Dynamic split tests of UHPFRC discs and failure mechanism analysis based on μXCT images
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摘要: 采用分离式霍普金森压杆对钢纤维体积分数为0~3%的超高性能纤维增强混凝土(ultra high performance fibre reinforced concrete, UHPFRC)圆盘试件进行应变率为1.72~7.42 s−1的动态劈裂试验,使用高速摄像机结合数字图像相关(digital image correlation, DIC)法获得试件表面裂缝扩展全过程图像和应变演化过程,并对冲击前后试件进行微观X射线计算断层扫描(micro X-ray computed tomography, μXCT),获得分辨率为56.7 μm的三维内部图像,并进行统计和破坏机理分析。结果表明:(1)相比无纤维试件,掺入1%~3%的钢纤维,静、动劈裂强度分别提高84%~131%和47%~87%,动劈裂强度增强因子(即动静强度比值)为1.07~1.72;(2) DIC应变图像分析表明,无纤维试件裂缝集中、破坏快、能耗低;含纤维试件裂缝弥散程度大、能耗高、延性好,且随着纤维含量的提高而提升;(3) μXCT图像分析表明,试件中钢纤维体积分数为1.04%~2.47%,与设计基本一致,孔洞体积分数为0.98%~1.71%,纤维掺量的提高,降低了孔洞数量和总体积分数,但孔洞的平均体积和平均等效直径增大;裂缝桥连纤维数量的增加,减小了主裂缝的体积和平均宽度,提高了裂缝面的粗糙度和相对表面积,从而提高了试件的强度、能耗、韧性和延性。
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关键词:
- 动态劈裂 /
- 超高性能纤维增强混凝土 /
- 微观X射线计算断层扫描 /
- 断裂机理 /
- 数字图像相关
Abstract: In order to better investigate the dynamic tensile properties and damage mechanism of ultra-high performance fibre reinforced concrete (UHPFRC), dynamic split tests with the strain rates of 1.72-7.42 s-1 were carried out by a split Hopkinson pressure bar for UHPFRC discs with the fibre volume fractions of 0-3%. The surface crack propagation processes of the UHPFRC discs were captured by a high-speed camera and the images were analyzed by the digital image correlation (DIC) technique for strain evolution. Micro X-ray computed tomography (μXCT) scanning of the UHPFRC disc specimens before and after the dynamic tests was also conducted. The 3D images of the internal micro structures of the specimens with a voxel resolution of 56.7 μm were reconstructed, and they were then processed to statistically quantify the distribution, volume fractions and sizes of pores, fibres and cracks. Moreover, the dynamic failure mechanisms, such as pullout from the matrix, bending and breakage of steel fibres, crack