First Asian Experienced Plaxis User Course 2003 -2

Full text

(1)1st Asian Course for Experienced. Plaxis Users. Dates. : 31 July to 2 August 2003. Location. : National University of Singapore. Course leader : Associate Professor Harry Tan, National University of Singapore. INTRODUCTION: This course will follow in the tradition of the International Course for Experienced Plaxis Users, held annually in The Netherlands. The course is scheduled to be held 4 days before the 12th Asian Regional Conference on Geotechnical Engineering in Singapore, so as to allow for maximum participation of Plaxis users in Asian countries. COURSE CONTENT: It is aimed to teach the use of advanced soil models and advanced features in the new Plaxis V8, and an introduction of the 3D Tunnel programs. The basic course covers the Mohr-Coulomb model, attention is now focused on the Hardening Soil model and the Soft Soil Creep model. These model and advanced features of Plaxis V8 are employed in handson practice in practical problems of excavations,. ratory soil investigations. As before, lectures will be followed by related exercises, which are real case studies. Also the 3D tunnel program will be introduced. • Deep excavations - Prof H. Tan • Consolidation in excavations and cut slopes Prof H. Tan • Tunneling - Prof P.A. Vermeer • Modeling of shield tunnels - Prof P.A. Vermeer • Introduction to 3D aspects of NATM tunneling Prof P.A. Vermeer The third day focused on the Soft Soil Creep model and its applications to embankments on weak foundations improved with PVD and geosynthetics. • Soft Soil Creep model - Prof P.A. Vermeer • Embankments on weak foundation with PVD and geosynthetics - Prof H. Tan SOFTWARE: Exercises and case studies are based on the PLAXIS computer program V8, which is used by geotechnical engineers worldwide. This user-friendly code has been developed for deformation analyses, stability. embankments, slopes and tunnels. The course provides both the knowledge and hands-on experience in using advanced soil models and new Plaxis features. The theoretical knowledge is provided in lectures, whereas the experience can be obtained from the exercises and case studies. Some of the main lectures concentrate on various aspects of excavations, embankments, slopes and tunnels, whereas others go into details of advanced modeling features. LECTURES: Experts with theoretical background and an extensive experience in practical computer modeling give lectures and prepare exercises of case studies. On the first day of the course the Hardening Soil model will be introduced and the effect of groundwater flow will be considered in detail. The specific areas of lectures are:. Organizers. : PAC, Faculty of Engineering, National University of Singapore PLAXIS BV Consoft International Pte Ltd. • • • • • •. Concepts of plasticity - Prof H. Tan Soil stiffness - Prof P.A. Vermeer Hardening Soil model - Prof P.A. Vermeer Drained and undrained behavior - Prof H. Tan Parameters of the HS model - Prof P.A. Vermeer Pore pressures and groundwater flow - Prof H. Tan. During the second day, the focus is on advanced engineering in the field of deep excavations and tunnels, and the determination of parameters from in-situ and labo-. assessment, groundwater flow and consolidation. It contains special options for soil-structures involving retaining walls, ground anchors,geosynthetics, tunnels linings, etc. The latest V8 has a fully automatic mesh generator based on graphical input of soil-layer geometries, and several new features to facilitate input and analysis of complex situations. Amongst other things, Plaxis V8 allows for fully coupled deformation-consolidation during staged construction. FORMAT: The course begins with registration on Thursday morning and ends on Saturday afternoon. Each session begins with 60 minutes of lectures followed by an application exercise of about the same length. Lectures are in English, and individual assistance will be provided by graduate students during exercises. COST: The cost of the course is $1200 per participant. This includes a full set of instruction manuals and the use of a computer. The fees also covers all lunches and two tea-breaks per day.. Prof Harry Tan - Department of Civil Engineering, NUS (course. Prof Pieter Vermeer - Professor of Geotechnical Engineering,. leader). University of Stuttgart (Germany). Harry teaches basic and graduate course in Geotechnical Engi-. Pieter teaches both basic courses on Soil Mechanics and special. neering at NUS. He has been a Plaxis user over the last 10 years,. courses of Geotechnical Engineering at the University of. and has taught Plaxis courses in Singapore, Malaysia and Korea. Stuttgart in Germany. He has been involved in constitutive mod-. over the last 3 years. He is involved in geosynthetics and earth. elling and finite element analysis since the early seventies and. reinforcement research, and is very much involved in consulting. initiated the development of the Plaxis code. His interests range. for industry in Singapore and Malaysia using the Plaxis pro-. from field and laboratory testing of soils and rocks up to the. gram. He is currently the Director of Centre for Soft Ground Engi-. analysis of geotechnical structures.. neering at NUS.. The Lecturers.

