	实际破坏模式
OS-1	162.7	141.1	0.87	219.8	1.35	冲切	冲切
OS-2	102.9	102.7	1.00	133.9	1.30	冲切	冲切
OS-3	179.4	181.5	1.01	283.4	1.58	冲切	冲切
OS-4	148.5	145.2	0.98	228.2	1.54	冲切	冲切
OS-5	147.5	129.7	0.88	177.5	1.20	冲切	冲切
OS-6	213.7	198.0	0.93	333.8	1.56	冲切	冲切
OS-7	176.9	178.0	1.01	232.8	1.32	冲切	冲切
OS-8	99.2	109.9	1.11	93.5	0.94	受弯	受弯
OS-9	86.7	121.8	1.41	80.5	0.93	受弯	受弯
OS-10	214.2	176.9	0.83	227.2	1.06	冲切	冲弯
OS-11	236.5	203.2	0.86	227.2	0.96	冲切	冲弯
注：预测破坏模式的判断依据为试件抗冲切承载力计算值与抗弯承载力计算值的相对大小，二者中的较低值即为试件的承载力预测值，相对应的破坏模式即为试件的预测破坏模式。

下载: 导出CSV

表 6 抗冲切承载力计算公式验证

Table 6. Verification of calculation formula of punching shear capacity

来源	总序号	加载区域/mm	板厚/mm	f_ct/MPa	f_c/MPa	纵向净跨/mm	横向净跨/mm	配筋率/(%)	λ_f	P_u/kN	P_pun/kN
本文	1	40.0	52.0	9.0	149.0	600	800	4.3	1.63	162.7	142.3
	2	40.0	40.0	9.0	149.0	600	800	5.7	1.63	102.9	103.4
	3	40.0	60.0	9.0	149.0	600	800	3.8	1.63	179.7	183.1
	4	40.0	50.0	9.0	149.0	600	800	4.5	1.63	148.5	135.4
	5	40.0	50.0	9.0	149.0	600	800	4.5	1.63	147.5	130.9
	6	40.0	63.0	9.0	149.0	600	800	3.6	1.63	213.7	199.8
	7	40.0	61.0	9.0	149.0	600	800	3.7	1.63	176.9	179.7
	8	70.0	53.0	9.0	149.0	600	800	4.3	1.63	214.2	179.4
	9	100.0	53.0	9.0	149.0	600	800	4.3	1.63	236.5	202.9
文献[19]	10	200.0	130.0	4.0	63.4	1100	1100	1.3	0.25	453.0	612.8
	11	200.0	130.0	4.3	62.5	1100	1100	1.3	0.50	525.0	615.2
	12	200.0	130.0	4.6	64.2	1100	1100	1.3	0.75	611.0	635.7
	13	200.0	130.0	5.0	64.9	1100	1100	1.3	1.00	672.2	648.3
	14	200.0	130.0	4.6	63.5	1100	1100	1.0	0.75	531.0	614.6
	15	200.0	130.0	4.6	63.5	1100	1100	1.7	0.75	752.8	649.0
	16	200.0	120.0	4.6	63.5	1100	1100	1.4	0.75	560.2	566.7
	17	200.0	150.0	4.6	63.5	1100	1100	1.1	0.75	753.8	764.0
	18	200.0	150.0	4.6	63.5	1100	1100	1.1	0.75	813.5	764.0
	19	200.0	130.0	3.9	53.5	1100	1100	1.3	0.50	501.3	550.9
	20	200.0	130.0	4.2	52.6	1100	1100	1.3	0.75	566.4	546.1
	21	200.0	150.0	4.2	52.6	1100	1100	1.1	0.75	702.5	658.6
文献[21]	22	200.0	50.0	6.2	124.0	1000	1000	2.5	1.30	325.0	276.1
	23	200.0	50.0	5.2	103.0	1000	1000	2.5	1.30	250.0	267.0
	24	200.0	50.0	5.5	110.0	1000	1000	2.5	1.30	295.0	271.0
	25	200.0	50.0	6.0	120.0	1000	1000	2.5	1.30	240.0	275.1
	26	200.0	50.0	6.4	127.0	1000	1000	2.5	1.30	355.0	276.7
文献[26]	27	38.1	55.1	11.0	221.3	914	914	0	1.30	103.6	95.1
	28	50.8	58.9	11.0	221.3	914	914	0	1.30	121.0	126.5
	29	25.4	53.8	11.0	221.3	914	914	0	1.30	100.5	81.0
	30	50.8	66.3	11.0	221.3	914	914	0	1.30	146.8	178.4
	31	38.1	64.5	11.0	221.3	914	914	0	1.30	135.7	154.7
	32	38.1	71.9	11.0	221.3	914	914	0	1.30	156.6	209.2
	33	25.4	77.0	11.0	221.3	914	914	0	1.30	178.4	235.9
文献[34]	34	50.0	30.0	13.7	126.6	1200	1200	0	1.34	42.2	48.9
	35	50.0	40.0	13.7	126.6	1200	1200	0	1.34	69.0	81.7
	36	50.0	50.0	13.7	126.6	1200	1200	0	1.34	119.0	121.4
	37	50.0	60.0	13.7	126.6	1200	1200	0	1.34	160.8	167.9
	38	50.0	40.0	12.3	124.0	1200	1200	0	0.90	71.7	80.4
	39	50.0	40.0	5.8	121.0	1200	1200	0	0.45	50.3	70.9
注：λ_f为钢纤维含量特征参数，λ_f=钢纤维体积掺量×钢纤维长度/钢纤维直径。

