高等土力學(xué)作業(yè)承德中密砂

1、14.根據(jù)承德砂在三種圍壓下的三軸試驗(yàn)結(jié)果，計(jì)算Duncan雙曲線，和，模型的參數(shù)。試驗(yàn)結(jié)果見下表。表1 承德中密砂常規(guī)三軸試驗(yàn)數(shù)據(jù)表圍壓100kPa圍壓300kPa圍壓500kPa應(yīng)力差軸向應(yīng)變體應(yīng)變應(yīng)力差軸向應(yīng)變體應(yīng)變應(yīng)力差軸向應(yīng)變體應(yīng)變50.80.002250.0007490.90.001250.0007575.60.000250.00057100.20.004490.0013228.60.00350.00151245.40.00250.00114146.30.006740.00176353.30.005750.00236458.70.004760.00199184.90.008980.

2、00223434.10.0080.00302634.90.007010.00275214.90.011230.00223520.30.010250.00329768.90.009260.00303233.10.013480.00214578.10.012510.00329875.10.011510.00341247.70.015720.00176620.20.014760.00329957.30.013760.00351258.70.017970.00158652.90.017010.003291022.40.016020.0036266.50.020210.00111678.90.01926

3、0.003021075.90.018270.00362730.022460.00056706.50.021510.002831119.70.020520.00341277.70.024710.00009723.30.023760.002361155.10.022770.00313281.20.026950.000037390.026010.001891183.70.025020.00294284.50.03032-0.00012751.50.029390.00161216.40.02840.00246287.80.03369-0.00195771.40.032760.000941243.90.

4、031780.00199288.90.03706-0.00286784.60.036140.000281265.20.035160.00152289.40.04043-0.00381793.90.03952-0.000471280.80.038540.00104288.90.04492-0.00474801.60.04402-0.001231295.30.043040.00009287.90.04941-0.00567804.30.04852-0.002071306.90.04754-0.00066286.90.0539-0.0065805.80.05302-0.002921314.80.05

5、205-0.00171285.30.05839-0.00752804.70.05753-0.0037713210.05655-0.00246283.60.06289-0.00827802.60.06203-0.004521323.90.06106-0.00322280.90.06738-0.00891799.20.06653-0.005371323.40.06556-0.00408-793.20.07216-0.006131321.10.0719-0.00423-785.90.07778-0.007071311.70.07682-0.005691，模型參數(shù)求解1.1 切線變形模量的5個(gè)參數(shù)求解

6、1.1.1 求解根據(jù)常規(guī)三軸試驗(yàn)結(jié)果按的關(guān)系進(jìn)行整理，二者近似成線性關(guān)系，則， （1）式中，為直線的截距，為直線的斜率。根據(jù)實(shí)驗(yàn)數(shù)據(jù)，可以擬合得到三條直線，如圖1所示。圖1 不同圍壓條件下關(guān)系曲線根據(jù)以上三條直線，可以分別得到三個(gè)，根據(jù)，求得；再根據(jù)，求得。計(jì)算結(jié)果見表2。表2 參數(shù)計(jì)算表圍壓100289.40.0000186240.00310.8971400.903417300805.80.0000079450.00110.8863805001323.90.0000051980.00070.926730可得，1.1.2 參數(shù)求解根據(jù)可得： （2）根據(jù)實(shí)驗(yàn)數(shù)據(jù)可以求得相關(guān)的，見表3。二者成線性

7、關(guān)系，根據(jù)表中數(shù)據(jù)可以擬合得到一條直線，則斜率即為，截距即為。見圖2。表3 ，計(jì)算數(shù)據(jù)10053694.162.72389-0.006300125866.913.093870.471500192366.883.27810.693 圖2 lg(Ei/pa)lg(3/pa)曲線由圖可得，。1.1.3 ，參數(shù)求解根據(jù)實(shí)驗(yàn)數(shù)據(jù)可以得到三組砂土破壞時(shí)的應(yīng)力大小，根據(jù)莫爾庫(kù)侖強(qiáng)度公式 （3）可以擬合出關(guān)于關(guān)系的直線，截距即為，斜率為，又因?yàn)?，從而進(jìn)一步求得，。相關(guān)數(shù)據(jù)圖表見表4，圖3。表4 破壞時(shí)的，數(shù)據(jù)100389.43001105.85001823.9 圖3 莫爾庫(kù)侖強(qiáng)度關(guān)系曲線由圖3可得，綜上，切線