(2) SCHEDULE 1st Asian Course for EXPERIENCED PLAXIS USERS Dates: 31/07, 1/08 and 2/08 2003 Thursday, 31 July 2003 0900-0915 0915-1000 1000-1015 1015-1100 1100-1200 1200-1300 1300-1345 1345-1415 1415-1515 1515-1530 1530-1615 1615-1700. CG01 Opening CG02 Concepts of Plasticity Break CG03 Stiffness of Soils CG04 Foundation (Exercise) Lunch CG05 Hardening Soil Model CG06 Drained and Undrained Soil Behavior CG07 Pile Loading Test (Exercise) Break CG08 Selection of Parameters for HS CG09 Pore Pressures and Groundwater Flow. Tan SA Tan SA Vermeer. Vermeer Tan SA. Vermeer Tan SA. Friday, 1 August 2003 0900-0945 0945-1015 1015-1030 1030-1200 1200-1300 1300-1400 1400-1500 1500-1515 1515-1630 1630-1700. CG10 Deep Excavations CG11 Consolidation Break CG12 New OG Excavation (Exercise) Lunch CG13 Tunnel Heading Stability CG14 Settlements due to Tunneling Break CG15 Shield Tunneling (Exercise) CG16 Plaxis 3D Tunnel (Demonstration). Tan SA Tan SA. Vermeer Vermeer. Saturday, 2 August 2003 0900-0945 0945-1030 1030-1045 1045-1200 1300-1400 1400-1415. CG17 Soft Soil Creep CG18 Embankment Modeling Break CG19 Muar Test Embankment (Exercise) Lunch CG20 Closure. Vermeer Tan SA. Vermeer/Tan.

(3) 1ST Asian Course for. EXPERIENCED PLAXIS USERS 31ST JULY to 2ND AUGUST 2003. THURSDAY, 31ST JULY 2003. CG02 CONCEPTS OF PLASTICITY.

(4) Concepts of Plasticity Ronald Brinkgreve Plaxis BV / Delft University of Technology. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Contents • Aspects of real soil behaviour • Stresses and strains • Stress paths in standard soil tests • Standard drained triaxial test (CD-test) • Oedometer test • Consolidated undrained triaxial test (CU-test). • Basic concepts of the Mohr-Coulomb model • Elastic strains, plastic strains • Yield function, plastic potential • Parameters. • Possibilities and limitations of the M-C model PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 2. 1.

(5) Aspects of real soil behaviour • • • • • • • • • •. Elasticity (reversible deformation; limited) Plasticity (irreversible deformation) Failure (ultimate limit state or critical state) Presence and role of pore water Undrained behaviour and consolidation Stress-dependent stiffness Time-dependent behaviour (creep, relaxation) Compaction en dilatancy Memory of pre-consolidation pressure Anisotropy (directional strength and/or stiffness). PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 3. Stresses and strains • Stresses Cartesian stresses: σ = σ xx σ yy σ zz. [. σ xy σ yz σ zx ]T. σ = σ '+σ w σ = total stresses σ’ = effective stresses σw = pore pressure (isotropic): • Hydrostatic (constant head) • Non-hydrostatic (variable head → groundwater flow) • Excess pore press. (undrained behaviour → consolidation) PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 4. 2.

(6) Stresses and strains • Stresses Principal stresses: σ 1 = s * −t *. (. s * = 12 σ ' xx +σ ' yy. σ 2 =σ zz σ 3 = s * +r *. t*=. 1 4. ). (σ 'xx −σ ' yy )2 + σ xy2. Stress invariants (p and q):. (. ). p=. 1 1 σ xx + σ yy + σ zz = (σ 1 + σ 2 + σ 3 ) 3 3. q=. 1 2 2 (σ xx − σ yy ) 2 + (σ yy − σ zz ) 2 + (σ zz − σ xx ) 2 + 6σ xy + 6σ 2yz + 6σ zx 2. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 5. Stresses and strains • Strains. [. Cartesian strains: ε = ε xx Normal strains ∂ ux ∂x ∂ uy ε yy = ∂y. ε xx =. ε zz =. ∂ uz ∂z. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. ε yy ε zz γ xy γ yz γ zx ]T Shear strains γ xy =. ∂ ux ∂ u y + ∂y ∂x. ∂ u y ∂ uz + ∂z ∂y ∂u ∂u γ zx = z + x ∂x ∂z. γ yz =. Concepts of Plasticity. 6. 3.

