1. Safety and soil-structure interaction: a question of scales Denys BREYSSE CDGA, Université Bordeaux I Probamat – JHU Baltimore – 5-7/01/2005

2. Variations in the longitudinal profile of a pavement: IRI Buried pipe collapse Longitudinal control of railway track (Mauzin) The longitudinal variation of soil properties has a major influence for many types of structures (pavements, buried pipes, raft foundations, railways...) since it induces stresses and/or displacements that cannot be predicted when assuming homogeneity.

3. pressure on ground [q] soil’s stiffness stiffness – geometry of the structure settlements [s] Geotechnical study Stresses in soil Stresses in the structure External loads [p] boundary conditions Stiffness - geometry pressure on ground [q] Structural study

4. pressure on ground [q] soil’s stiffness stiffness – geometry of the structure settlements [s] Geotechnical study 3 Stresses in soil 2 Stresses in the structure 4 1 External loads [p] boundary conditions Stiffness - geometry pressure on ground [q] Structural study

5. non linear behavior of interface non linear behaviour of soil effect of boundary conditions on load redistributions effect of loading on structural stiffness 1 4 3 2 Ground spatial variabilityStructural stiffness

6. First case : when variability reduces to uncertainty p E(x) E(x) ? Estimate of a design (or « risky ») value of E  Estimate of a design (or « risky ») value of settlement It is the role of the engineer, who must choose design values Duncan (2000) : 3-sigma rule “a conscious effort should be make the range between higher conceivable value and lower conceivable value as wide as seemingly possible, or even wider, to overcome the natural tendancy to make the range too small”

7. Second case : when spatial correlation has an influence p E(x) Role of lc which explains and influences differential settlements: existence of a « critical range » of lc values 20 m Various correlation lengths lc

8. lc B L Explaining the influence of correlation length: when it reduces to purely geometrical causes Variance reduction below shallow foundation  (B, lc) Distance between supports L Correlation coefficient between the two settlements s and s’ (Tang, 1984)  (s, s’) = [  k (-1) k L k ²  s ²(L k )] / [2 B B’  s (B)  s (B’)] k = 0 - 3 L 0 = L – B/2 – B’/2, L 1 = L + B, L 2 = L + B + B’, L 3 = L + B’  ²(x) variance reduction function (depends on the shape of the autocorrelation fct)

9. lc B L Variance reduction below the foundation  (B, Lc) Correlation between supports fct (L, Lc) Var(  ) = 4 (Lc/B)² (B/Lc – 1 + e -B/Lc ). (1-  (s, s’)). Var (so) Three dimensions (B, L et Lc) drive the problem Explaining the influence of correlation length: when it reduces to purely geometrical causes Var (so) comes from the magnitude of local scatter of soil properties Var (so) = 1

10. Third (general) case: stiffness(es) play a role p E(x) p K R = (E c J)/E s L 3 relative structure/soil stiffness ratio K R > 0.5  “stiff” structure f.i., with Es = 20 MPa and Ec = 30 000 MPa - cylindric pipe L = 3 m, width R/10, stiff if R > 0,5 m, - slab L = 8 m stiff if depth > 1m30, - multi-storey building (wall thickness 20 cm), stiff if H>L/3 EN 1992 (Annex G - informative): must account for interactions and its consequences on loads (on soil and structure) and displacements structure very soft  loads on soil easy to compute structure very stiff  displacements easy to compute Reality intermediate

11. Needs a detailed modelling of: - soil heterogeneity - materials response and soil/structure interaction Ex. 1: beam on three supports (coll. G. Frantziskonis) Ex. 2: buried pipe (coll. SM. Elachachi) Ex. 3: poutre sur 3 appuis (coll. H. Niandou) Explaining the influence of correlation length: when it does not reduce to purely geometrical causes Several dimensions (defining the structure geometry and the soil correlation scale) have an influence Two stiffnesses (soil Es and structure [Ec, J, L]) have an influence Statistics and geostatistics Mechanics and material modelling

12. Example 1: beam on three supports E(soil) = 10 MPa (coll. G. Frantziskonis) Moments on supports and at midspan (kN.m) fixed supports elastic supports meanst.-dev. fractile 95 % fractile 99 % central support midspan - 250 - 16325.2- 196- 205 + 125+ 16912.4 +191 (+53%) +208 (+66%)

13. Example 2 : buried pipe (sewer) M95 (kN.m) L c /L k (MN/m 3 ) Statistical analysis of bending moments The problem is driven by ratios : - length ratio : L / lc - stiffness ratio k (soil) / EI (pipe)

14. Example 3 : raft foundation on piles 2 reference solutions (q = 400 kN/m) : - k  0 (stiff raft)  uniform load in all piles = 1,38 MN - k  infinity (stiff piles)  load R3 = 1,63 MN Lc = 10 m

15. Example 3 : raft foundation on piles The response is statiscally driven by: -a length ratio L/Lc -a stiffness ratio h 3 /k (= cte x K R ) Ref. stiff raft Consequences: different loads in piles and in raft  safety estimate ? + 52 % Critical value of the ratio

16. Example 3 : raft foundation on piles safety index  is mean, V is c.o.v. E regards load effect and R regards strength Vr = 0,2, deterministic F.S. = 2,7 Deterministic load effect  = 4,97 P f = 0,34 10 -6 Interaction and probabilistic load effect  = 3,20 P f = 0,69 10 -3

17. Critical value of L/Lc = fct (stiffnesses and behavior, studied output)  enables to reduce the cost of Monte-Carlo simulations (Lc is not a variable or an unknown) Trying to synthetize Full interaction ? yes no Influence of geometry/scales Influence of geometry AND stiffness ratio L’/Lc ratio « EcI’/EsJ » ratio « EcI/EsJ » ratio L/Lc According the problem complexity According the problem complexity

18. Disorders/damage will depend on - soil properties (scatter, correlation length lc) - structural geometry (D, B…) - mechanical behaviour of the system Accounting for spatial variability of soilsand settlements of supports makes possible the description of main phenomena: differential settlements, load redistribution Predicting safety levels requires inputs representative of soil randomness Identifying « worst cases» (worst ratios)can enable the use of deterministic models while including the statistical effects of randomness Accounting for damage sensitivity must be the following step Conclusions