Stability analyses of quick clay using FEM and an anisotropic strain softening model with internal length scale

Transcription

1 Stability analyses of quick clay using FEM and an anisotropic strain softening model with internal length scale Gustav Grimstad Associate Professor at Oslo and Akershus university college of applied sciences (former project leader at NGI) Hans Petter Jostad Discipline leader for numerical modeling at NGI Adjunct Professor at NTNU

2 Sokkelvik 1959 Rissa 1978 Bekkelaget 1953 Kattmarka2009

3 Some examples on slides in clay in Norway Year L [m] Groruddalen 6300 B.C. Lørenfallet 1794 Tesenfallet 1795 Verdalen Borgen 1953 Bekkelaget Furre Sokkelvik Skjeldstadmarka 1962 Skjønhaug 1967 Båstad Rissa Vestfossen Balsfjord Finneidfjord Leistad Kattmarka Lyngen Byneset Leistad 2002

4 KATTMARKA 2009 LEISTAD 2002 LYNGEN 2010

5 Slides in quick clay can be categorized as follow Downward progressive failure Upward progressive failure (retrogressive) Retrogressive failure (upward and sideways) NVE

6 Slides in quick clay can be categorized as follow Downward progressive failure Upward progressive failure Retrogressive failure (upward and sideways) NVE

7 Some probable downward progressive slides in sensitive materials in Norway and Sweden

8 Examples on recent R&D in Norway PhD Studies Lars Andresen (2002) Capacity Analysis of Anisotropic and Strain softening clay Vikas Thakur (2007) Strain Localization in Sensitive Soft Clays Anders Gylland ( ) Characterization and modeling of shear bands in soft sensitive clay

9 R&D at NGI I) Effect of progressive failure for development in quick clay areas ( ) (Jostad/Grimstad) 1. Development of calculation procedure 2. Back calculation 3. Probabilistic analyses 4. Recommendations Financed by Norwegian Public Roads Administration Norwegian Water Resources and Energy Directorate The Research Council of Norway and NGI II) Strategic project (SP1) ( ): Slides in sensitive clays (Project leader V. Gjeldsvik)

10 1. Development of calculation procedure 2. Back calculation 3. Probabilistic analyses 4. Recommendations

11 Material model NGI-ADPSoft (3D) f ( σ, p ) s u (, p ) =0 o zz 45 o xz 90 o z xx

12 On Modelling - Softening Trivial solution: h H h/h

13 Localization Localized deformation: t SB /H = 1 h H unloading t sb 0.1 Elastic unloading 0.5 h/h Mesh dependent results!

14 Over non-local strain z h 1 t sb d h /dz Gives control on the thickness of the shearband! p 1 V w p dv

15 Effect of shear band thickness 4 Previous work: p max = 3.69 s u Jostad & Andresen (2004) Load p /s u C 3 2 p tsb = 150 cm tsb = 50 cm tsb = 1 cm Peak load dependent on shear band thickness 1 Reduced capacity Foundation displacement max /B

16 How much does strain compatibility matter and how much progressive failure matters example bearing capacity LE strain compatibility 8% FEA (both) 25% reduction ACTIVE PASSIVE DSS AV

17 1. Development of calculation procedure 2. Back calculation 3. Probabilistic analyses 4. Recommendations

18 Quick clay slide at Vestfossen in 1984 Initiated by filling for football field Size: 120 m 130 m

19 Vestfossen Profile E E Kvikkleire Endelig bruddflate Ny fylling Level (m) Vestfosselva 40 m m 20 s u A from SHANSEP Terrain 100 y x 0

20 Finite element calculations Analyses without fill and softening, F = LE, F = 1.264

21 Limit equilibrium prev. study FOS before filling: After: M M dr st R x A l s u ~ 24.5 m ( ) = knm = knm F ~ / = 1.1 Reality: 1.0!

22 New LE analyses with strain compatibility

23 FE Results with softening and fill Incremental displacements: Total vertical displacements:

24 Calibration of the design requirements Case Vestfossen A variation of the input parameters were done to check how large difference one would get between perfectly plastic model and with strain softening model. By loading to failure with softening (F = 1) and using the same load with perfectly plastic material and phi/c reduction (F > 1) the a factor could be found This was typically, for Vestfossen, in the range of LE analyses with and without strain compatibility suggested 1.06 (i.e. much comes from strain compatibility) However, not systematic enough to give general advise

25 1. Development of calculation procedure (FEM) 2. Back calculation (always room for more) 3. Probabilistic analyses 4. Recommendations

26 Flow chart of finding distribution for the correction factor for one problem RND material input, from distribution of each input parameter Analysis with strain softening Take out the FOS Take out failure load and set in file for perfectly plastic analysis Do phi/c reduction with this load

27 A routine to do this automatically Input is generated for up to 80 material parameters and 10 materials using a Monte Carlo approach Then analyses are ran subsequently (or in parallel) through the list given To speed up the calculation loading is stopped automatically at a specified numbers of steps over the peak and phi-c reduction is stopped based on the current stiffness parameter (CSP) and change in FOS from previous step The results of failure load and FOS is logged Post processing is done in separate program

28 Results from test on a bearing capacity problem p [ ] FOS [ ]

29 1. Development of calculation procedure (FEM) 2. Back calculation (always room for more) 3. Probabilistic analyses (not completed) 4. Recommendations

30 Required calculated factor of safety The increased calculated safety for sensitive clays should now be 7% 14% p [ ] FOS [ ]

31 For the future The program will be used on several cases, both historical slides and hypothetical cases. This could result in one correction factor as it is today Or the final result could be a factor dependent on the initial stability of the slope etc.

32 Thanks!