(7) Stresses and strains • Visualisation of stresses: -σ1. -σ1 p-axis. q-axis. √2. Rendulic plane q-axis. p-axis 1. -σ3 σ2= σ3. -σ2. -σ3√2. Principal stress space PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Rendulic plane Concepts of Plasticity. 7. Stresses and strains • Visualisation of stresses:. -σ1. -σ1 p-axis Deviator plane -σ3. -σ2. -σ3. -σ2 Principal stress space. Deviator plane (π-plane) (p = constant). PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 8. 4.

(8) Stress paths in standard soil tests • Standard drained triaxial test (CD test) Stress-strain and strain diagram: σ1 εv. ⏐σ1-σ3⏐ ⇓ ε1. σ3. σ3. -ε1. εv. -ε1. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 9. Stress paths in standard soil tests. Loose sand PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Dense sand Concepts of Plasticity. 10. 5.

(9) Stress paths in standard soil tests • Standard drained triaxial test (CD test) Stress paths: σxy -σ’1 Axial loading. -σ3. σn -σ3. -σ’3. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 11. Stress paths in standard soil tests • Consolidated undrained triaxial test (CU test) Stress-strain diagram: σ1 ⏐σ1-σ3⏐ εv ≈ 0 σ3. ⇓ ε1 σ3. pw. -ε1 -ε1. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 12. 6.

(10) Stress paths in standard soil tests. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 13. Stress paths in standard soil tests • Consolidated undrained triaxial test (CU test) Stress paths: -σ’1 Axial loading. -σ3 -σ3. -σ’3. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 14. 7.

(11) Stress paths in standard soil tests • Oedometer loading test Stress-strain diagram:. σ1. σ1 -ε1 ln σ1. ⇓ ε1. -ε1 PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 15. Stress paths in standard soil tests • Oedometer loading test Stress paths: -σ’1. Axial loading. -σ’3 PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 16. 8.

(12) Stress paths in standard soil tests • Simple shear test Stress-strain diagram: dσxy. σxy. ⇒ dγxy γxy εv γxy PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 17. Stress paths in standard soil tests • Simple shear test Stress paths:. -σ’1 Shearing. -σ’3 PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 18. 9.

(13) Basic concepts of the M-C model • Division of strains and strain increments: ε =ε e + ε p. (strains). dε = dε e + dε p. (strain increments). Strains (or increments) are divided into elastic strains and plastic strains A soil model relates increments of stress to increments of strain. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 19. Basic concepts of the M-C model • Elastic strain increments: e ⎡ d ε xx ⎢ ⎢ ⎢dε e ⎢ yy ⎢ ⎢ e ⎢ d ε zz ⎢ ⎢ e ⎢ d γ xy ⎢ ⎢ ⎢ d γ eyz ⎢ ⎢ ⎢dγ e ⎣ zx. ⎤ ⎡ 1 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢− ν ⎥ ⎢ ⎥ ⎢ ⎥ ⎢− ν ⎥ 1 ⎢ ⎥ = ⎢ E ⎢ ⎥ ⎥ ⎢ 0 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 0 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢⎣ 0 ⎦. From Hooke’s law:. −ν. −ν. 0. 0. 1. −ν. 0. 0. −ν. 1. 0. 0. 0. 0. 2 + 2ν. 0. 0. 0. 0. 2 + 2ν. 0. 0. 0. 0. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. ⎤ ⎡ d σ ' xx ⎥⎢ ⎥⎢ 0 ⎥ ⎢ d σ ' yy ⎥⎢ ⎥⎢ 0 ⎥ ⎢ d σ ' zz ⎥⎢ ⎥⎢ ⎥⎢ 0 ⎥ ⎢ d σ ' xy ⎥⎢ ⎥⎢ 0 ⎥ ⎢ d σ ' yz ⎥⎢ ⎥⎢ 2 + 2ν ⎥⎦ ⎢⎣ d σ ' zx 0. ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦. 20. 10.

