Correlation between Wave Velocity and Deformation Modulus of Basalt Masses as Dam Foundation in Hydropower Projects
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摘要: 岩体变形模量是岩体工程设计最重要的参数之一.由于受到资金、时间、尺寸效应等限制, 在工程勘察设计阶段往往不可能大量开展岩体现场和室内变形模量试验, 试验结果也不具有普遍代表性.因此, 水电工程常常采用岩体纵波波速与变形模量之间的相关关系来估算大范围及深部岩体变形模量.根据波动微分方程从理论上解释了岩体纵波波速与变形模量之间内在的联系.以我国西南金沙江干流上坝基主要为玄武岩体的4个大型水电工程为例, 根据132组现场变形模量试验结果与同向波速测试结果建立玄武岩体波速与变形模量相关方程, 并与也有的研究成果对比分析.研究成果表明, 玄武岩体波速与变形模量具有较好的相关性.当波速小于4 500 m/s时, 不同类型玄武岩根据波速计算变形模量差别较小; 当波速大于4 500 m/s时, 差别逐渐增加.选取最优的相关方程用于估算坝基玄武岩体变形模量, 为水电工程坝基玄武岩体变形模量的快捷评价提供科学依据.Abstract: Deformation modulus is an important parameter for rock engineering design. However, the relation between longitudinal wave velocity and deformation modulus is often used to estimate the deformation modulus of large-scale and deep rock mass in the hydroelectric projects because it is difficult to conduct many in-situ and laboratory deformation modulus tests due to the limited funds, time and test size during the engineering survey and the test results have no general representativeness. In this paper, the intrinsic relation between longitudinal wave velocity and rock deformation modulus is theoretically explained based on the wave differential equation. Meanwhile, 132 in-situ test data derived from 4 hydropowers are used to set up an experience formula between longitudinal wave velocity and deformation modulus for basalt in the Jinsha River area. The results show that there is close relation between the basalt longitudinal wave velocity and its deformation modulus. The deformation modulus difference of different basalt rock masses by calculating of longitudinal wave velocity is small when Vp < 4 500 m/s. While it becomes larger when Vp > 4 500 m/s. The optimal equation is helpful to evaluate the deformation modulus of basalt rock mass, and it offers a quick and scientific method for selecting basic parameters of dam foundation in the hydropower projects.
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图 1 金安桥水电站坝基玄武岩体波速与变形模量关系
Fig. 1. Relation of wave velocity and deformation modulus of basalt in Jinanqiao hydropower station
图 2 白鹤滩水电站坝基玄武岩体波速与变形模量关系
Fig. 2. Relation of wave velocity and deformation modulus of basalt in Baihetan hydropower station
图 3 溪洛渡水电站坝基玄武岩体波速与变形模量关系
Fig. 3. Relationship of wave velocity and deformation modulus of basalt in Xiluodu hydropower station
