Some Recent Advances in (understanding) the Cyclic Behavior of Soils

Transcription

1 39 th SPRING SEMINAR and 19 th LA GEO EXPO American Society of Civil Engineers Geo-Institute, Los Angeles Section Wednesday April 13, 216 Queen Mary, Long Beach, CA 982 Invited lecture: Some Recent Advances in (understanding) the Cyclic Behavior of Soils by Mladen Vucetic, Ph.D. Professor, Civil and Environmental Engineering Department University of California, Los Angeles, USA 1

2 Introduction The topic of the presentation belongs to the field of Geotechnical Earthquake Engineering, and more specifically in the domain of Response of the local ground to earthquakes (Source: Internet - modified from Kajima Co. Slide) Three main factors are affecting the ground surface shaking and cyclic behavior of local soil deposits: source, path and local soil conditions 2

3 In practice, most commonly just the shear components of the vertically propagating wave are considered, because they are causing horizontal motions of the ground surface that are most damaging to the supported structures. Predominantly vertically propagating shear waves Ground surface Water table v ' h ' = hc ' u u u Soil element d v ' = vc ' u v ', h ' : effective normal stress vc ', hc ' : effective normal consolidation stress before shearing : shear stress : shear strain = dh u : hydrostatic pore water pressure before shearing u : excess pore water pressure due to sharing Bedrock h ' H Vertically propagating shear waves In the case of the vertically propagating plane seismic shear waves, the stressstrain conditions are those of pure shear cyclic stresses,, and associated shear strains,, applied on top of the normal vertical and horizontal principal effective stresses vc and hc existing prior to the earthquake. 3

4 Such analysis considering exclusively the vertical propagation of shear waves through horizontally layered soil deposits is performed by computer codes such as: SHAKE (Schnabel et al., 1972) that employs a vertical shear beam model excited at its base. DESRA (Lee and Finn, 1978) and its modifications (e.g., DESRAMOD by Vucetic and Dobry, 1986; D-MOD by Matasovic and Vucetic, 1993) that employ a multi-degree-of-freedom lumped parameter model shaken at its base. DEEPSOIL (Hashash, 29) that employ a multi-degree-of-freedom lumped parameter model shaken at its base. The above analyses are called the local site response analyses and to run them and obtain reliable results certain cyclic properties of soil layers need to be known. 4

5 The most suitable cyclic testing device for the simulation of the behavior of soil element under pure shear stresses is the direct simple shear device. Setup of specimen in standard NGI DSS device (Bjerrum and Landva, 1966) Setup of specimens in UCLA dual-specimen NGI DSS device (DSDSS device) for small-strain testing (Doroudian and Vucetic,1995;1998). 5

6 In the DSS tests soils are most commonly cyclically characterized with the help of uniform cyclic tests although the actual behavior is irregular Sketch of time histories of strains, stresses and pore water pressures Actual cyclic strain-controlled behavior of a clay Uniform cyclic strain-controlled behavior of fully saturated soil 6

7 Sketch of time histories of stresses, strains and pore water pressures Actual cyclic stress-controlled behavior of a sand Uniform cyclic stress-controlled behavior of fully saturated soil 7

8 The elementary components of soil behavior in such tests are uniform cyclic loops The most important loop in a single test is the initial loop corresponding to the first one and a quarter cycles. The initial loop describes the cyclic behavior of intact soil. c Shear stress, c O c G s 1 G max 1 c Shear strain, The most important characteristics of any loop are: its slope,g s, describing average stiffness and area, w, describing specific energy loss that defines the equivalent viscous damping ratio,. W c c W 2 Shear stress, c c O c c Shear strain, 1 W 1 W 4 W 4 c c 2 Idealized initial cyclic loop (first cycle loop) with definition of parameters c, c, G max and G s Definition of the equivalent viscous damping ratio, In summary: the initial cyclic loop parameters are c, c, G max, G s and 8

9 Secant shear modulus, G s Normalized secant shear modulus, G s /G max Equivalent viscous damping ratio, G max 1 1 Cyclic shear strain amplitude, Cyclic shear strain amplitude, Cyclic shear strain amplitude, c (in logarithmic scale) c (in logarithmic scale) Damping curve Secant shear modulus reduction curve Normalized secant shear modulus reduction curve c (in logarithmic scale) The variation of G s and with c is typically described by the secant shear modulus reduction curve, G s - log c, or the normalized secant shear modulus reduction curve, G s /G max log c, and the damping -log c curve. These curves are key input in the local site response analyses and outcome of the analyses depends very much on their shapes. The outcome of the analyses in time domain that consider the variation of cyclic soil properties with time also depend on how G s and change with the number of cycles, N. 9