(14) Basic concepts of the M-C model • Plastic strain increments: d ε p = dλ. From flow rule:. ∂g ∂σ '. dλ = magnitude of plastic strains (multiplier) dg/dσ’ = direction of plastic strains (vector) g = plastic potential (function) Classical plasticity: g = f. (associated plasticity). For soils in general: g ≠ f. (non-associated plasticity). f = yield function PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 21. Basic concepts of the M-C model • When do plastic strains occur? Determination on the basis of a yield function f = f(σ’,ε) • If f < 0 • If f = 0 and df < 0 • If f = 0 and df = 0 • f>0. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Pure elastic behaviour Unloading from a plastic state (= elastic behaviour) Elasto-plastic behaviour Non-acceptable stress state. Concepts of Plasticity. 22. 11.

(15) Basic concepts of the M-C model • Yield function: Can be represented as a contour in (principal) stress space σ1 f>0. Not acceptable. f=0. Plasticity. f<0. Elasticity. σ3. σ2. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 23. Basic concepts of the M-C model • Mohr-Coulomb yield criterion: σ’yy. τα. σxy σ’α τα. c’ cosϕ’ t*. σxy σ’xx. ϕ’ c’ -σ3. -s* sinϕ’. -σ1. -σα. -s*. α. The condition τα ≤ c’ - σ’α tanϕ’ must hold for arbitrary angles α Equivalent expression: PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. t* ≤ c’ cosϕ - s* sinϕ’ Concepts of Plasticity. 24. 12.

(16) Basic concepts of the M-C model • Mohr-Coulomb yield criterion and yield function: t* ≤ c’ cosϕ’ - s* sinϕ’ t* = ½(σ’3 - σ’1). t *=. s* = ½(σ’3+σ’1). s*=. 1 2. ( (. ) ). 2 1 σ ' −σ ' xx yy 4 1 σ ' +σ ' xx yy 2. 2 + σ xy. (σ '3 −σ '1 ) ≤ c' cos ϕ ' − 12 (σ '3 +σ '1 )sin ϕ '. f = 12 (σ '3 −σ '1 ) +. 1 2. (σ '3 +σ '1 )sin ϕ '− c' cos ϕ '. Note: Compression is negative and σ’1≤ σ’2≤ σ’3 PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 25. Basic concepts of the M-C model • Mohr-Coulomb yield function: f = 12 (σ '3 −σ '1 ) +. 1 2. (σ '3 +σ '1 )sin ϕ '− c' cos ϕ '. • Mohr-Coulomb plastic potential: g = 12 (σ '3 −σ '1 ) +. 1 2. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. (σ '3 +σ '1 )sinψ '− c' cosψ '. Concepts of Plasticity. 26. 13.

(17) Basic concepts of the M-C model -σ1. • Yield directions in deviator plane: ϕ = 30° ψ = 0°. -σ2. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. -σ3. Concepts of Plasticity. 27. Basic concepts of the M-C model • Mohr-Coulomb parameters: E ν c’ ϕ’ ψ. Young’s modulus Poisson’s ratio (effective) cohesion (effective) friction angle Dilatancy angle. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. [kN/m2] [-] [kN/m2] [º] [º]. 28. 14.

(18) Basic concepts of the M-C model • Elasticity parameters: E , ν - dε1 ⇓ dε3 ⇐. - σ1 E=. dσ1 dε1. ν=−. E. dε 3 dε1. 1 - ε1. ν. 1. ε3 PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 29. Basic concepts of the M-C model • Alternative elastic parameters: Shear modulus: G=. dσ xy dγ xy. dσxy ⇒ dγxy. E = 2(1 + ν ). dp. Bulk modulus: K=. E dp = dε v 3(1 − 2ν ). - dσ1. Oedometer modulus: Eoed. E (1 − ν ) dσ = 1= dε1 (1 + ν )(1 − 2ν ). PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. dεv. Concepts of Plasticity. ⇓ - dε1. 30. 15.

(19) Basic concepts of the M-C model • Plasticity parameters: c’, ϕ’ -σ’1 σxy. b. ϕ’. 1 a. c’ σ’n. -σ’3 a=. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. 2c ' cos ϕ ' 1 − sin ϕ '. b=. 1 + sin ϕ ' 1 − sin ϕ '. Concepts of Plasticity. 31. Basic concepts of the M-C model • Plasticity parameter: εyy. σxyxy σσxy σxy. ψ σxy. γxy p dε yy p dγ xy. γxy = tanψ. εyy. ψ. γxy. dilatancy ψ PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 32. 16.