下载: 导出CSV

参考文献(36)

[1]	陈宝春, 韦建刚, 苏家战, 等. 超高性能混凝土应用进展[J]. 建筑科学与工程学报, 2019, 36(2): 10 − 20. doi: 10.3969/j.issn.1673-2049.2019.02.003 Chen Baochun, Wei Jiangang, Su Jiazhan, et al. State-of-the-art progress on application of Ultra High Performance Concrete [J]. Journal of Architecture and Civil Engineering, 2019, 36(2): 10 − 20. (in Chinese) doi: 10.3969/j.issn.1673-2049.2019.02.003
[2]	Russell H G, Graybeal B A. Ultra High Performance Concrete: a state-of-the-art report for the bridge community [R]. United States: Federal Highway Administration, Office of Infrastructure Research and Development, 2013.
[3]	徐明雪, 梁兴文, 汪萍, 王照耀. 超高性能混凝土梁正截面受弯承载力理论研究[J]. 工程力学, 2019, 36(8): 70 − 78. Xu Mingxue, Liang Xingwen, Wang Ping, Wang Zhaoyao. Theoretical investigation on normal section flexural capacity of uhpc beams [J]. Engineering Mechanics, 2019, 36(8): 70 − 78. (in Chinese)
[4]	王景全, 王震, 高玉峰, 诸钧政. 预制桥墩体系抗震性能研究进展: 新材料、新理念、新应用[J]. 工程力学, 2019, 36(3): 1 − 23. Wang Jingquan, Wang Zhen, Gao Yufeng, Zhu Junzheng. Review on aseismic behavior of precast piers: new material, new concept, and new application [J]. Engineering Mechanics, 2019, 36(3): 1 − 23. (in Chinese)
[5]	刘君平, 徐帅, 陈宝春. 钢-UHPC组合梁与钢-普通混凝土组合梁抗弯性能对比试验研究[J]. 工程力学, 2018, 35(11): 92 − 98, 145. doi: 10.6052/j.issn.1000-4750.2017.06.0454 Liu Junping, Xu Shuai, Chen Baochun. Experimental study on flexural behaviors of steel-UHPC composite girder and steel-conventional concrete composite girder [J]. Engineering Mechanics, 2018, 35(11): 92 − 98, 145. (in Chinese) doi: 10.6052/j.issn.1000-4750.2017.06.0454
[6]	Zhang Z Y, Ding R, Nie X, Fan J S. Seismic performance of a novel interior precast concrete beam-column joint using Ultra High Performance Concrete [J]. Engineering Structures, 2020, 222: 111145. doi: 10.1016/j.engstruct.2020.111145
[7]	Wang Z, Nie X, Fan J S, Lu X Y, Ding R. Experimental and numerical investigation of the interfacial properties of non-steam-cured UHPC-steel composite beams [J]. Construction and Building Materials, 2019, 195: 323 − 339. doi: 10.1016/j.conbuildmat.2018.11.057
[8]	徐海宾, 邓宗才. 超高性能混凝土在桥梁工程中的应用[J]. 世界桥梁, 2012, 40(3): 63 − 67. Xu Haibin, Deng Zongcai. Application of Ultra High Performance Concrete in bridge engineering [J]. World Bridges, 2012, 40(3): 63 − 67. (in Chinese)
[9]	陈宝春, 季韬, 黄卿维, 等. 超高性能混凝土研究综述[J]. 建筑科学与工程学报, 2014, 31(3): 1 − 24. doi: 10.3969/j.issn.1673-2049.2014.03.002 Chen Baochun, Ji Tao, Huang Qingwei, et al. Review of research on Ultra High Performance Concrete [J]. Journal of Architecture and Civil Engineering, 2014, 31(3): 1 − 24. (in Chinese) doi: 10.3969/j.issn.1673-2049.2014.03.002
[10]	Graybeal B A. Material property characterization of Ultra High Performance Concrete [R]. United States: Federal Highway Administration, Office of Infrastructure Research and Development, 2006.
