Numerical Analysis in Geotechnical Engineering

Transcription

1 M.Sc. in Geological Engineering: Subject No. 8183B2 Numerical Analysis in Geotechnical Engineering Hong-Hu ZHU ( 朱鸿鹄 ) School of Earth Sciences and Engineering, Nanjing University Lecture 4: Real Soil Behavior 土的力学性质 4.1 Synopsis and 4.2 Introduction 4.3 Behavior of clay soils 4.4 Behavior of sands 4.5 Behavior of soils containing both clay and sand 4.6 Concluding remarks 4.7 Summary 1

2 4.1 Synopsis Review of real soil behavior 黏性土 无黏性土 4.2 Introduction 弹性 塑性和黏性 Soil behavior is neither linear nor elastic Soil failure will occur Real behavior from 1-D compression tests, triaxial tests and other advanced tests 4.3 Behaviour of clayey soils 黏土的压缩和剪切特性 Behavior under 1-dimensional compression Non-liner, plastic, creep, strain rate effects Behavior under triaxial compression & extension shear Non-liner, plastic, creep, strain rate effects, difference in compression and extension, k o -consolidation behavior Effect of stress path direction Effect of the intermediate principal stress Anisotropy Behavior at large strain residual strength 2

3 4.3.1 Behavior under 1-dimensional compression 上覆荷载 2mm 6mm 1 independent variable in 1-D test OCR (Over consolidated ratio, 超固结比 )= Preconsolidation pressure ( 先期固结压力 ) 正常固结状态 (OCR=1) 原压曲线 超固结状态 (OCR>1) 对数坐标 3

4 正常固结状态 (OCR=1) 压缩指数 超固结状态 (OCR>1) 回弹指数 压缩指数 > 回弹指数 : 说明土体刚度何时较大? 何时会急剧降低? 单杠杆固结仪 太沙基时代的固结仪 气压固结仪 4

5 液压加载 Hydraulic consolidation cell Rowe cell (GDS) 孔压监测 排水阀 堆石料固结蠕变试验仪 ( 大连理工大学 ) 5

6 Normal stress: Shear stress: no change Effective stresses control: both deformationand shear resistance(or shear strength) since they reflect soil particle interaction 沉降由三部分组成 S = S + S + S e pc sc elastic settlement (S e ), primary consolidation settlement (S pc ) and secondary consolidation settlement (S sc ) 6

7 C σ + σ c Spc = H log 1+ e o σ C t α 2 Ssc = H log 1+ ep t1 缺陷 : 时间趋向于无穷, 则次固结沉降为无穷 σ E E 1 τ 1 α σ Time Lower bound Settlement 85 9 E (EOP) Primary consolidation S e S pc α =.1 Δα =.2 α =.9 Upper bound Secondary consolidation S sc ε e ε E 1 ε ve 分数导数流变模型 (Zhu et al. 216) 上下限明确 Furthermore, another observable feature of the FM model is that the secondary consolidation comes to an end when the load duration is infinite, which has an advantage over the conventional solution where the settlement is infinite if the time is infinite. Obviously, this is physically impossible. Regarding this problem, the FM model is more rational than the conventional one. Zhu, H.-H., Zhang, C.-C., Mei, G.-X., Shi, B., and Gao, L. (216). Prediction of one-dimensional compression behavior of Nansha Clay using fractional derivatives. Marine Georesources and Geotechnology. DOI: 1.18/164119X Vertical strain vs. log(time) for ratio C4 (1% HKMD and % sand) L o g ( t i m e ) ( m i n ) ( C 4 ) Vertical Strain (% ) (a) loading L o g ( t im e ) ( m i n ) ( C 4 ) 1 k P a 2 5 k P a 5 k P a 4 k P a 1 k P a 2 k P a 多级加载Yin, J.-H. (1999). Properties and behaviour of Hong Kong marine deposits with different clay contents. Canadian Geotechnical Journal, Vol.36, No.6, pp

8 L o g ( t im e ) ( m i n ) ( C 4 ) Vertical Strain (% ) Vertical Strain (%) (b) unloading 2 k P a L o g ( t i m e ) ( m i n ) ( C 4 ) k P a 1 k P a 2 k P a 4 k P a 5 k P a 1 k P a 8 k P a 卸载继续多级加载 3 1 (c) reloading Vertical strain vs. log(stress) with loading, unloading and reloading for mixing ratio C4 (Yin 1999) V e rt ic a l S t re s s (k P a ) ( C 4 ) C c ε = , R 2 = Vertical Strain (% ) 卸载 C r e e p 3 2 d a y s 加载 2 5 C r ε = , R 2 = Bjerrum 等时曲线理论 再加载 C re e p 1 8 d a y s 3 5 8