(20) Basic concepts of the M-C model ψ. • Plasticity parameter: dε ije = (D e )ijkl dσ 'kl = 0 −1. dε ijp = dλ. ∂g ∂σ 'ij. dε xx = 0. dε xxp = dλ. ⎛ σ ' −σ ' yy 1 ⎞ ∂g + 2 sinψ ⎟ = = dλ ⎜ xx ∂σ ' xx ⎝ 4 t* ⎠. 0. dε yyp = dλ. ⎞ ⎛ σ ' −σ ' xx 1 ∂g = dλ ⎜ yy + 2 sinψ ⎟ = ∂σ ' yy ⎠ ⎝ 4 t*. dλ sinψ. dγ xyp = dλ. ⎛σ ' ⎞ ∂g = dλ ⎜ xy ⎟ = ∂σ ' xy ⎝ t* ⎠. p dε yy. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. dλ cosψ. p dγ xy. = tanψ. Concepts of Plasticity. 33. Basic concepts of the M-C model • Meaning of M-C parameters in drained triaxial test: ⏐σ1-σ3⏐. σ’3 = confining pressure. E’. 2c' cos ϕ '−2σ '3 sin ϕ ' 1 − sin ϕ '. -ε1. εv. 2 sinψ 1 − sinψ. 1-2ν’ PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. -ε1. Concepts of Plasticity. 34. 17.

(21) Basic concepts of the M-C model • Meaning of M-C parameters in oedometer test: σ1. -σ1. 1 Eoed. 1-ν ν. -ε1. -σ3. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 35. Possibilities and limitations of M-C • Possibilities and advantages: • • • • • •. Simple and clear model (elastic perfectly-plastic model) First order approach of soil behaviour in general Suitable for many practical applications Limited number and clear parameters Good representation of failure behaviour (drained) Dilatancy can be included. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 36. 18.

(22) Possibilities and limitations of M-C • Limitations and disadvantages: • • • •. Isotropic and homogeneous behaviour Linear elastic behaviour until failure No stress-dependent stiffness No distinction between primary loading and unloading or reloading • Dilatancy continues for ever (no critical void) • Undrained behaviour not always realistic • No anisotropy, no time-dependency (creep) PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 37. Thank you for your attention. Questions ?. PLAXIS FINITE ELEMENT CODE FOR SOIL AND ROCK ANALYSES. Concepts of Plasticity. 38. 19.

(23) 1ST Asian Course for. EXPERIENCED PLAXIS USERS 31ST JULY to 2ND AUGUST 2003. THURSDAY, 31ST JULY 2003. CG03 Stiffness of Soils.

(24) On the stiffness of soils 1. Hooke´s law linear elasticity. (in MC-model). 2. Exponential compression law. (in HS-model). 3. Logarithmic compression law as a special case. IGS, Stuttgart. By Pieter A. Vermeer University of Stuttgart, Germany. Oedometer for one-dimensional compression. Axial load. Soil sample. Porous filter. Containing ring. The soil sample is enclosed in an impermeable rigid cylindrical ring with top and bottom porous filter stones. Hence, the pore water flow and the strain are one-dimensional. The water pressure in the porous filter stones is always zero. The pore water pressure in the soil sample varies with varying axial load. In common oedometer tests the axial load on the upper plate is varied and the change in height of the sample is measured.. IGS, University of Stuttgart. 1.

(25) Stresses and strains σ´z ∆lx. ∆lx l0. εx =. ∆lz. σ´x. ∆ly. εy =. l0. εz =. ∆lz l0. l0. εx = εy = 0. Effective normal stresses cause strains and determine the shear strength.. Oedometer test. Compressive stresses are positive when we use a dash.. Compressive strains are positive when we use a dash.. IGS, University of Stuttgart. Part I:. Hooke´s law of linear elasticity. σ´z. 1 (σx − ν ⋅ σ y − ν ⋅ σz ) E 1 (σ y − ν ⋅ σz − ν ⋅ σ x ) εy = E 1 (σz − ν ⋅ σ x − ν ⋅ σ y ) εz = E εx =. σ´x. σý. σ´x. ... (1). ... (2) ... (3). E = modulus of elasticity or Young´s modulus. ν = Poisson‘s ratio. IGS, University of Stuttgart. 2.

(26) Oedometer test on an elastic material σz. σz. ∆h. Eoed 1. h0. εz =. elastic material. (1) ... (2) .... 1 (σ x − ν σ y − ν σ z ) = 0 E 1 = (σ y − ν σ z − ν σ x ) = 0 E. εx = εy. σ´ x = σ y =. ν σz 1− ν. ν 1− ν. K0 =. hence:. ∆h h0. IGS, University of Stuttgart. Oedometer test on an elastic material σ´z. σ´z. Eoed = oedometer modulus or 1 constrained modulus ∆h εz = h0 elastic material. ∆h h0. (3) .... 1 ( σz − ν σx − ν σy ) E ν σx = σy = σz 1− ν. εz =. hence:. εz =. (1 − 2ν ) (1 + ν ) ⋅ σz E (1 − ν ). Eoed =. (1 − ν ) (1 − 2ν )(1 + ν ). ⋅E. In many countries Eoed is denoted as M (in Germany Es ).. IGS, University of Stuttgart. 3.

