FROM THEORY TO PRACTICE IN GEOTECHNICAL ENGINEERING: THE MISSING LINKS. Yannis F. Dafalias

Transcription

1 FROM THEORY TO PRACTICE IN GEOTECHNICAL ENGINEERING: THE MISSING LINKS Yannis F. Dafalias Department of Civil and Environmental Engineering, University of California at Davis, & Department of Mechanics, National Technical University of Athens November 25 Acknowledgement: The support by the NSF Grant No. CMS of the program directed by Dr Richard Fragaszy is acknowledged.

2 FORWORD: The following presentation is within the context of the present workshop and the meaning associated therewith to such words as Theory and Practice is properly adjusted. WHAT IS THEORY? Theory is the development of constitutive relations for geo-materials and their numerical implementation for the solution of boundary value problems, where an important aspect is the interaction of the geo-mass with non-geotechnical structures in the form of fixed or variable boundary conditions. WHAT IS PRACTICE? Practice is the specification of the detailed design steps for the construction of a geostructure and/or the foundation of a non-geotechnical structure, accounting for the soilstructure interaction, based on the documentation of mechanical and other properties of the relevant geotechnical site.

3 DIFFERENCE IN OBJECTIVES Theory is mainly an analysis tool used for design purposes, while Practice is the design process itself, which uses different methods of analysis as some of the means of design. DIFFERENCE IN NATURE Theory is an exact analytical method presupposing accurate knowledge of in-situ properties (in a deterministic or probabilistic sense), while Practice is a design method which uses both analytical and empirical tools of analysis based on a feasibly accurate level of knowledge of in-situ properties. NOTE: Practice is not necessarily the Raison d Etre of Theory, but it does certainly gives it a wider base of socio-economical importance.

4 FIRST MISSING LINK: User-Confidence on Constitutive Models User: The practitioner Modeler: The researcher User-confidence may be compromised because of the following reasons: Complexity Not an important reason for the user, because he is not interested in the internal working of a model. However, complexity may be the reason for unforeseen cases of internal inconsistencies and/or non-convergence of associated numerical implementations. Calibration Model constants and initiation values of model variables may be difficult to determine. They must be measurable from experiments and in-situ measurements. Easiness of determination is more important than physical meaning of a constant or a variable for a user (e.g. ODF of particles). Numerical Stability and Convergence The model structure may be the reason for creating problems of numerical instability and convergence. The user cannot (and should not be obliged to) overcome this problem. The modeler must account for this attribute of his model.

5 FIRST MISSING LINK: User-Confidence on Constitutive Models User-confidence may be compromised because of the following reasons (continued): Relevance to Specific Loading and Design Conditions The following examples illustrate this reason: i. A very good model for monotonic loading which is not able to address the response under stress reversals and cyclic loading, is useless for the analysis of earthquake related problems. ii. A very good model which cannot address localization events, cannot be used for the analysis of post localization calculations. iii. A enhanced model (gradient, Cosserat, non-local etc) which is not realistic in simulating the soil response, cannot capture the correct localization/failure event. iv. A model good for moderate to large strains but inaccurate for very small strains, is not appropriate for many excavation problem designs. v. A model good for very small strains but inaccurate for moderate to large strains, is not appropriate for combined deformation and failure analysis of excavations. Black-Box Attributes A model whose performance resembles a black-box process (input-output), does not appeal to the user s engineering intuition about the effect of material response on design investigation.

6 FIRST MISSING LINK: User-Confidence on Constitutive Models User-confidence may be compromised because of the following reasons (continued): Relation to Microstructure It is of no major importance to the user (practitioner), while it is to the researcher. The simulation of the model must be in accordance to standard macroscopic experimental data. Generic Attributes This is of great importance to both user and researcher. It determines the general profile of the model. Such attributes provide general rules of behavior irrespective of the specific constitutive model details used. For example such generic attributes are the framework of Critical State in soil mechanics, of Bounding Surface in plasticity and of non-local extensions of local models in elasto-plasticity. REMEDY for the First Missing Link The training of practitioners by researchers to use a constitutive model, and the subsequent design of a geotechnical project by the practitioners using, among other means, the model analysis entirely on their own. It presupposes a minimum level of acquaintance of the practitioner with inelasticity theories, and the action by the researcher/modeler to address all the previously mentioned reasons for lack of confidence. NOTE: It does not intend to change the practitioner into a modeler.