8、模量中的5個(gè)參數(shù)都已求得，分別為，1.2 切線泊松比的3個(gè)參數(shù)求解假定在常規(guī)三軸試驗(yàn)中軸向應(yīng)變與側(cè)向應(yīng)變之間也存在雙曲線關(guān)系，則與之間為線性關(guān)系，可由下式表示： （4）可根據(jù)數(shù)據(jù)擬合出三條關(guān)于與關(guān)系的直線，從而求得。擬合圖如圖4所示。（相關(guān)與數(shù)據(jù)的計(jì)算結(jié)果見附表。）圖4 -31-3關(guān)系曲線由于圍壓500kPa時(shí)的第一組數(shù)據(jù)（-000016，-0.64）與其他數(shù)據(jù)偏差太大，且對(duì)擬合的直線影響較大，因此在擬合過(guò)程中把該組數(shù)據(jù)剔除。由上面三個(gè)圖可分別得到對(duì)應(yīng)的三組值，見表5。認(rèn)為與圍壓無(wú)關(guān)，是一個(gè)常數(shù)，因此可以取為三組數(shù)的平均值。實(shí)驗(yàn)表明初始泊松比與實(shí)驗(yàn)的圍壓有關(guān)，假設(shè)它們之間符合如下關(guān)系： （5）

9、則可以通過(guò)數(shù)據(jù)擬合出的直線關(guān)系，從而求得參數(shù)。擬合圖如圖5所示。表5 值0.38855.96116.1841-0.0060.33426.53960.4710.33996.05170.693 圖5 關(guān)系圖由圖5可得，綜上，切線泊松比的3個(gè)參數(shù)分別為，2模型參數(shù)求解通過(guò)三軸試驗(yàn)并用下式確定特定圍壓條件下的體變模量 （6）相關(guān)數(shù)據(jù)見表6。表6 相關(guān)參數(shù)計(jì)算表100289.4202.580.0022330281.02298.6294-0.0062.475300805.8564.060.0032957148.94563.5990.4712.7515001323.9926.730.0034789023.0

10、5877.93940.6932.943根據(jù)計(jì)算數(shù)據(jù)看出，與有關(guān)，二者在雙對(duì)數(shù)坐標(biāo)系中可近似為直線，即： （7）根據(jù)表6中的數(shù)據(jù)，可以擬合出一條直線，并求出。如圖6所示。圖6 擬合曲線由圖6得，綜上，體變模量的參數(shù)分別為附表100時(shí)300時(shí)500時(shí)100時(shí)300時(shí)500時(shí)100時(shí)300時(shí)500時(shí)0.000040.000010.000000.0007550.00025-0.000160.33555560.2-0.640.000040.000020.000010.0015950.0009950.000680.35523390.28428570.2720.000050.000020.000010.00

11、2490.0016950.0013850.36943620.29478260.2909660.000050.000020.000010.0033750.002490.002130.37583520.311250.3038520.000050.000020.000010.00450.003480.0031150.40071240.33951220.3363930.000060.000020.000010.005670.004610.004050.42062310.36850520.3518680.000060.000020.000010.006980.0057350.0051250.444020

12、40.38855010.3724560.000070.000030.000020.0081950.006860.006210.45603780.40329220.387640.000080.000030.000020.009550.008120.0073350.47253830.42159920.4014780.000080.000030.000020.010950.009340.0085550.48753340.43421660.416910.000090.000030.000020.012310.01070.009820.49817890.45033670.4312690.000100.0

13、00040.000020.013460.012060.011040.49944340.46366780.4412470.000110.000040.000020.015220.0138950.012970.50197890.47277990.456690.000120.000040.000030.017820.015910.0148950.52894030.48565320.4686910.000130.000050.000030.019960.017930.016820.53858610.49612620.4783850.000140.000050.000030.022120.0199950

14、.018750.54711850.50594640.4865080.000160.000050.000030.024830.0226250.0214750.55276050.51397090.4989540.000170.000060.000040.027540.0252950.02410.5573770.52133140.5069420.000190.000070.000040.03020.027970.026880.56029680.52753680.5164270.000200.000070.000040.0329550.030650.0295050.56439460.53276550.5217510.000220.000080.000050