[11]	Shafieifar M, Farzad M, Azizinamini A. Experimental and numerical study on mechanical properties of Ultra High Performance Concrete (UHPC) [J]. Construction and Building Materials, 2017, 156: 402 − 411. doi: 10.1016/j.conbuildmat.2017.08.170
[12]	Ahlborn T M, Peuse E J, Misson D L. Ultra High Performance Concrete for Michigan bridges, material performance: phase I [R]. Michigan: Dept. of Transportation, 2008.
[13]	赵金侠, 黄亮, 谢建和. 不同配比和养护条件对超高性能混凝土微观结构的影响[J]. 中国公路学报, 2019, 32(7): 111 − 119. Zhao Jinxia, Huang Liang, Xie Jianhe. Effects of mix proportion and curing condition on the microstructure of Ultra High Performance Concrete [J]. China Journal of Highway and Transport, 2019, 32(7): 111 − 119. (in Chinese)
[14]	Wu Z, Shi C, He W, et al. Effects of steel fiber content and shape on mechanical properties of Ultra High Performance Concrete [J]. Construction and building materials, 2016, 103: 8 − 14. doi: 10.1016/j.conbuildmat.2015.11.028
[15]	Meng W, Samaranayake V A, Khayat K H. Factorial design and optimization of Ultra High Performance Concrete with lightweight sand [J]. ACI Materials Journal, 2018, 115(1): 129 − 138.
[16]	王俊颜, 边晨, 肖汝诚, 马骉. 不同轴拉性能的超高性能混凝土圆环约束收缩性能[J]. 中国公路学报, 2019, 32(9): 115 − 123. Wang Junyan, Bian Chen, Xiao Rucheng, Ma Biao. Restrained shrinkage behavior in ring test of Ultra High Performance Concrete with different tensile properties [J]. China Journal of Highway and Transport, 2019, 32(9): 115 − 123. (in Chinese)
[17]	史才军, 肖江帆, 曹张, 等. 材料组成对UHPC性能的影响[J]. 硅酸盐通报, 2013, 32(6): 1005 − 1011. Shi Caijun, Xiao Jiangfan, Cao Zhang, et al. Effects of UHPC constituents on its properties [J]. Bulletin of the Chinese Ceramic Society, 2013, 32(6): 1005 − 1011. (in Chinese)
[18]	Graybeal B A, Baby F. Tension testing of Ultra High Performance Concrete [R]. 6300 Georgetown Pike McLean, VA: United States, Federal Highway Administration, Office of Infrastructure Research and Development, 2019.
[19]	林旭健, 郑作樵, 钱在兹. 钢纤维高强混凝土冲切板的试验研究[J]. 建筑结构学报, 2003, 24(5): 72 − 77, 97. doi: 10.3321/j.issn:1000-6869.2003.05.010 Lin Xujian, Zheng Zuoqiao, Qian Zaici. Research on steel fiber High Strength Concrete slab subjected to punching shear [J]. Journal of Building Structures, 2003, 24(5): 72 − 77, 97. (in Chinese) doi: 10.3321/j.issn:1000-6869.2003.05.010
[20]	谢晓鹏. 钢筋局部钢纤维高强混凝土板冲切性能研究[D]. 郑州: 郑州大学, 2007. Xie Xiaopeng. Research on punching shear behavior of steel fiber locally reinforced concrete slabs with reinforcement [D]. Zhengzhou: Zhengzhou University, 2007. (in Chinese)
[21]	陈浩. UHPC桥面板抗冲切性能及承载力计算方法研究[D]. 福州: 福州大学, 2017. Chen Hao. Research on punching shear performance and bearing capacity calculation method of UHPC bridge deck [D]. Fuzhou: Fuzhou University, 2017. (in Chinese)
