基于DIC的含3D打印起伏節理試樣破裂特性及損傷本構

王本鑫; 金愛兵; 趙怡晴; 孫浩; 劉加柱

doi:10.13374/j.issn2095-9389.2021.04.11.001

基于DIC的含3D打印起伏節理試樣破裂特性及損傷本構

doi: 10.13374/j.issn2095-9389.2021.04.11.001

王本鑫^{1, 2, 3, 4},
金愛兵^{1, 2},
趙怡晴^{1, 2, ,},
孫浩^{1, 2},
劉加柱^{1, 2}

1.
北京科技大學金屬礦山高效開采與安全教育部重點實驗室，北京 100083
2.
北京科技大學土木與資源工程學院，北京 100083
3.
查爾姆斯理工大學建筑與土木工程學院，哥德堡 41296
4.
五礦有色金屬股份有限公司，北京 100044

基金項目: 國家自然科學基金資助項目（52004017，52174106）；中國博士后科學基金資助項目（2020M670138）；中央高校基本科研業務費專項資金資助項目（FRF-TP-19-026A1）

詳細信息

通訊作者:
E-mail: yiqingzhao@126.com

中圖分類號: TU45.1
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- 被引次數: 0
出版歷程
- 收稿日期: 2021-04-11
- 網絡出版日期: 2021-05-31
- 刊出日期: 2022-12-01

Fracture characteristics and the damage constitutive model of 3D printing undulating joint samples based on DIC

WANG Ben-xin^{1, 2, 3, 4},
JIN Ai-bing^{1, 2},
ZHAO Yi-qing^{1, 2
, ,},
SUN Hao^{1, 2},
LIU Jia-zhu^{1, 2}

1.
Key Laboratory of Ministry of Education for Efficient Mining and Safety of Metal Mines, University of Science and Technology Beijing, Beijing 100083, China
2.
School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China
3.
Department of Architecture and Civil Engineering, Chalmers University of Technology, Gothenburg 41296, Sweden
4.
China Minmetals Nonferrous Metals Co., LTD, Beijing 100044, China

More Information

Corresponding author: E-mail: yiqingzhao@126.com

摘要

摘要: 受地質構造的影響，巖體工程中經常賦存起伏結構面(如扭轉皺褶)，由于形態復雜，目前起伏節理巖體的破裂及損傷本構研究仍不充分. 采用3D打印技術制作不同傾角的起伏節理模型，通過單軸壓縮試驗和數字圖像相關技術(DIC)對起伏節理試樣的力學及破裂特性進行研究，并基于斷裂力學原理，首次提出采用DIC位移場求解節理尖端應力強度因子(SIF：一型SIF，K_I；二型SIF，K_II)進而探究損傷本構特性的思路. 結果表明：通過分析最小強度確定了起伏節理對試樣的損傷上限為46.6%，起伏節理試樣單軸強度對傾角的敏感性大于平直節理試樣；起裂發生在峰值應力附近，破裂過程可分為破裂路徑上微裂隙的產生和同步貫通，破裂模式表現為多條裂隙張剪組合模式；峰前SIF隨荷載增加而增加，峰后同一荷載下K_II>K_I，節理左右兩端均勻以剪切裂隙形式擴展；起伏節理對試樣的損傷與傾角呈正弦關系，節理和荷載對試樣的總損傷與應變均大致呈“S”型曲線.
- 起伏節理 /
- 數字圖像相關技術(DIC) /
- 應力強度因子 /
- 破裂特性 /
- 損傷本構
Abstract: Due to the influence of geological structures, various forms of joint structural planes are present in rock mass engineering. The undulating structural planes, such as a torsional fold surface, are unique geological structures. These structures affect the stability of rock masses and cause potential hazards to rock mass engineering. Because of their shape complexity, the research on the fracture and damage constitutive law of rock mass with undulating joints is not thoroughly conducted. Undulating joints with various dip angles were fabricated using three-dimensional printing technology. The uniaxial compression test and digital image correlation (DIC) technology were used to study the mechanical and fracture characteristics of undulating joint specimens. Based on the principle of fracture mechanics, an idea was proposed to use the DIC displacement field for solving the stress intensity factor (SIF: type one K_I and type two K_II) at the joint tips and to study the damage constitutive law. The results show that the upper limit of undulating joint damage to specimens is determined with 46.6% through the minimum strength analysis. The sensitivity of uniaxial strength to a joint dip angle of undulating joint specimen is greater than that of a straight joint specimen. The fracture initiation occurs near peak stress. The fracture process can be divided into the initiation and synchronous penetration of microcracks on the fracture path. Additionally, the fracture mode shows a combination of multiple tension and shear fractures. The SIF increases with loading at the prepeak stage, and the cracks propagate in shear fracture at the joint left and right tips in the postpeak stage because K_II>K_I under the same stress. The undulating joint damage to the specimen with the dip angle is in a sinusoidal curve form. The relationships between the total damage coupled by joint and load with strain are all “S” curves.
- undulating joint /
- DIC /
- stress intensity factor /
- fracture characteristics /
- damage constitutive model