图 4 龙开口水电站坝基玄武岩体波速与变形模量关系
Fig. 4. Relation of wave velocity and deformation modulus of basalt in Longkaikou hydropower station
图 5 不同类型玄武岩体波速与变形模量关系
Fig. 5. Different basalt rock mass relation curve of wave velocity and deformation modulus
图 6 玄武岩波速与变形模量关系
Fig. 6. Basalt rock mass relation of wave velocity and deformation modulus
表 1 金安桥水电站坝基玄武岩体波速与变形模量试验结果
Table 1. Experiment result of wave velocity and deformation modulus of Basalt in Jinanqiao hydropower station
试点编号 岩性 试验位置 Vp(m/s) E0(GPa) PTB1 绿泥石化玄武岩 右岸Ⅱ线试验平台 2 245 2.7 PTB2 绿泥石化玄武岩 右岸Ⅱ线试验平台 2 276 2.8 PTB3 绿泥石化玄武岩 右岸Ⅱ线试验平台 2 463 3.1 PTB4 绿泥石化玄武岩 右岸Ⅱ线试验平台 2 324 3.2 PTB5 绿泥石化玄武岩 右岸Ⅱ线试验平台 2 558 3.3 PTB6 绿泥石化玄武岩 右岸Ⅱ线试验平台 3 267 3.9 PTB7 绿泥石化玄武岩 右岸Ⅱ线试验平台 2 683 4.1 PTB8 绿泥石化玄武岩 右岸Ⅱ线试验平台 2 821 4.4 PTB9 绿泥石化玄武岩 右岸Ⅱ线试验平台 2 845 4.8 PTB10 绿泥石化玄武岩 右岸Ⅱ线试验平台 2 946 5.0 PTB11 绿泥石化玄武岩 右岸Ⅱ线试验平台 3 840 5.4 PTB12 绿泥石化玄武岩 右岸Ⅱ线试验平台 4 231 7.1 PTB13 绿泥石化玄武岩 右岸Ⅱ线试验平台 3 750 8.3 PTB14 绿泥石化玄武岩 右岸Ⅱ线试验平台 4 648 9.2 PTB15 绿泥石化玄武岩 右岸Ⅱ线试验平台 4 350 12.4 PTB16 绿泥石化玄武岩 右岸Ⅱ线试验平台 5 077 18.8 PTB17 绿泥石化玄武岩 右岸Ⅱ线试验平台 5 789 18.6 
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表 2 白鹤滩水电站坝基玄武岩体波速与变形模量试验结果
Table 2. Experiment result of wave velocity and deformation modulus of Basalt in Baihetan hydropower station
试点编号 岩性 试验位置 Vp(m/s) E0(GPa) ZBX01 柱状节理玄武岩 PD111-198 m 4 000 9.2 ZBX02 柱状节理玄武岩 PD111-194.8 m 5 100 20.8 ZBX03 柱状节理玄武岩 PD111-190.1 m 4 170 10.8 ZBX04 柱状节理玄武岩 PD111-176.6 m 5 900 30.7 ZBX05 柱状节理玄武岩 PD111-154.7 m 5 530 26.4 ZBX06 柱状节理玄武岩 PD111-146 m 5 300 21.6 ZBX07 柱状节理玄武岩 PD111-121.5 m 5 800 29.8 ZBX08 柱状节理玄武岩 PD111-119 m 5 340 22.6 ZBX09 柱状节理玄武岩 PD111-53.9 m 4 800 18.2 ZBX10 柱状节理玄武岩 PD111-47.8 m 4 400 15.7 ZBX11 柱状节理玄武岩 PD111-23.8 m 2 260 1.4 ZBX12 柱状节理玄武岩 PD111-7.4 m 2 070 1.3 ZBX13 柱状节理玄武岩 PD111-30.7 m 3 360 6.8 YBX01 杏仁玄武岩 PD716-6.6 m 2 700 2.6 YBX02 杏仁玄武岩 PD716-11.9 m 3 540 5.0 YBX03 杏仁玄武岩 PD716-26.3 m 3 100 2.9 YBX04 杏仁玄武岩 PD716-35.1 m 4 200 10.3 YBX05 杏仁玄武岩 PD716-39.65 m 3 160 3.8 YBX06 杏仁玄武岩 PD716-55 m 3 530 5.0 YBX07 杏仁玄武岩 PD716-79.1 m 2 500 1.5 YBX08 角砾熔岩 PD716-101.65 m 4 820 17.1 YBX09 角砾熔岩 PD716-104.35 m 4 720 16.3 YBX10 角砾熔岩 PD716-107.55 m 5 100 22.2 ZBX14 隐晶玄武岩 PD923-11 m 3 110 5.0 ZBX15 隐晶玄武岩 PD923-28.5 m 3 670 11.6 ZBX16 隐晶玄武岩 PD923-34 m 4 150 11.2 ZBX17 隐晶玄武岩 PD113-117 m 4 800 16.5 YBX11 隐晶玄武岩 PD112-118.3 m 5 300 21.7
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表 3 溪洛渡水电站坝基玄武岩体波速与变形模量试验结果