10 The subsequent loops exhibit the effects of continuous cyclic loading that are typically characterized with respect to the properties of the initial loop.: The corresponding parameters are: G N G SN CN C CN S1 C1 C1 C Degradation index log N t logn Degradation parameter - slope of log-logn line - Another important parameter is the threshold shear strain: Threshold shear strain for cyclic degradation, td Cyclic degradation in a series of cyclic strain-controlled test on clay and evaluation of the threshold shear strain for cyclic degradation, td 1

11 This presentation covers some new or relatively recent findings in the domain of cyclic soil behavior related to: G s and G s /G max log c curve damping ratio and -log c curve change of G s with N during cyclic loading referred to as the cyclic degradation and the contribution of cyclic pore water pressure to cyclic degradation values of the cyclic threshold shear strains, t, dividing domains of small-strain nondestructive and larger strains destructive cyclic soil behavior 11

12 Effect of the rate of straining and loading and the frequency of cyclic strainig or loading on the secant shear modulus G s Shear stress, Shear stress, Time, t Shear strain, (a) Creep phenomenon Shear strain, Shear stress, Time, t Shear strain, (b) Relaxation phenomenon 12

13 Shear stress, (kpa) 8 4 DSDSS test Kaolinite, MH, PI = 2 vc = 388 kpa 1 2 Time, t (sec) As bserved in DSDSS device (Tabata and Vucetic, 24): Phenomena of creep and relaxation also exist at very small strains and therefore even G max is affected by the strain rate Shear strain, (%) Time, t (sec) Shear stress, (kpa) (a) Results of creep test Shear strain, (%) Time, t (sec) Time, t (sec) Shear stress, (kpa) Shear strain, (%) Shear stress, (kpa) 8 4 DSDSS test Kaolinite MH, PI = 2 vc = 388 kpa.6.12 Shear strain, (%) (b) Results of relaxation test 13

14 Effect of the frequency and associated average strain rate on G s Is quantified by the strain-rate shear modulus factor that describes what is the Gs increase for the tenfold increase of the average strain rate : (a) (b) Shear strain, c c T ( c ) high f Time, t 2T c Low frequency test High frequency test f. = 1/T is low, f. = 1/T is high, = 4 c is low. = 4 c is high. ( c ) low f Shear strain, Shear stress, c Shear strain, c ( c ) low f c T 1 1 2T G s ) high f (G s ) low f (G s ) high f > (G s ) low f 3T Time, t 4T Average rate of straining in cyclic test Gs S G log log 4 T c 4 f Stain-rate shear modulus parameter G G G G high high S log low low c S high log high low S low ( c ) high f (c) Secant shear modulus, G s (G s ) high f (G s ) low f (G s ) high f (G s ) low f 1 1 G G Smaller c Larger c Strain-rate shear modulus factor introduced by Isenhower and Stokoe (1981) N G G G S high S low 1 log high low G GS ref G S ref.. low high. Average shear strain rate, (in log scale) 14

15 Strain rate shear modulus factor, N G (%). Strain rate shear modulus factor, N G. (%) DSDSS test Step 1:.35 < c (%) <.47 DSDSS test Step 3:.25 < c (%) < Plasticity index, PI DSDSS test Step 2:.94 < c (%) <.14 DSDSS test Step 4:.86 < c (%) < Plasticity index, PI Trend of the strain-rate shear modulus factor with soil s plasticity index, PI (presented in Tabata and Vucetic, 24 based on data from Matesic and Vucetic, 23; Tabata and Vucetic, 24; Vucetic, Tabata and Matesic, 23), Strain-rate shear modulus factor (%) ' vc 5-65 kpa Plasticity index, PI (%) c =.1%.4%.1%.3 %.1% General trends of the strain-rate shear modulus factor with soil s plasticity index, PI, and cyclic shear strain amplitude (derived from Matesic and Vucetic, 23; Tabata and Vucetic, 24; Vucetic and Tabata,23; and Vucetic at al.,23) c 15

16 Effect of the variable rate of straining and loading in a single cycle on the equivalent viscous damping ratio, Obseravtion: Due to creep and relaxation the area of the loop is larger if the area under the strain-time curve is larger. Sketches of loops for triangular, sinusoidal and trapezoidal straining of clayey soil (derived from Vucetic et al., 1998a,b; Lanzo and Vucetic, 1999) Definition of the strain-time history shape parameter, θ, measuring the effect of the shape of cyclic straining on the equivalent viscous damping ratio (Vucetic et al., 1998) 16