7 SECOND MISSING LINK: Proof of Superiority in Predictable-Response Designs Practice has achieved the completion of remarkable construction projects for which the predictability of response to various loading conditions has been, to a large extent, confirmed by experience. Thus, advanced methods may not appear as necessary in such cases. However, to a large extent does not cover all cases. For example the prediction of large lateral displacements under earthquake loading is beyond the capabilities of practice based methods. REMEDY for the Second Missing Link Analysis of existing catastrophic failures (Case-studies) by advanced methods, must be able to show that a corresponding design process would have predicted and, therefore, avoided the failure by proper design modifications. Large research projects such as VELACS, have addressed the issue by centrifuge experiments instead of real case-study situations. If this is realized to a convincing level for the practitioner, then advanced methods may also be adopted for routine type of problems in practice.

8 THIRD MISSING LINK: Proof of Economic Benefits This is a very subtle point in regards to who benefits by using advanced methods of analysis for design. A more accurate design will reduce the cost of construction to the client, but also the level of economic gains to the construction companies if calculated at a percentage of the cost. Question: Why then construction companies would adopt such advanced methods? Answer: Because it may be the case that one competing company uses such method to reduce both cost and gains in order to take the project, thus, others will follow. In other words, this missing link between Theory and Practice, may be more of an economic and political nature rather than technical. REMEDY for the Third Missing Link A set of representative projects of various levels of complexity and size, must be designed with and without use of advanced methods for near-real situations (experience from existing projects can be used). The final designs must be given to an experienced construction team and asked to estimate the cost of each one, accounting for the different demands of input data required by each different design method. The possible savings by using the advanced methodology will address the issue of importance of economic benefits.

9 GENERIC CONSTITUTIVE INGREDIENTS INTRODUCE DEPENDENCE OF DILATANCY AND PLASTIC MODULUS FOR ANY SAND MODEL ON: A. STATE PARAMETER B. INHERENT FABRIC ANISOTROPY C. EVOLVING FABRIC ANISOTROPY IN ORDER TO OBTAIN SIMULATIONS OF RESPONSE UNDER DIFFERENT PRESSURES, DENSITIES, DIRECTIONS OF LOADING, INHERENT FABRICS, MONOTONIC & CYCLIC LOADING, etc METHODOLOGY: GENERIC

10 DEPENDENCE ON STATE PARAMETER - Triaxial q M b M M d Recall: η ( b Κ = h M η) p D = A d ( d M η) p M b = M k b ψ (Manzari & Dafalias, 1997; Wood et al, 1994) M b = Mexp( n b ψ) (Li & Dafalias, 2) M M d = d = M + k d ψ Mexp(n d ψ) (Manzari & Dafalias, 1997) (Li & Dafalias, 2)

11 TOYOURA SAND: TRIAXIAL, p = 1 3kPa, e = Data (Verdugo & Ishihara 1996) Simulations (Dafalias & Manzari 24) q = ó 1 - ó 3 (kpa) ( a ) 3kPa 2kPa 1kPa p o =1kPa Data e = ( c ) 3kPa 2kPa 1kPa p o =1kPa Simulations å 1 (%) å 1 (%) q = ó 1 - ó 3 (kpa) ( b ) Data e = ( d ) Simulations p = (ó 1 + 2ó 3 ) / 3 (kpa) p = (ó 1 + 2ó 3 ) / 3 (kpa)