propagation and merging in the mortar, etc., were visualized and analyzed. The main results obtained are as follows. (1) The addition of 1%-3% steel fibres raises the static and dynamic splitting strength by 84%-131% and 47%-87%, respectively. The dynamic increase factor (ratio of dynamic to static strength) is 1.07-1.72. (2) DIC images demonstrate that the fibres lead to more dispersed cracks, slower crack propagation, higher energy consumption and higher ductility. (3) The μXCT image analysis shows that the fibre volume fraction is 1.04%-2.47%, consistent with the designed proportion, while the porosity is 0.98%-1.71%. Fibres reduce the porosity and the number of pores, but increase their average volume and equivalent diameter. The increase of crack-bridging fibres reduces the volume and width of main cracks and raises the surface roughness and the relative surface area of cracks, resulting in the increase of strength, energy dissipation, toughness and ductility of specimens. The research data are useful for improvement of dynamic design guidelines and optimization for UHPFRC materials and structures. -
立井井筒开挖主要施工方式钻爆法中,随着立井井筒施工综合机械化水平提升,炮孔深度随之不断增加。炮孔深度超过5 m时,现有的孔内连续装药的形式难以满足高效掘进[1-2]。为此,本文针对孔内分段装药结构,开展爆炸应变场以及裂隙场研究。
针对条形柱状药包爆炸研究,颜事龙等[3]采用高速摄影对有机玻璃中条形药包破碎区分布特征进行研究,认为条型药包粉碎区可分为柱部和端部两个区域,端部的破坏效应比柱部弱,并且从中部到端部发展速度逐渐减弱。龚敏等[4-5]运用三维动态光弹性爆破模型实验系统,首次对条型药包端部、中间及两端同时起爆条件下物理模型应力场进行研究,发现两端同时起爆及中间起爆的应力场强度的分布比较均匀。郭洋等[6]以高速摄影和数值模拟为手段,研究不同位置起爆柱状药包爆生裂纹扩展和损伤破碎特征,得出正反向起爆时炮孔周围产生多条径向裂纹,爆生裂纹面经历了“密集波纹状→光滑平坦→少量径向微裂纹→密集径向裂纹”的逐步转变的四个典型过程。杨仁树等[7]结合动态焦散线、超动态应变测试系统和数值计算对中间起爆柱状药包的应力应变场演化规律进行研究,得出中间起爆可以显著改善沿炮孔轴线爆炸应力场的均匀程度,有效减少岩石爆破大块率的产生。向文飞等采用Starfield迭加法与动力有限元法,研究起爆点数量与起爆点位置对条形药包爆炸应力场影响规律,认为合理安排起爆点的数量及位置、缩小条形药包完成爆轰的时间有利于改善爆破效果[8]。李启月等[9]通过数值计算和现场试验,发现合理分段装药高度和空孔参数,能够有效提高深孔爆破一次成井爆破效果。杨国梁等[10]提出了三种轴向分段装药结构,分别对正向、反向和两端起爆时的应力波传播规律进行研究,认为增加分段装药上分层药量应力分布更加均匀并且平均压力最大。胡涛等[11]利用数值计算对比深孔爆破连续装药结构和分段装药结构有效应力、自由面有效应力峰值及孔壁压力,结果表明分段装药结构降低了压缩应力波和爆轰气体产物作用于孔壁的初始压力及周围点振动速度。杨仁树等[12-13]将分段装药应用于井巷掘进掏槽爆破,提出了先裂后掏的分段装药爆破核心,认为上段炸药爆破后下段爆破提供新的自由面及补偿空间,从而减低炮孔底部岩石夹制作用,增加岩石的破碎程度,改善了掏槽爆破效果,提高井巷掘进效率。上述研究成果多是集中在连续装药数值计算、模型试验及现场试验等,少见基于分段装药条件下全场应变以及三维裂隙场及损伤特性,因此开展分段装药爆炸应变场与裂隙场分布规律研究,为深井开挖爆破参数优化提供理论指导与科学依据。