17 Time, t (sec) 4 DSDSS test Kaolinite MH, PI = 2 vc = 388 kpa Time, t (sec) 6 DSDSS test Kaolinite MH, PI = 2 vc = 388 kpa Time, t (sec) 8 DSDSS test Kaolinite MH, PI = 2 vc = 284 kpa Time, t (sec) 15 DSDSS test Kaolinite MH, PI = 2 vc = 388 kpa Shear strain, (%).1.1 Shear strain, (%).1.1 Shear strain, (%).1.1 Shear strain, (%) Shear stress, (kpa) Shear stress, (kpa) Shear stress, (kpa) Shear stress, (kpa) Shear strain, (%).1.1 Shear strain, (%).1.1 Shear strain, (%).1.1 Shear strain, (%) Shapes of the stress-strain cyclic loops due to various cyclic straining shapes at very small cyclic strains of approx..1% (Tabata and Vucetic, 24) 17

18 Equivalent viscous damping ratio, (%) 1 5 DSDSS test Kaolinite, MH, PI = 2.7 < c (%) <.11 OCR = 1 vc = 196 kpa vc = 284 kpa vc = 388 kpa.5 1 Strain time history shape parameter, Trend of the equivalent viscous damping ratio,, with the strain-time history shape parameter θ for kaolinite clay in the range of very small cyclic shear strain amplitudes c =.7% to.15% (Tabata and Vucetic, 24) 18

19 Effect of the variable rate of straining and loading in a single cycle on the damping ratio -log c curves for different soils Sketches of the Cyclic loops of clean sand and plastic clay at small and large cyclic strain amplitudes obtained for sinusoidal cyclic straining (Lanzo and Vucetic, 1999) 19

20 Effect of the sinusoidal shape of cyclic straining on damping curve: Damping curves for sand and clay obtained for sinusoidal cyclic straining crossing each other at small cyclic shear strain amplitudes between c =.1% and.1% (Lanzo and Vucetic, 1999 the phenomena was also studied by Vucetic et al.,1998; Stokoe et al.,1999) Based on discussions about the roundness of the cyclic loops for clays presented in Vucetic (1986) and in Dobry and Vucetic(1987) Pyke in 1993 in an EPRI report suggested the above relative locations of damping ratio curves for soils having different PI without having actual test data. 2

21 Effect of the frequency of cyclic straining on the modulus reduction G s /G max log c curves for different soils Normalized modulus reduction curve is actually positive branch of dynamic backbone curve, -, plotted in G s /G max log c format Monotonic loading curve Dynamic backbone curve For sands the dynamic backbone curve and monotonic loading curve coincide CLAY SAND This means that the G s /G max log c curve can be constructed approximately from the, - monotonic loading curve. 21

22 Effect of the strain rate on the modulus reduction curve derived from the monotonic loading test Time, t (sec) Shear stress, (kpa) =.12 %/sec DSDSS test Kaolinite, MH, PI = 2 vc = 281 kpa. =.12 %/sec. =.27 %/sec. =.43 %/sec. =.43 %/sec. =.27 %/sec..1.2 Shear strain, (%) Secant shear modulus, G s (MPa) Normalized secant shear modulus, G s / G max =.27 %/sec. =.43 %/sec =.12 %/sec DSDSS test Kaolinite, MH, PI = 2 vc = 281 kpa.. =.27 %/sec. =.43 %/sec =.12 %/sec Shear strain, (%) Strain-time histories and stress-strain curves in the constant strain-rate monotonic loading DSDSS tests (Tabata and Vucetic, 24) Modulus reduction curves for constant strain-rate monotonic loading tests (Tabata and Vucetic, 24) 22

23 Time, t (sec) DECREASES: DSDSS test Kaolinite, MH, PI = 2 vc = 193 kpa..5.1 Time, t (sec) 8 4. SLIGHTLY INCREASES: DSDSS test Kaolinite, MH, PI = 2 vc = 193 kpa..5.1 Time, t (sec) STRONGLY INCREASES: DSDSS test Kaolinite, MH, PI = 2 vc = 193 kpa Shear stress, (kpa) 4 Shear stress, (kpa) 4 Shear stress, (kpa) Shear strain,..5.1 Shear strain,..5.1 Shear strain, Strain-time histories and stress-strain curves obtained from the DSDSS tests conducted at three different regimes of variable strain rate (Tabata and Vucetic, 24) 23

24 When the strain rate strongly increases with strain, G s /G max first increases with strain and then decreases. Consequently, the G s /G max log c curve may plot above the level G s /G max =1. Normalized modulus reduction curves obtained from the variable-strain-rate tests (Tabata and Vucetic, 24) 24