12 q = σ z - σ r (kpa) q = σ z - σ r (kpa) EXPERIMENTAL MOTIVATION Triaxial Data TC (b=, α= ο ) p o p = (σ z + σ r + σ θ ) / 3 (kpa) TC (b=, α= ο ) TE (b=1 α=9 ο ) TE (b=1, α=9 ο ) γ = ε z - ε r (%) F v T p i σ 1 b = σ 2 σ 3 σ 1 σ 3 tan(2α)= σ θ σ 3 SAME inherent fabric DIFFERENT loading directions α 2σ zθ σ z - σ θ σ z σ zθ q = σ 1 - σ 3 (kpa) σ 2 = σ r q = σ 1 - σ 3 (kpa) Non-Triaxial Data b =.5 (= const.) Data, b =.5 e=.82 45ο α=15 ο 75 ο 1 p = (σ 1 + σ 2 + σ 3 ) / 3 (kpa) Data, b =.5 e=.82 α=15 ο 3 ο 45 ο 6 ο 75 ο γ = ε 1 - ε 3 (%) (Yoshimine et al, 1998) (Yoshimine et al, 1998)

13 SCALAR MEASURE OF INHERENT FABRIC ANISOTROPY (Li & Dafalias, 22 ; Dafalias, Papadimitriou & Li, 24) FABRIC TENSOR FOR TRANSVERSE ANISOTROPY F = a ½(1-a) ½(1-a) a 1 Isotropy: a = 1/3 RELATION OF LOADING DIRECTION n to F IS MEASURED BY SCALAR-VALUED ANISOTROPIC STATE VARIABLE A = g(θ, c) F : n.1 a =.29.5 A e TE p o F v σ 3 σ z σ zθ T σ 1 α p i σ2 σ3 σ θ ; b = σ1 σ3 σ 2 = σ r A -.5 TC b=.75 A c b= b=1 b=.5 b= angle α (degrees)

14 DEPENDENCE ON INHERENT FABRIC ANISOTROPY Dependence of D on A Dependence of K p on A D=A Κ p = B h ο [Mexp(-n b d [Mexp(n d ψ) η] ψ) η] 1 e c = e o λ (p/p a ) ξ e o = e A exp( A) e A =.875 (λ =.2, ξ =.7) Β = f(p, e, ) h o = h A 1 + k h -k h A e A A e A c 1 void ratio e.9.8 e oc e A e oe CSL (A=A c ) CSL (A = ) h o / h A CSL (A=A e ) k h p (kpa) A c ( - ) ( + ) variable A A e

15 TOYOURA SAND: Tests with constant b (= 1) & α (= 9 ο ) Data (Yoshimine et al, 1998) Simulations (Dafalias et al, 24) q = σ 1 - σ 3 (kpa) Data, b =.5 (e= ) α=15 ο 3 ο 45 ο 6 ο 75 ο 2 ( a ) ( c ) simulations α=15 ο 3ο 45 ο 6 ο 75 ο q = σ 1 - σ 3 (kpa) γ = ε 1 - ε 3 (%) Data, b =.5 (e= ) 45 ο 75 ο α=15 ο 2 ( b ) ( d ) γ = ε 1 - ε 3 (%) simulations 75 ο 45 ο α=15 ο p = (σ 1 + σ 2 + σ 3 ) / 3 (kpa) p = (σ 1 + σ 2 + σ 3 ) / 3 (kpa)

16 EXPERIMENTAL MOTIVATION EVOLVING ANISOTROPY shear stress τ (kpa) effective axial stress σ a ' (kpa) Ι. After dilation, subsequent contractive behavior is enhanced II. Fabric changes (contact normals) during dilation are such that explain subsequent contraction τ τ q [kpa] p [kpa] 8 III. This results in the so-called butterfly stress path and imminent liquefaction

17 EVOLVING FABRIC EFFECT ON DILATANCY (Dafalias & Manzari, 24) D = A d (M d η) TENSOR internal variable z: A d = A o (1 + < z:n >) Data (Verdugo & Ishihara 1996) Simulations (Dafalias & Manzari, 24) q (kpa) p (kpa) q (kpa) 4-2 [ n z] p z & B ε& v z + = max TOYOURA SAND: TRIAXIAL testing including shear reversal q (kpa) data z max =4 z max = p (kpa) internal variable z å a (%) successful simulation only with z max

18 CONCLUSION The missing links for bridging the gap between Theory and Practice in Geotechnical Engineering are: A. User-Confidence on Constitutive Models B. Proof of Superiority in Predictable-Response Designs C. Proof of Economic Benefits Remedies for each one are suggested