本文针采用数字图像相关(digital image correlation, DIC)分析方法,探讨分段装药下全场应变的演化过程,分析不同分段装药比例下爆炸全场应变传播规律;采用大型工业电子计算机断层扫描仪(CT)研究手段,建立连续装药、分段装药爆破前后“岩石-爆炸裂纹”三维重构模型,获得岩石爆炸三维裂隙网络位置、形态的空间分布情况,分析爆后岩石三维裂隙场的体分形维数与损伤度,探索分段装药对岩体损伤破裂程度的影响。
1. 分段装药全场应变特征分布研究
1.1 数字图像相关法实验系统
数字图像相关法(digital image correlation, DIC)是通过待测介质受力变形前后的灰度矩阵进行相关计算,通过对测点位置受力变形前后的空间位置信息计算,获得试件分析点处表面位移与变形应变的光学方法[14]。
实验所采用的实验设备为超高速数字图像相关实验系统,如图1所示。该实验系统主要包含超高速摄像机、爆炸与摄像同步控制系统、补光与拍摄同步控制系统、VIC-2D分析软件。超高速相机采集幅数为180幅,每秒最高可拍500万幅图片,完全满足爆炸荷载应变监测过程,本实验采样频率为200 000 s−1。同步控制系统为自主开发的多通道电火花发爆器,能够精准控制起爆时间,同时可以与照明系统、高速相机相连,调控三者的启动顺序,满足多通道同时、微差爆破。
1.2 分段装药实验模型设计
本实验旨在研究孔内分段装药全场应变特征,分段掏槽的目的是缓解炮孔底部岩体所受的夹制力作用。考虑在工程实践中,当上分段装药比例过小时,上部岩体类似浅孔爆破,下部岩体还处于高夹制作用状态,不符合设计初衷;当上分段比例过大,小分段比例过小时,下分段炸药能量有限,不能很好地把炮孔底部岩体抛掷出来。为此,本实验设计上分段装药占比0.4、0.6两种方案。
试件采用聚碳酸酯(PC)板。试件尺寸为400 mm×300 mm×8 mm,柱状药包尺寸为100 mm×3 mm×4 mm,炸药为叠氮化铅,爆速为4600 m/s,密度为4.71×103 kg/m3,装药量为160 mg。设计上分段装药占比为0.4、0.6两种方案,第一种方案,上分段炸药长L1=40 mm,如图2(a)所示,第二种方案,上分段炸药长L1=60 mm,如图2(b)所示,装药实物如图2(c)所示。对于两分段微差起爆时间的确定,在实验过程中,发现如果微差时间过大,那么两分段相互作用明显减弱;微差时间过小,两分段爆炸应力场的相互影响增大,不利于分析各分段产生的爆炸应力应变状态,根据前期实验调试结果,确定两段间隔起爆时差为20 μs。沿炮孔上部10 mm处,间隔20 mm布置6个测点测点,E1对应下分段L2起爆端(0 mm),E6位于上分段顶端(100 mm),对比分析其全场应变的演化规律,采用孔底起爆的方式。
1.3 分段装药全场应变分析
图3~4分别为两种分段装药的全场应变,分别选取径向应变(εyy)和轴向应变(εxx)演化过程进行分析。图3(a)为分段装药上分段占比0.6的径向全场应变,由于炸药起爆和传爆过程在炮孔中完成,高速相机无法记录此过程,实验捕捉到的应变过程为爆炸应力波开始作用介质的时刻。t=30 μs时,炮孔上下两侧受爆炸应力波作用表现为压应变,此时上分段炸药对下分段炸药及介质没有产生影响;t=40 μs时,随上分段炸药爆轰的传递,压应变作用区域增大;t=50 μs时,下分段炸药起爆,炮孔两侧同样表现为压应变,这时上分段炸药爆轰传播完成;t=70 μs时,上分段炸药起爆时产生的压应变继续向外传播,同时在炮孔周围形成第二组压应变场,两组压应变场之间为拉应变场,下分段压应变场作用范围增大,两组应变场之间开始相互作用;t=80 μs时,上分段炮孔周围压应变场增大,下分段炮孔周围压应变场范围有所减小,这是由于下分段炸药起爆形成的爆炸应力波向上分段传递,造成上分段应变区域增大,说明两者在此区间内有应变场的相互叠加;t=100 μs时,全场应变的分布状态以上分段为主。