Table 3. Experiment result of wave velocity and deformation modulus of basalt in Xiluodu hydropower station
试点编号 岩性 试验位置 Vp(m/s) E0(GPa) ZB440 斑状玄武岩 左岸EL440下游幅 5 956 29.9 ZB430 斑状玄武岩 左岸EL430拱轴线 4 653 12.7 YB451 斑状玄武岩 右岸EL451上游幅 4 683 12.1 YB440 斑状玄武岩 右岸EL440下游幅 5 271 25.5 YB430 斑状玄武岩 右岸EL430下游幅 4 065 9.4 YB398 斑状玄武岩 右岸EL398上游幅 5 097 22.7 ZB411 斑状玄武岩 左岸EL411坝轴线 4 535 13.6 ZB386 斑状玄武岩 左岸EL386上游幅 4 821 17.3 ZB561X 角砾熔岩 左岸EL561下游幅 3 044 4.5 ZB561S 角砾熔岩 左岸EL561上游幅 3 163 4.6 ZB355 角砾熔岩 左岸EL355 4 528 13.7 YB570X 角砾熔岩 右岸EL570下游幅 3 800 6.2 YX570S 角砾熔岩 右岸EL570上游幅 4 286 11.2 YB561S 角砾熔岩 右岸EL560上游幅 3 903 7.4 YB523 角砾熔岩 右岸EL523排水洞下方 4 186 12.0 YB510X 角砾熔岩 右岸EL510下游幅 4 041 8.3 YB500 角砾熔岩 右岸EL500坝轴线 3 631 7.7 YB461 角砾熔岩 右岸EL460上游幅 2 649 4.6 YB370 角砾熔岩 右岸EL370 m坝轴线 2 353 2.3 YX-BX 角砾熔岩 右岸缺陷B区 3 838 9.6 ZB470 凝灰岩 左岸灌浆洞6 m 2 540 1.9 YB481 杏仁玄武岩 右岸EL481 4 750 14.8 ZB610-4 致密玄武岩 左岸灌浆洞82.6 m 4 870 16.9 ZB610-3 致密玄武岩 左岸灌浆洞54 m 3 133 5.0 ZB610-2 致密玄武岩 左岸灌浆洞39 m 3 300 6.0 ZB610-1 致密玄武岩 左岸灌浆洞15 m 3 051 4.8 ZB580 致密玄武岩 左岸EL580下游幅 3 736 9.4 ZB575S 致密玄武岩 左岸EL575上游幅 2 415 2.1 ZB565X 致密玄武岩 左岸EL565下游幅 3 593 8.2 ZB565S 致密玄武岩 左岸EL565上游幅 1 890 1.8 ZB563-1 致密玄武岩 左岸排水洞7.3 m 3 755 8.4 ZB563-2 致密玄武岩 左岸排水洞35 m 2 610 3.9 ZB551S 致密玄武岩 左岸EL551坝轴线 3 649 7.9 ZB541 致密玄武岩 左岸EL541坝轴线 3 709 9.7 ZB522X 致密玄武岩 右岸EL560上游幅 3 503 6.5 ZB491 致密玄武岩 左岸EL491拱轴线 2 381 2.3 ZB486 致密玄武岩 左岸EL486拱轴线 2 060 2.2 ZB461 致密玄武岩 左岸EL461上游幅 3 553 5.9 ZB451 致密玄武岩 左岸EL450上游幅 3 898 7.5 ZB405 致密玄武岩 左岸EL405下游幅 5 556 24.1 ZB382 致密玄武岩 左岸EL382上游幅 4 601 15.1 YB610-6 致密玄武岩 右岸灌浆洞81 m 4 491 13.1 YB610-5 致密玄武岩 右岸灌浆洞58 m 2 952 4.5 YB610-4 致密玄武岩 右岸灌浆洞57 m 3 486 7.7 YB610-3 致密玄武岩 右岸灌浆洞47 m 2 631 2.4 YB610-2 致密玄武岩 右岸灌浆洞31 m 3 922 11.0 YB610-1 致密玄武岩 右岸灌浆洞10.5 m 4 893 16.9 YB601X 致密玄武岩 右岸EL601下游幅 2 233 3.3 YB601S 致密玄武岩 右岸EL601 m上游幅 4 092 9.3 YB581 致密玄武岩 右岸EL581 m下游幅 1 761 0.5 YB563 致密玄武岩 右岸排水洞7.3 m 3 626 7.3 YB563-1 致密玄武岩 右岸排水洞46.5 m 5 327 28.9 YB563-2 致密玄武岩 右岸排水洞93.3 m 4 741 13.0 YB563-3 致密玄武岩 右岸排水洞108 m 5 900 45.4 YB562X 致密玄武岩 右岸EL562 m下游幅 2 586 3.5 YB551 致密玄武岩 右岸551 m拱轴线 2 390 2.9 YB541X 致密玄武岩 右岸541下游幅 2 487 3.2 YB531 致密玄武岩 右岸531 m坝轴线 4 319 12.6 YB420 致密玄武岩 右岸EL420上游幅 2 970 2.1 YB391 致密玄武岩 右岸EL391上游幅 4 663 14.0 YB382 致密玄武岩 右岸EL382 m上游幅 4 048 7.5 YB367 致密玄武岩 右岸EL367上游幅 3 231 6.2 YB347 致密玄武岩 右岸EL347 m上游幅 2 047 1.6
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表 4 龙开口水电站坝基玄武岩体波速与变形模量试验结果