9 1-D compression under isotropic stressing 等向压缩 Volume strain vm (%) M e a n e ffe c ti v e s tre s s p ' m (k P a ) 平均有效应力 1 p ' m o σ 1 + 2σ 3 p = ( σ 1 + σ 2 + σ 3 ) = λ -lin e 3 3 T e s t: 1 d a y U n /r e lo a d in g L o a d in g κ -li n e 2 个剑桥模型参数 4 Yin, J.-H. and Zhu, J.-G. (1999). Measured and predicted time-dependent stress-strain behavior of Hong Kong marine deposits. Canadian Geotechnical Journal, Vol.36, No.4, pp Volume strain (%) Tim e (m in) Primary consolidation ( 主固结 ) Creep before and after EOP! Secondary consolidation ( 次固结 ) End-of- Primary (EOP) consolidation u (kpa) Tim e (m in) 9

10 4.3.2 Behavior when sheared 最常见的两种室内剪切试验 直剪试验 (direct shear test) 三轴试验 (triaxialtest) 直剪试验的三种方法 快剪 固结快剪 慢剪 三轴试验的三种方法 Unconsolidated Undrained test (UU) Consolidated Undrained test (CU) Consolidated Drained test (CD) 太沙基时代的直剪仪 1

11 11

12 剑桥大学的直剪仪 Equipment of shear test of clay limestone contact 原位剪切试验 12

13 不同三轴试验的类型对于于现场的不同剪切状态! Example of an engineering application of the triaxial test. A σ1 σ3 Triaxial compression σ1 ζ σ3 B σ1 ζ 45 σ3 Potential failure plane σ3 C Simple shear D Triaxial extension σ1 三类三轴试验 Unconsolidated Undrained test (UU) Consolidated Undrained test (CU) Consolidated Drained test (CD) 围压 13

14 太沙基时代的三轴仪 现代常规三轴仪 Conventional triaxial apparatus 14

15 第一主应力增加, 位移加载速率可控制 围压 ( 第三主应力 ) 不变 排水条件可控制 剪切面和水平面夹角是多少? 45 度 + 内摩擦角的一半! 15

16 Advanced triaxial apparatus (GDS) 数据采集模块 围压 / 反压加载器 体积变形控制 / 传感器 应力路径控制式三轴仪 Stress-path triaxial apparatus 16

17 Computer-controlled triaxial testing system - 2Hz Cyclic loading, stress-path testing, k o -consolidation and extension shear testing 动荷载 堆石料蠕变三轴仪 ( 河海大学 ) 17

18 Comparison of measured and predicted results (a) deviator stress vs. axial strain in consolidated undrained (CU) shear in compression and extension at three axial strain rates (CUC1, CUC2, CUC3 at.25%/min,.25%/min,.25%/min; CUE1, CUE2, CUE3 at -.25%/min, -.25%/min, -.25%/min Deviator stress q=( a - r) (kpa) C U C 1 - te s t C U C 2 - te s t C U C 3 - te s t C U E 1 - t e s t C U E 2 - t e s t C U E 3 - t e s t C U C 1 - E V P C U C 2 - E V P C U C 3 - E V P C U E 1 - E V P C U E 2 - E V P C U E 3 - E V P 应变率对应力 - 应变关系的影响 ( 时间相关性 ) 2 independent variables in all triaxial tests A x i a l s tr a i n ε a ( % ) Porewater pressure u (kpa) εɺ a = Comparison of measured and predicted results - (b) porewater pressure vs. axial strain in consolidated undrained (CU) shear in compression and extension at three axial strain rates (CUC1, CUC2, CUC3 at.25%/min,.25%/min,.25%/min; CUE1, CUE2, CUE3 at -.25%/min, -.25%/min, -.25%/min 应变率对孔压 - 应变关系的影响 ( 不排水剪切 ) 无论三轴压缩还是拉伸, 孔压均为正, 即有剪缩效应 ( 有排水趋势 ) A x i a l s tr a i n ε a ( % ) C U C 1 - te s t C U C 2 - te s t C U C 3 - te s t C U E 1 - te s t C U E 2 - te s t C U E 3 - te s t C U C 1 - E V P C U C 2 - E V P C U C 3 - E V P C U E 1 - E V P C U E 2 - E V P C U E 3 - E V P 18