图3(b)为上分段占比0.6的轴向全场应变,t=30 μs时,炮孔左右两侧受爆炸应力波作用表现为压应变;t=40 μs时,随上分段炸药爆轰的传递,压应变作用范围逐渐扩大;t=50 μs时,下分段炸药起爆,炮孔两侧同样表现为压应变,下分段压应变场与上分段压应变场在连接处发生叠加;t=70 μs时,在各分段的两端形成压应变场,其余炮孔位置表现为拉应变,t=100 μs时,上分段产生的压应变在介质中继续传播,随后紧跟的是拉应变作用。炮孔中由于分段装药形式,产生了三组压应变作用区域,分别为炮孔两端位置以及上下分段的连接处。这就表明在分段装药结构下,下分段堵塞区域主要为压应变作用区域。
图4(a)为分段装药上分段占比0.4的径向全场应变,t=30 μs时,炮孔受爆炸应力波作用表现为压应变,此时上分段炸药对下分段炸药及介质没有产生影响;t=40 μs时,随着上分段炸药爆轰的传递,压应变作用区域增大;t=50 μs时,下分段炸药起爆,炮孔两侧表现为压应变,这时上分段炸药爆轰传播完成;t=70 μs时,下分段应变场压应变作用区域增大,上分段应变场作用强度随着应力波的向外传递而减小;t=80 μs时,炮孔应变场主要集中在下分段装药处,应变场的作用范围较上分段大,直至100 μs时,由于下分段爆炸应力波的传播,全炮孔周边应变场作用范围扩大,但主要集中在下半段装药位置。
图4(b)为分段装药上分段占比0.4的轴向全场应变,t=30 μs时,炮孔左右两侧受爆炸应力波作用表现为压应变;t=40 μs时,随上分段炸药爆轰的传递,压应变作用范围同样逐渐增大;t=50 μs时,下分段炸药起爆,炮孔两端表现为压应变,下分段压应变场与上分段压应变场发生叠加;t=70 μs时,在各分段的两端形成压应变场,其余炮孔位置表现为拉应变,此时下分段形成的压应变场作用强度最大;t=100 μs时,和上分段装药0.6相比,此时炮孔的两端表现为压应变,中间区域则为拉应变。介质在此分段比例下炮孔周边区域沿装药方向主要受拉伸应变的作用,更有利于介质的破坏。
图5为孔内分段装药测点径向应变时程曲线,针对分段装药形式,无论上下分段占比如何,这种装药形式改变了炸药的爆炸应力波传播形式。针对上分段占比0.6的情况,上分段爆破的介质产生的压应变作用大于下分段,同时下分段产生的爆炸作用对上分段会产生二次应变,这种作用形式会加大对介质的破坏能力。但由于下半段炸药对介质产生的应变强度小,在工程实践中掏槽区域往往下半段岩石受夹制作用更大,岩石更难抛掷,所需的爆破能量更多。从介质的应变曲线可以看出,对于上分段装药0.4的情况,下分段介质受爆炸作用应变峰值更大,更好满足工程实践中下半段岩体对爆炸能量的需求。与文献[15]中连续装药爆炸应变场结论进行对比,分段装药改变了连续装药对介质的全场应变形态,由原来对介质产生一次应变改变为两次应变。在满足第一段炸药对介质的破坏作用下,同时加大了第二段炸药对介质的作用效应。
2. 孔内分段装药三维裂隙场的分布
2.1 孔内分段岩石爆破实验方案
为了探究分段装药爆炸裂隙场,采用红砂岩作为实验材料,红砂岩的单轴抗压强度为68.30 MPa,单轴抗拉强度为5.95 MPa,密度为2.48×103 kg/m3,如图6所示,红砂岩试样直径为50 mm,高为150 mm。在试件中心轴线钻取直径为4 mm,高度为120 mm的炮孔。连续装药时,采用装药系数66.7%,即柱状药包装药高度为80 mm,封堵为40 mm。采用分段装药时,根据以上研究结果,着重分析上分段装药占比为0.4的情况,即上分段装药中,炸药为30 mm,封堵为20 mm,下分段装药中,炸药为50 mm,封堵为20 mm。炸药装药直径为3 mm的细管,炸药为叠氮化铅。分段装药时,上段先爆,下段后爆,两者间隔20 μs。
红砂岩样品放置在内径50 mm的被动围压装置内,装置如图7所示,被动围压装置分内外两层,外层为法兰;里层为内胆装置,用于放置试件;把试件放置在内胆后,上部用法兰盖拧紧。
2.2 分段爆破岩石CT扫描与三维重构
CT扫描仪器型号ACTIS300-320/225,扫描电压为280 kV,试样扫描区段为0~150 mm,每隔0.15 mm扫描一层,共扫描1000张图片,CT扫描输出图像的尺寸为55 mm×55 mm,像素数量为1024×1024。