25 (a) (b) Normalized secant shear modulus, G s / G max (MPa) Normalized secant shear modulus, G s / G max (MPa) constant f curve, f =.3 Hz constant f curve, f = 3 Hz.. constant curves,.1 < (%/sec)< ESC 4 MH soil, PI = DSDSS test.9 Sand Clay Arleta 1 SW soil, NP.8 4 c 4 f c.7 constant f curve, f =.3 Hz T constant f curve, f = 3 Hz.. constant curves,.1 < (%/sec)< Cyclic shear strain amplitude, c (%) Constant f Constant Effect of the rate of straining on the modulus reduction curves obtained from cyclic testing f 4 c Examples of the constant average strain-rate and constant-frequency normalized modulus reduction curves G s /G max log c for sandy and clayey soils (Tabata and Vucetic, 24). Same phenomena were studied by Isenhower and Stokoe (1981) and Matesic and Vucetic (23). 25

26 Improved modulus reduction (G s /G max - log c ) curves that account for the effects of the rate of straining Older curves frequently used in practice: Suggested newer curves: Original relationship between the G s /G max -log c curves and soil s PI constructed by Vucetic and Dobry (1991) from the data published by different researchers until 1989 note that the starting points of the curves are at the level G s /G max =1. indicating linear behavior at c below these points, which is unrealistic. 26

27 Threshold shear strains for cyclic pore water pressure, tp, and the threshold shear strains for cyclic degradation, td, in clays - new findings (Mortezaie and Vucetic, 216) Variation of strain, stress and pore water pressure with time in a multi-stage cyclic strain-controlled test on kaolinite clay. 27

28 N G G SN CN C CN S1 C1 C1 C degradation index log N t logn degradation parameter Threshold shear strain for cyclic degradation, td Cyclic degradation in the stages of the multi-staged cyclic strain-controlled test on kaolinite clay Variation of the average degradation parameter, t, with the cyclic shear strain amplitude, c, in the multi-staged cyclic test on kaolinite clay presented in the semi-log format 28

29 Threshold shear strain for cyclic pre water pressure, tp Change of the normalized equivalent cyclic pore water pressure, u Ni*, with the cyclic shear strain amplitude, c, in the stages of the multi-staged cyclic strain-controlled test Kao32 on normally consolidate clay. u Ni *=u Ni / vi ) Threshold shear strain for cyclic pre water pressure, tp Change of the normalized equivalent cyclic pore water pressure, u Ni*, with the cyclic shear strain amplitude, c, in the stages of the multi-staged cyclic strain-controlled test Kao11 on overconsolidated clay. 29

30 td =.6-.5% Relationship between the threshold shear strain for cyclic degradation, td, and soil s plasticity index, PI, from the cyclic simple shear test data obtained by Mortezaie and Vucetic (226) and the study by Tabata and Vucetic (24; 21). tp =.1-.1% Relationship between the threshold shear strain for cyclic pore water pressure generation, tp, and soil s plasticity index, PI, obtained by Mortezaie and Vucetic (226) and in 4 previous studies. 3

31 Relationship between the cyclic pore water pressure and cyclic degradation in sands new findings (Vucetic and Mortezaie, 215) c, =.8%. c, =.8%. Cyclic strain-controlled behavior of sand in undrained conditions in the NGI simple shear test at relatively small cyclic shear strain amplitude c, =.8%. Because the degradation index N first increases and then decreases with N it is renamed the stiffness index. 31

32 u N.35 vo Variation of stiffness index, N, with the number of cycles, N, and its relationship with cyclic pore water pressure, u N *, obtained in the simple shear cyclic strain controlled tests on Nevada sand. 32

33 c <.1% c >.2% Relationships between the stiffness index, N, and cyclic pore water pressure, u N *, for the Wildlife Site silty sand (Vucetic and Dobry, 1986) and Nevada clean sand obtained in cyclic triaxial and simple shear tests. Relationship between the normalized cyclic pore water pressure, u N / 3, and the stiffness index, N =G SN /G S1, obtained in the triaxial cyclic strain controlled tests on reconstituted specimens of Monterey No. sand at smaller c =.3% and.1% (derived from Dobry et al., 1982) Important observation: Cyclic threshold shear strain for cyclic degradation, td, in sand cannot be clearly defined, except that it is evident that if c >.2% fully saturated sand will degrade from the 2 nd cycle on. If c <.1% sand will stiffen in the first few cycles and then start degrading. 33

34 Example of potential error in modeling degradation in DESRA, DESRAMOD and D-MOD computer codes If at small cyclic strains below.1% u*=.3, G mt =.84 G mo instead of just G mo, and mt =.7 mo instead just mo 34

35 Conceptual model of the variation of stiffness index, N, in fully saturated sands during the undrained cyclic strain controlled loading with relatively small cyclic shear strain amplitude, c, greater than the threshold shear strain tp. 35

36 36