19 Deviator stress q=( a - r) (kpa) εɺ a = q = σ σ Mc=1.265 φ '=31.5 o 偏应力快速慢三轴压缩 CSL Mean effective stress p' (kpa) CUC1-test CUC2-test CUC3-test CUE1-test CUE2-test CUE3-test Mc-line Me-line CUC1-EVP CUC2-EVP CUC3-EVP CUE1-EVP CUE2-EVP CUE3-EVP 有效应力路径向左弯曲, 剑桥模型参数土体产生了正孔压速三轴拉伸 CSL 1 σ + 2σ 平均有效应力 p = ( σ1 + σ 2 + σ3 ) = 由于不排水 ( 无法剪缩 ), 不同的应力路径 ( 不排水剪切 ) Comparison of measured and predicted results effective stress paths in consolidated undrained shear in compression and extension at three axial strain rates (CUC1, CUC2, CUC3 at.25%/min,.25%/min,.25%/min; CUE1, CUE2, CUE3 at -.25%/min, -.25%/min, -.25%/min Comparison of measured and predicted results (a) deviator stress vs. axial strain, (b) volume strain vs. axial strain and (c) effective stress paths (ESP) and total stress paths (TSP) in two consolidated drained shear tests q (kpa) 不同固结应力下的排水剪切试验结果 A x ia l s t r a in ( % ) C D 1 C D 2 C D 1 - E V P C D 2 - E V P Volume strain (%) C D 1 C D 2 C D 1 - E V P C D 2 - E V P A x ia l s t r a in ( % ) 19

20 Comparison of measured and predicted results (a) deviator stress vs. axial strain, (b) volume strain vs. axial strain and (c) effective stress paths (ESP) and total stress paths (TSP) in two consolidated drained (CD) shear tests 9 CD1 8 7 q = σ 1 σ 3 6 q (kpa) CD2 Strength line TSP1 TSP2 2 1 ( ) 1 3 总 ( 有效 ) 应力路径为直线, 斜率是? σ 6 + 2σ p = σ σ 2 + σ 3 = 3 3 p or p' (kpa) Effect of stress path direction 1<OCR<3( 弱超固结土 ): 有效应力路径向左弯曲, 由于不排水 ( 无法剪缩 ), 土体产生了正孔压 OCR>3( 强超固结土 ): 有剪胀 ( 膨胀吸水 ) 趋势, 因此产生负孔压 剪胀 三轴压缩试验 OCR 大三轴拉伸试验 剪缩 OCR 小 2

21 OCR 小 三轴压缩试验 OCR 大 OCR 小 三轴拉伸试验 OCR 大 不排水模量 E 随着剪切变形增大, 而变得越来越小 ( 刚度减小 ) 固结应力大 固结应力小 在不同的固结应力 ( 围压 ) 下, 扭剪时剪切模量 G 也会不断减小 Kenichi 21

22 4.3.3 Effect of stress path direction σ 1 σ 3 ( σ 1 σ + 2 σ 3 ) 1 2 p = + + = 3 3 不同的应力路径下, 体积模量 K 不是定值, 随剪切而不断下降 22

23 剪切模量 G 也不是定值 Effect of the magnitude of the intermediate principal stress b σ 2 σ 3 = σ σ 1 3 = = = 1 triaxial triaxial compression extension <b<1 Hollow cylinder or truly traxial testing 非饱和黄土三轴伸长试样 23

24 Hollow Cylinder Apparatus (HCA): control of 4 independent parameters 空心柱实验 HCA 2Hz Truly Triaxial System (TTS): control of 3 independent parameters 24

25 国外学者研究发现, 中主应力对黏土不排 水强度有一定的影响, 但对有效内摩擦角 影响很小 砂土或混合土则不然 Anisotropy 25

26 4.3.6 Behavior at large strain (>2%) 必定软化 环剪试验 26

27 residual strength=peak strength/2 Large-size direct shear box :34mm wide x 34mm (or 45mm) long x 24mm high 27

28 Shear stress (kpa) (a) China State Construction Engineering Co. Ltd Topsoil 1 with % S.C. and 95% compaction H o rizo ntal d isp lacement (mm ) 1 kp a 2 kp a 4 kp a 必定软化 Vertical displacement (mm)_ (b ) 1 kp a 2 kp a 4 kp a 剪胀效应 "-" for dila tion "+" for c om pre ssion H o rizo ntal d isp lacement (mm) Shear stress (kpa) (a) China State Construction Engineering Co. Ltd Topsoil 1 with % S.C. and 95% compaction y =.9153x Normal stress (kpa) Peak strength - test data Linear (Peak strength - test data) Peak strength: φ=42.5 o, c= 26.8kPa Shear stress (kpa) (b) y =.6148x Normal stress (kpa) Final strength -test data Linear (Final strength -test data) Final strength: φ=31.6 o, c=16.3kpa 28

29 4.4 Behaviour of sands 砂土的特性 Behavior under 1-dimensional compression Non-liner, plastic Behavior under triaxial compression & extension shear Non-liner, plastic, difference in compression and extension, k o -consolidation behavior, OCR Effect of the intermediate principal stress Anisotropy Behavior under 1-dimensional compression 正常压缩曲线 原压曲线 土颗粒强度 29

30 4.4.2 Behavior when sheared 直剪试验中, 砂土初始密度对强度的影响非常明显应变软化 应变硬化 剪胀 剪缩 三轴试验中, 砂土应力路径和超固结比 ( 初始密度 ) 的影响也很明显 Behavior under triaxial compression & extension shear -Effective stress paths -OCR 破坏线 剪胀 剪缩 松砂剪切过程中 ( 由松变密 ) 3

