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=16kN/m3，隧道开挖半径 a=3.0m，围岩的粘聚力c=0.10MPa，内摩擦角=30弹性模量E=100MPa，泊松比=0.5，试求：1）手算初始应力场呈轴对称分布时（=1）围岩的塑性区半径r0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（=1）围岩的塑性区半径r0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 z=16150=2.4 Mpa Rb=2ccos1-sin=20.1cos3

2、01-sin30=0.23 =1+sin1-sin=1+sin301-sin30=3求r0 r0=a2+1Z-1+RhRh1-1 =32422.4+0.230.2312 =8.176m 求应力 塑性应力 arr0 rp=Rb-1(ra)-1-1 =0.232(r3)2-1 p=Rb-1ra-1-1 =0.232r323-1弹性应力 rr0 re=z1-r02r2+Rb-1(r0a)-1-1r02r2 e=z1+r02r2-Rb-1(r0a)-1-1r02r2计算表格如下： 单位：kpa塑性弹性位置应力35r08.210.215.220.225r0307.91113.41115.31430200

3、222412354346.41270.13686.63684.633692797255824452).如下excel表格参数计算表： 单位：kpa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： =2.4(1-0.5)-0.13 /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）附表一埋深容重洞径粘聚力内摩擦角Rbzr0附表一15016310030346.4102324008.176419塑性应力弹

4、性应力位置rpp位置ree30346.41028.21115.3463684.6543.1517.75352399.67078.71176.1893623.8113.336.37307455.52949.21257.413542.593.4555.85864513.98619.71344.4573455.5433.676.21024575.040910.21430.3733369.6273.7597.42786638.693710.71511.943288.063.9119.5115704.944711.21587.8223212.1784.05142.4612773.793711.71657

5、.6433142.3574.2166.2769845.240812.21721.5113078.4894.35190.9586919.28612.71779.7633020.2374.5216.5064995.929213.21832.8322967.1684.65242.92011075.17113.71881.1812918.8194.8270.19991157.0114.21925.2632874.7374.95298.34581241.44714.71965.5012834.4995.1327.35761328.48315.22002.2842797.7165.25357.235514

6、18.11715.72035.9662764.0345.4387.97941510.34816.22066.8612733.1395.55419.58931605.17816.72095.2512704.7495.7452.06531702.60617.22121.3872678.6135.85485.40721802.63217.72145.492654.516519.61521905.25618.22167.7592632.2416.15554.68932010.47818.72188.3692611.6316.3590.62932118.29819.22207.4762592.5246.

7、45627.43542228.71619.72225.2192574.7816.6665.10752341.73320.22241.7222558.2786.75703.64562457.34720.72257.0952542.9056.9743.04982575.5621.22271.4372528.5637.05783.322696.3721.72284.8372515.1637.2824.45622819.77922.22297.3752502.6257.35866.45842945.785232315.8152484.1857.5909.32673074.39242336.42463.

8、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0.057897upa02.40.0581.1111130.0022.3555560.061.0683020.0042.3111110.0650.9728020.0062.2666670.070.8909440.0082.2222220.0750.8200010

9、.012.1777780.080.7579250.0122.1333330.0850.7031530.0142.0888890.090.6544660.0162.0444440.0950.6109050.01820.10.5716990.021.9555560.1050.5362280.0221.9111110.110.5039810.0241.8666670.1150.4745380.0261.8222220.120.4475490.0281.7777780.1250.4227180.031.7333330.130.3997980.0321.6888890.1350.3785760.0341.6444440.140.3588690.0361.60.1450.3405220.0381.5555560.150.3233980.041.5111110.1550.3073780.0421.4666670.160.292360.0441.4222220.1650.2782520.0461.3777780.170.2649740.0481.3333330.1750.2