Table 4. Experiment result of wave velocity and deformation modulus of Basalt in Longkaikou hydropower station
试点编号 岩性 试验位置 Vp(m/s) E0(GPa) PDB1 致密玄武岩 PD11-67.5 m 5 164 21.1 PDB2 致密玄武岩 PD11-83.5 m 4 353 7.8 PDB3 致密玄武岩 PD13-75.8 m 5 143 20.7 PDB4 致密玄武岩 PD13-47.5 m 4 176 9.1 PDB5 致密玄武岩 PD11-15 m 3 543 5.7 PDB6 致密玄武岩 PD11-17.5 m 4 669 14.2 PDB7 致密玄武岩 PD11-18.2 m 4 304 10.2 PDB8 致密玄武岩 PD13-33 m 4 466 12.5 PDB9 致密玄武岩 PD13-40 m 4 737 13.1 PDB10 致密玄武岩 PD16-20 m 4 954 17.3 PDB11 致密玄武岩 PD16-33 m 5 379 25.8 PDB12 致密玄武岩 PD16-63 m 5 115 20.7 PDB13 致密玄武岩 PD23-46 m 2 028 2.0 PDB14 致密玄武岩 PD23-76 m 4 002 7.1 YBX2 致密玄武岩 右岸江边露头 4 366 8.8 YBX4 致密玄武岩 右岸江边露头 3 388 6.4 YBX5 致密玄武岩 右岸江边露头 3 857 7.6 ZBX2 致密玄武岩 左岸江边露头 2 888 4.7 PT1-1 致密玄武岩 右岸江边1号平台 5 256 23.8 PT1-2 致密玄武岩 右岸江边1号平台 4 585 15.6 PT1-3 致密玄武岩 右岸江边1号平台 4 703 11.0 PT2-1 致密玄武岩 右岸江边2号平台 4 974 15.5 PT2-2 致密玄武岩 右岸江边2号平台 4 868 18.5 PT2-3 致密玄武岩 右岸江边2号平台 4 105 13.1 PT3-3 致密玄武岩 右岸江边3号平台 4 496 9.8
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表 5 不同玄武岩体根据波速计算的变形模量
Table 5. Different basalt rock mass values of deformation modulus by different equations
VpVp(m/s) E(斑状玄武岩)Vp(GPa) E(角砾熔岩)Vp(GPa) E(绿泥石化玄武岩)Vp(GPa) E(杏仁玄武岩)Vp(GPa) E(隐晶玄武岩)Vp(GPa) E(致密玄武岩)Vp(GPa) E(柱状节理玄武岩)Vp(GPa) E0平均值Vp(GPa) 1 000 1.2 0.9 1.5 0.4 1.7 0.9 0.7 1.1 1 500 1.7 1.3 2.1 0.7 2.3 1.3 1.0 1.5 2 000 2.4 1.9 2.8 1.1 3.1 2.0 1.5 2.1 2 500 3.4 2.6 3.8 1.9 4.2 3.0 2.2 3.0 3 000 4.9 3.8 5.1 3.1 5.7 4.5 3.2 4.3 3 500 6.9 5.3 6.9 5.1 7.7 6.7 4.8 6.2 4 000 9.9 7.6 9.3 8.4 10.4 9.9 7.2 8.9 4 500 14.0 10.7 12.6 13.8 14.0 14.8 10.7 13.0 5 000 19.8 15.2 17.0 22.8 18.9 22.1 16.0 18.8 5 500 28.2 21.6 22.9 37.6 25.5 33.0 23.9 27.5 6 000 40.0 30.7 30.9 62.0 34.4 49.2 35.7 40.4
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表 6 不同公式计算得到的玄武岩体变形模量
Table 6. Estimated deformation modulus values by different equations
Vp(m/s) E0(GPa) 式(6) 式(7) 式(20) 式(21) 式(22) 表 5平均值 1 000 1.47 0.01 1.48 0.73 0.48 1.1 1 500 2.15 0.07 2.10 1.09 0.72 1.5 2 000 3.16 0.28 2.98 1.63 1.07 2.1 2 500 4.64 0.81 4.22 2.44 1.60 3.0 3 000 6.81 1.95 5.99 3.64 2.39 4.3 3 500 10.00 4.09 8.50 5.42 3.57 6.2 4 000 14.68 7.76 12.07 8.09 5.32 8.9 4 500 21.54 13.66 17.12 12.07 7.94 13.0 5 000 31.62 22.65 24.30 18.01 11.84 18.8 5 500 46.42 35.79 34.48 26.86 17.67 27.5 6 000 68.13 54.34 48.93 40.07 26.36 40.4
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