31 Behavior under triaxial compression & extension shear 剪胀 -Effective stress path -OCR 密砂 Behavior under triaxial compression & extension shear -Young s modulus on OCR and axial strain 松砂的 E 不是定值, 而是越来越小 31

32 密砂的 E 也不是定值, 而是越来越小 固结应力大 固结应力小 不同固结压力下, 剪切模量 G 随着剪应变不断减小, 该规律受到应力水平的影响 32

33 4.4.3 Effect of the magnitude of the intermediate principal stress σ 2 σ 3 b = σ σ 1 3 = triaxial compression = = 1 triaxial extension Hollow cylinder or true traxial testing Anisotropy 砂土强度的各向异性很明显 33

34 Anisotropy 砂土刚度的各向异性也很明显 4.5 Behaviourof soils with both clay and sand Comparison of sedimentary soils Residual soils Residual strength as function of clay content Hong Kong Marine Deposits (HKMND) with different clay contents (see Yin, J.-H. (1999). Properties and behaviour of Hong Kong marine deposits with different clay contents. Canadian Geotechnical Journal, Vol.36, No.6, pp ) 34

35 4.5.1 Comparison of sedimentary soils 砂土 黏土 35

36 黏粒含量增加 36

37 37

38 38

39 4.5.2 Residual soils formed in-situ by weathering of parent rock (bonded structures) 残积土 Residual strength (as function of clay content) 黏粒含量 39

40 Residual strength as function of clay content Hong Kong Marine Deposits (HKMD) with different clay contents (Yin, J.-H. (1999). Properties and behaviour of Hong Kong marine deposits with different clay contents. Canadian Geotechnical Journal, Vol.36, No.6, pp ) Percentage Smaller (%) Size (mm) Particle size distribution curves for four different mixing ratios C1 C2 C3 C4 4

41 Percentages of clay, silt and sand Mixing ratios and mixed soils Clay content size<.2mm Silt content.2mm<size <.63mm C1: 25% HKMD and 75% silica sand 6.% 14.% 8.% C2: 5% HKMD and 5% silica sand 1.% 3.5% 59.5% Sand content.63mm<size <1.18mm C3: 75% HKMD and 25% silica sand 2.% 42.8% 37.2% C4: 1% HKMD and % silica sand 27.5% 58.4% 14.1% Specific gravity, Atterberg limits, and water content C1 C2 C3 C4 Specific gravity (G s ) Initial water content w (%) Liquid limit ( w L ) % Plastic limit ( w p ) % Plasticity index ( I p ) % w L, w P, and IP (% ) w L Test Fitting Test Fitting Test Fitting w P I P w L =1.7C+13.5 (R 2 =.995) I P =1.26C (R 2 =.9) 2 w p =.44C Clay Content C (%) Measured data and best-fitting lines of clay content vs. (a) liquid limit w L, (b) plasticity index I P, and (c) plastic limit w P. 41

42 Ip (% ) Calcium montmorillonite (1.5) Sand-bentonite (1.6) Shellhaven (1.33) HKMD-1 (1.26) London clay (.95) Weald clay (.63) Horten (.42) Clay Content (%) I p vs. clay content - (a) comparison with various clays.9 Cc, Cr (x1), Cα(x1) C c C r C α C r =.219I p -.14, R 2 =.892 C c =.138I p +.732, R 2 =.96 C α =.369I p -.55, R 2 = I p (%) 42

43 C c =.151I p +.151, R 2 =.25 Cc I p (%) Test Calculation.4 Cc C c =.12w L w L (%) 43

44 1 ' HKMD-1 c v (m 2 /year) 1 Upper bound (Koutsoftas et al. 1987) Low er bound (Koutsoftas et al. 1987) Liquid Limit w l (%) (a) Plastic index I p vs. c v for HKMD-1 and (b) liquid limit w L vs. log(c v ) test data on HKMD-1 and lower bound and upper bound for upper marine clay (after Koutsoftas et al. 1987) (a ) H K M D - 1 L u p i n i e t a l. ( ) C l a y C o n t e n t ( % ) 1 8 ( b ) σs 3 = 1 k P a σs 3 = 2 k P a E 5 (kpa) 6 4 σs 3 = 4 k P a C l a y C o n t e n t ( % ) 44

45 4.6 Concluding remarks Real soil behavior is complicated No models can capture/reproduce all soil behavior features Simple models are developed and used. But they shall at least reproduce the soil behavior that is dominant in the problem under investigation For example: (a) for soil instability (slope failure), the soil failure shall be reproduced (b) for settlement analysis, proper stiffness shall be reproduced 4.7 Summary 45

46 46