图8为不同层位的扫描原图和灰度处理图像,连续装药表面没有产生爆炸裂隙,分段装药试件表面产生了爆炸裂隙,从直观上看,分段装药对岩体的破碎程度更大一些。这是由于深孔装药下,在装药系数以及炸药量一定的情况下,连续装药封堵段长,炸药爆炸能量对封堵段破坏小,造成炸药的能量利用效率降低。由于分段装药改变了炸药在炮孔中的分布形式,使得炸药在炮孔中分布的更为均匀。
图9和图10分别为两种装药形式下岩体的三维裂隙重构图,由图可知,爆炸裂纹主要沿径向扩展,轴向应力应变所形成的环向裂纹不明显,径向是岩石破坏的主要方向。连续装药结构下,爆炸裂纹没有贯穿试件整体,距孔口20 mm内爆炸裂隙较少,这也说明在工程实践中,由于装药深度的增大,非装药段岩体破碎效果差,更容易产生大块。分段装药结构下,由于提高了炸药的位置,使得上部分岩体能够更好地利用炸药爆炸的能量破碎岩石。
2.3 分形维数计算与分析
目前对于分形维数的计算方法有计盒维数、相似维数、信息维数等,其中计盒维数计算简单,能够直观反映介质所选区域目标的占有情况。计盒维数表达式为[16]:
lgNδk=−Dflgδk+b (1) 式中:
Nδk 为含有裂纹区域的盒子数目,Df 为区域裂纹场的分形维数,δk 为裂纹区域分割小方网格边长,b为拟合参数。计盒维数的计算方法为:建立一个边长为δk 的小立体盒;然后改变不同边长对应形成若干小盒子,计算覆盖集的小盒子数Nδk ,经过转换得到δk -Nδk 数据;最后取对数,采用最小二乘法求斜率,即为计盒维数。材料损伤度
ω 与分形维数的关系表达式为[17]:ω=Dt−D0Dmaxt−D0 (2) 式中:
Dt 为介质爆后内部造成损伤面积的分形维数;D0 为介质爆前内部初始损伤面积的分形维数;Dmaxt 为介质达到最大损伤面积时的分形维数,对于平面问题Dmaxt=2 ;对于三维问题Dmaxt=3 。图11为连续装药与分段装药爆后岩体的分形维数图,从图中可以看出:分段装药分形维数为2.5073,对岩体造成的损伤度为0.84;连续装药岩体的分形维数为2.0258,对岩体造成的损伤度为0.68;分段装药下岩石的损伤度提高23.5%。
由于岩石上分段装药长度为50 mm,以上分段50 mm、下分段100 mm分别作对比,分别重构出裂隙的三维分布图,如图12所示。上分段岩体爆炸裂隙差别最大,分别计算上下分段两种装药结构的分形维数和损伤度,如图13所示,连续装药上分段分形维数为1.6889,损伤度为0.56;分段装药上分段分形维数为2.4693,损伤度为0.82,比连续装药上分段提高了46.4%;连续装药下分段分形维数为2.6679,损伤度为0.89;分段装药上分段分形维数为2.5228,损伤度为0.84,下半段连续装药损伤度大于分段装药,这是由于连续装药炸药集中在下部,单位体积的炸药比分段装药大,单两者从对岩体的损伤角度来看差别不大。
3. 结 论
本文分析了孔内分段装药结构下爆炸全场应变传播规律,建立了爆后“岩石-爆炸裂隙”的三维重构模型,精准描述了爆炸裂纹位置与形态的空间分布情况,结合分形理论,得到岩石材料爆炸裂隙的分形维数与损伤度,定量研究岩石在爆炸作用下的三维裂隙场与损伤程度,得到以下结论:
(1) 分段装药改变了连续装药对介质的全场应变形态,由原来对介质产生一次应变改变为两次应变;通过装药比例的改变,上分段装药占比0.4时,下分段爆破对介质产生的压应变作用效应大于上分段,在满足第一段炸药对介质的破坏作用下,加大了第二段炸药对介质的作用效应,同时延长了介质受爆炸应力波作用时间;
(2) 连续装药结构下,爆炸裂纹没有贯穿试件整体,炮孔封堵段内的爆炸裂纹较少,更容易产生大块;分段装药结构下,由于提高了炸药的位置,使得上部分岩体能够更好的利用炸药爆炸的能量破碎岩石;
(3) 分段装药对岩体造成的损伤度为0.8401,连续装药对岩体造成的损伤度为0.6802,分段装药岩石的损伤度较连续装药提高了23.5%,其中上分段岩体两者的差异性分析显示,上分段50 mm、下分段100 mm清醒,上分段爆炸产生的裂隙差别最大,分段装药上分段损伤度比连续装药提高46.4%。
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表 1 各组UHPFRC试件的配合比
Table 1. Mixing proportions of UHPFRC specimens for each test group