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圖 1 含3D打印起伏節理試樣制作流程示意圖

Figure 1. Schematic diagram of the production process of specimens with 3D printing of undulating joints

下載: 全尺寸圖片幻燈片

圖 2 起伏節理試件幾何參數示意圖

Figure 2. Schematic diagram of geometric parameters of an undulating joint specimen

下載: 全尺寸圖片幻燈片

圖 3 單軸壓縮測試系統示意圖

Figure 3. Schematic diagram of a uniaxial compressive test system

下載: 全尺寸圖片幻燈片

圖 4 試樣的應力?應變曲線

Figure 4. Stress?strain curves of joint specimens

下載: 全尺寸圖片幻燈片

圖 5 不同傾角起伏節理和平直節理試樣的單軸強度對比

Figure 5. Comparison of the uniaxial strength of undulating and straight joints specimen with various dip angles

下載: 全尺寸圖片幻燈片

圖 6 不同傾角起伏節理試樣的ε₁主應變云圖

Figure 6. ε₁ principal strain nephogram of undulating joint specimens with various dip angles

下載: 全尺寸圖片幻燈片

圖 7 試樣的破裂模式. (a)起伏節理試樣；(b)平直節理試樣

Figure 7. Fracture modes of: (a) undulating joint specimens; (b) straight joint specimens

下載: 全尺寸圖片幻燈片

圖 8 α=45°起伏節理試樣破裂隨應力?應變的演化過程

Figure 8. Fracture evolution in an undulating joint specimen with stress?strain at α = 45°

下載: 全尺寸圖片幻燈片

圖 9 節理尖端極坐標示意圖

Figure 9. Polar coordinate diagram of a joint tip

下載: 全尺寸圖片幻燈片

圖 10 應力峰值和峰后破裂時各試樣的SIF

Figure 10. SIF in specimens at peak stress and postpeak stress

下載: 全尺寸圖片幻燈片

圖 11 α=30°試樣應力、節理兩端SIF和水平位移場隨時間的變化

Figure 11. Variation of stress, SIF at both ends of joints and horizontal displacement field with time in a specimen with α = 30°

下載: 全尺寸圖片幻燈片

圖 12 不同傾角條件下節理尖端SIF_P/σ_max和α的擬合關系

Figure 12. Fitting relationship between SIF_P/σ_max of joint tips and α in various deformation stages

下載: 全尺寸圖片幻燈片

圖 13 節理損傷D_j隨節理傾角α的變化

Figure 13. Change in joint damage D_j with joint dip angle α

下載: 全尺寸圖片幻燈片

圖 14 不同傾角條件下總損傷D_js演化曲線

Figure 14. Evolution curves of total damage D_js under various dip angles

下載: 全尺寸圖片幻燈片

圖 15 不同傾角條件下試樣的應力?應變關系

Figure 15. Stress?strain relationship under various dip angles

下載: 全尺寸圖片幻燈片

表 1 不同變形階段節理尖端SIF

Table 1. SIF of joint tips at various deformation stages

SIF/(MPa·m^0.5)	Deformation stages	Joint angle, α/(°)
SIF/(MPa·m^0.5)	Deformation stages	0	30	45	60	90
K_I__l	Compaction	0.26	0.23	0.35	0.38	0.30
	Elasticity	0.27	0.35	0.51	0.77	0.45
	Yield	0.36	0.35	0.70	1.00	0.52
	Peak	0.52	0.43	0.91	1.10	0.58
	Post peak	0.32	0.57	1.25	1.53	0.64
K_II__l	Compaction	0.35	0.26	0.31	0.42	0.34
	Elasticity	0.37	0.41	0.71	0.83	0.53
	Yield	0.43	0.41	0.83	1.10	0.62
	Peak	0.41	0.49	0.85	1.18	0.69
	Post peak	0.36	0.66	1.34	1.62	0.77
K_{I_r}	Compaction	0.10	0.06	0.03	0.04	0.07
	Elasticity	0.11	0.09	0.06	0.09	0.10
	Yield	0.13	0.10	0.07	0.11	0.11
	Peak	0.12	0.10	0.08	0.12	0.13
	Post peak	0.11	0.14	0.16	0.16	0.12
K_{II_r}	Compaction	1.36	0.22	0.09	0.11	0.24
	Elasticity	1.42	0.32	0.16	0.21	0.33
	Yield	1.74	0.32	0.18	0.26	0.37
	Peak	1.56	0.37	0.19	0.28	0.42
	Post peak	1.48	0.52	0.21	0.35	0.40

下載: 導出CSV

表 2 擬合曲線對應公式系數

Table 2. Corresponding formula coefficient of a fitting curve

SIF_P/σ_max	a₀	a₁	b₁	w
K_I_r/σ_max	?0.02906	0.03421	0.3566	0.007055
K_II_r/σ_max	6.444	?6.374	0.8606	?0.1331
K_I_l/σ_max	0.03958	?0.02441	?0.01834	3.365
K_II_l/σ_max	0.04643	?0.02781	?0.01712	3.31

下載: 導出CSV

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