[22]	Bunje K, Fehling E. About shear force and punching shear resistance of structural elements of Ultra High Performance Concrete [C]// International Symposium on UHPC. Kassel, Germany, 2004: 401 − 411.
[23]	Moreillon L, Nseir J, Suter R. Shear and flexural strength of thin UHPC slabs [C]// International Symposium on UHPC and Nanotechnology for High Performance Construction Materials. Kassel, Germany, 2012: 749 − 756.
[24]	曹清. 混凝土箱梁顶板受力性能的理论及试验研究[D]. 长沙: 湖南大学, 2017. Cao Qing. Theoretical and experimental investigation on mechanical performance of top slabs in concrete box girder [D]. Changsha: Hunan University, 2017. (in Chinese)
[25]	CECS 38 − 2004, 纤维混凝土结构技术规程[S]. 北京: 中国计划出版社, 2004. CECS 38 − 2004, Technical specification for fiber reinforced concrete structures [S]. Beijing: China Planning Press, 2004. (in Chinese)
[26]	Harris D K. Characterization of punching shear capacity of thin UHPC plates [D]. Virginia: Virginia Tech, 2004.
[27]	Al-Quraishi H A A. Punching shear behavior of UHPC flat slabs [D]. Kassel: University of Kassel, 2014.
[28]	Xie T, Ali M S M, Visintin P. Behaviour and analysis of Ultra High Performance Fibre Reinforced Concrete (UHPFRC) skew slabs [J]. Engineering Structures, 2019, 199: 109588. doi: 10.1016/j.engstruct.2019.109588
[29]	姚玲森. 桥梁工程 [M]. 北京: 人民交通出版社, 2008. Yao Lingsen. Bridge engineering [M]. Beijing: China Communications Press, 2008. (in Chinese)
[30]	郭晓宇, 亢景付, 朱劲松. 超高性能混凝土单轴受压本构关系[J]. 东南大学学报(自然科学版), 2017, 47(2): 369 − 376. doi: 10.3969/j.issn.1001-0505.2017.02.028 Guo Xiaoyu, Kang Jingfu, Zhu Jingsong. Constitutive relationship of Ultra High Performance Concrete under uniaxial compression [J]. Journal of Southeast University (Natural Science Edition), 2017, 47(2): 369 − 376. (in Chinese) doi: 10.3969/j.issn.1001-0505.2017.02.028
[31]	T/CBMF 37−2018, T/CCPA 7−2018, 超高性能混凝土基本性能与试验方法[S]. 北京: 中国建材工业出版社, 2018. T/CBMF 37−2018, T/CCPA 7−2018, Ultra-high performance concrete - basic performance and test method [S]. Beijing: China Building Materials Press, 2018. (in Chinese)
[32]	俞茂宏, 刘凤羽. 双剪应力三参数准则及其角隅模型[J]. 土木工程学报, 1988(3): 90 − 95. Yu Maohong, Liu Fengyu. Twin shear stress three parameter criterion and its corner model [J]. China Civil Engineering Journal, 1988(3): 90 − 95. (in Chinese)
[33]	Dresden G. Ultra High Performance Concrete under biaxial compression [C]// International Symposium on Ultra High Performance Concrete. Kassel, Germany, 2008: 477 − 484.
[34]	Park J H. Estimation of punching shear on UHPC slab [D]. Seoul: Seoul National University, 2015.
[35]	AFGC. Ultra High Performance Fibre Reinforced Concretes recommendations [S]. France: AFGC publication, 2013.
[36]	Esmaeily A, Xiao Y. Behavior of reinforced concrete columns under variable axial loads: analysis [J]. ACI Structural Journal, 2005, 102(5): 736 − 744.