试件 钢纤维体积分数/% 配合比/(kg·m−3) 静力压缩 准静态劈裂 动态劈裂 水泥 硅灰 水 细砂 石英粉 减水剂 钢纤维 C0 ST0 DT0 0 1054 263 263 580 316 24 0 C1 ST1 DT1 1 1054 263 263 580 316 24 78 C2 ST2 DT2 2 1054 263 263 580 316 24 156 C3 ST3 DT3 3 1054 263 263 580 316 24 234 表 2 静力压缩试验结果
Table 2. Results of static compression tests
试件 钢纤维体积分数/% 峰值应变/% 峰值应力/MPa 弹性模量/GPa SC0 0 0.325±0.039 106.82±5.03 39.68±1.88 SC1 1 0.327±0.030 118.82±4.18 40.31±1.34 SC2 2 0.351±0.064 138.43±6.51 44.12±1.19 SC3 3 0.359±0.016 155.12±0.40 45.14±1.26 表 3 静力劈裂试验结果
Table 3. Results of static split tests
试件 钢纤维体积分数/% 劈裂强度/MPa 试件 钢纤维体积分数/% 劈裂强度/MPa ST0 0 11.41±0.46 ST2 2 23.47±1.04 ST1 1 20.98±1.23 ST3 3 26.37±0.22 表 4 动态劈裂试验结果
Table 4. Results of dynamic split tests
试件 ˙σ/(GPa·s−1) ˙ε/s−1 T/μs σT/MPa σT,a/MPa δt DT0-1 66.80 1.72 228 15.23 16.62 ± 2.12 1.33 DT0-2 89.40 2.30 168 15.02 1.32 DT0-3 118.13 3.04 166 19.61 1.72 DT1-1 258.37 6.41 94 24.29 24.41± 0.11 1.16 DT1-2 191.70 4.76 128 24.54 1.17 DT1-3 217.20 5.39 112 24.33 1.16 DT2-1 186.67 4.23 134 25.01 25.65± 0.79 1.07 DT2-2 233.08 5.28 108 25.17 1.07 DT2-3 196.76 4.46 136 26.76 1.14 DT3-1 177.31 3.93 170 30.14 31.06 ±0.83 1.14 DT3-2 334.93 7.42 96 32.15 1.22 DT3-3 166.04 3.68 186 30.88 1.17 表 5 试件DT0-3~DT3-3孔洞分布统计
Table 5. Statistics of pore distribution of specimens DT0-3-DT3-3
试件 孔洞体积
分数/%孔洞数目 孔洞平均
体积/mm3平均等效
直径/mm孔洞数目(占比) de=56.7~400 μm de=>400~800 μm de=>800~1600 μm de>1600 μm DT0-3 1.71 38671 0.053 0.466 27089
(70.05%)10012
(25.89%)1439
(3.72%)131
(0.34%)DT1-3 1.58 21384 0.089 0.554 12859
(60.13%)7389
(34.55%)983
(4.60%)153
(0.72%)DT2-3 1.20 15508 0.093 0.563 8847
(57.05%)5736
(36.99%)810
(5.22%)115
(0.74%)DT3-3 0.98 10158 0.101 0.579 6404
(63.04%)3134
(30.85%)548
(5.39%)72
(0.71%)表 6 裂缝及桥连纤维的统计分析
Table 6. Statistical analysis of cracks and bridged fibers
试件 桥连纤维
根数裂缝体积/
mm3裂缝表面积/
mm2相对表面积/
mm−1DT1-3 328 7118.97 10963.40 1.54 DT2-3 747 3234.73 6319.61 1.95 DT3-3 1 468 3081.81 6545.25 2.12 -
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