隧道的二次应力计算

1、兰州交通大学隧道及地下工程（隧道的二次应力计算）班级:姓名:学号:某隧道埋深H=150.0m容重Y=16kN/m3隧道开挖半径a=3.0m,围岩的粘 聚力c=0.10MPa,内摩擦角 小=30弹性模量E=100MPa泊松比 仙=0.5 ,试求： 1）手算初始应力场呈轴对称分布时（入=1）围岩的塑性区半径和二次应力场，并以图示出；2）采用自己擅长的计算机语言编程或 excel表格计 算初始应力场呈轴对称分布时（入=1）围岩的塑性区半径和二次应力场，并以图示出；3）编程计算确定该围岩特征曲线（支护需求曲线）。解：1）二次应力状态=丫 H=16X 150=2.4Mpa2ccosl-sm2 x 0.1

2、 x cos 30l-sin30fl=0.2l + sin01-sin。l + sin3（Tl-sin30fl=32 %（- l） + & 工 1Ie + 1& J=3 x - x0.2白2 2x2.4+0231=8.176m求应力塑性应力 a r 0.2计算表格如下：单位：kpa塑性弹性位置应力358.210.215.220.225务0307.91113.41115.31430200222412354346.41270.13686.63684.63369279725582445/一IlTIllJ.mJ2）,如下excel表格参数计算表：单位：kpa容至洞径粘聚力内摩擦苑nRb |.：L631

3、0030346.41324008. 17ti4应力计算表格：（见下方附表1）塑性区半径及二次应力分布图：（见下方附表1）3）,不出现塑性区时的最小支护抗力为:Pi = tr JI -sin)-ccos=2.4 X (1-0.5)- 0.1 XV3/2 =1.1133代入Ua=0.057897即弹塑性分界线Ua=0.057897参数计算表：单位：kpa容重 洞径粘聚力内擦角| Rb I E | - I 口6 a 10030346.4132400 乩 17r64围岩特征曲线计算表格：（见下方附表2）围岩特征曲线图：（见下方附表2）附表埋深谷重洞径粘聚力内擦 角Rb0- zr0附表一15016310

4、030346.4102324008.176419塑性应力弹性应力位置0- rp0- 0 p位置0- reo- 0 e30346.41028.21115.3463684.6543.1517.75352399.67078.71176.1893623.8113.336.37307455.52949.21257.413542.593.4555.85864513.98619.71344.4573455.5433.676.21024575.040910.21430.3733369.6273.7597.42786638.693710.71511.943288.063.9119.5115704.944711.

5、21587.8223212.1784.05142.4612773.793711.71657.6433142.3574.2166.2769845.240812.21721.5113078.4894.35190.9586919.28612.71779.7633020.2374.5216.5064995.929213.21832.8322967.1684.65242.92011075.17113.71881.1812918.8194.8270.19991157.0114.21925.2632874.7374.95298.34581241.44714.71965.5012834.4995.1327.3

6、5761328.48315.22002.2842797.7165.25357.23551418.11715.72035.9662764.0345.4387.97941510.34816.22066.8612733.1395.55419.58931605.17816.72095.2512704.7495.7452.06531702.60617.22121.3872678.6135.85485.40721802.63217.72145.492654.516519.61521905.25618.22167.7592632.2416.15554.68932010.47818.72188.3692611

7、.6316.3590.62932118.29819.22207.4762592.5246.45627.43542228.71619.72225.2192574.7816.6665.10752341.73320.22241.7222558.2786.75703.64562457.34720.72257.0952542.9056.9743.04982575.5621.22271.4372528.5637.05783.322696.3721.72284.8372515.1637.2824.45622819.77922.22297.3752502.6257.35866.45842945.7852323

8、15.8152484.1857.5909.32673074.39242336.42463.67.8997.66133339.394252354.632445.3781058.4753521.837262370.8482429.1528.1764191113.3973686.603272385.3372414.663附表二不出现塑性区时的最小支护力 pa=1.113397& =3Rb=0.34641弹性区位移塑性区位移upa弹塑分界0.057897upa02.40.0581.1111130.0022.3555560.061.0683020.0042.3111110.0650.9728020.00

9、62.2666670.070.8909440.0082.2222220.0750.8200010.012.1777780.080.7579250.0122.1333330.0850.7031530.0142.0888890.090.6544660.0162.0444440.0950.6109050.01820.10.5716990.021.9555560.1050.5362280.0221.9111110.110.5039810.0241.8666670.1150.4745380.0261.8222220.120.4475490.0281.7777780.1250.4227180.031.7333330.130.3997980.0321.6888890.1350.3785760.0341.6444440.140.3588690.0361.60.1450.3405220.0381.5555560.150.3233980.041.5111110.1550.3073780.0421.4666670.160.292360.0441.4222220.1650.2782520.0461.3777780.170.2649740.0481.3333330.175