(27) 1-D settlement analysis with a single representative oedometer modulus. Settlements due to nearly 1D compression! new dam q s soil sample from representative position. h. rock The soil deformation under the centre of a wide dam resembles that of an oedometer test. σ´0 σ´ σ´0 = representative initial stress ∆σ´ ∆σ´ = q ∆ε ∆σ´ ⋅h s = ∆ε´⋅ h = Eoed = ∆σ´/ ∆ε´ Eoed ε´ Stress-strain curves of an oedometer test are generally non-linear. To determine the oedometer modulus, the curve should be linearized for the representative stress range. Applied modulus is a so-called secant modulus.. IGS, University of Stuttgart. Definition of oedometer modulus as secant or tangent modulus σ´. σ´. ∆σ´ midpoint. ∆ε ε´. final stress initial stress. secant modulus. Eoed ≡. ∆σ´ ∆ε´. ε´. tangent modulus. Eoed ≡. dσ´ dε´. Secant modulus is roughly equal to the tangent modulus in midpoint.. IGS, University of Stuttgart. 4.

(28) Example of 1-D settlement analysis with a single representative oedometer modulus σ´. For clays the tangent modulus is mostly proportional to stress. We will consider an example with Eoed = 10 ⋅ σ′. ε´ 40 kPa representative point γ´ = 10 kN / m. σ′0 = 6 ⋅ 10 = 60 kPa σ′0 + ∆σ = 100 kPa. 12 m. 3. σ0´ + ∆σ´/ 2 :. approximation with Eoed as tangent modulus for. ∆ε´ =. ∆σ´ 40 = = 0.05 Eoed 800. s = h ⋅ ∆ε´ ≈ 12 ⋅ 0.05 = 0.6 m. IGS, University of Stuttgart. Same exercise but a more accurate solution considering sublayers. This method can also be used for subsoil with different layers For this particular example the tangent modulus is given to be E oed = 10 ⋅ σ´ 40 kPa. sublayer A. sublayer B. sublayer C. σ´ 4m. σA. 4m. σB. 4m. σC. σÁ = 40 kPa Eoed = 400 kPa. ε´Α = 0.1 ∆s = 0.4 m. σ´B = 80 Eoed = 800. ε´B = 0.05 ∆s = 0.2 m. σĆ = 120 Eoed = 1200. εĆ = 0.033 ∆s = 0.133 m. z. s = 0.733 m. Difference with single layer procedure is about 20 %.. IGS, University of Stuttgart. 5.

(29) Method of single representative oedometer modulus for foundations. Load spreading has to be considered ! q=qo+∆q σzo'. σ z'. q o= γ d ∆σz. representative point for σz0 and ∆σz. h. ∆εz. 1 Eoed. limiting depth ε´z. b ∆q. ∆q. qo. σ´z. ∆σz. z = 0.5 b. ∆σz. z=b. σzo. ∆σz. z = 1.5 b. z. 1 Tangent modulus for σ′z 0 + ∆σ´z might be used in elastic FE-analysis or one might use the 2 2 settlement 1− ν s= ⋅ b ⋅ ∆q ⋅ factor E formula .. IGS, University of Stuttgart. Sublayering to account for stress-level dependency. EA. Eoed from. σ′z 0 +. A Eoed. EB. EBoed. EC. ECoed. ED. EF. 1 ∆σ´z 0 2. Settlements around the foundation and horizontal displacements will not be well predicted as stiffness is based on stresses underneath the foundation.. Selection of suitable stiffnesses is more complex than for foundation problems. It is an unloading problem, which requires high stiffnesses.. IGS, University of Stuttgart. 6.

(30) Settlements of shallow foundations on soft soils. 460 kPa 70 kPa. 59 m. 15 m. b. soft clay. soft clayey silt soft clay Pisa, Italy average settlement 300 cm. Constance, Germany settlement 3 – 6 cm Many buildings in Constance have raft foundations. Settlement would be considerably overpredicted when „limiting“ depth and “geological factor” would not be considered.. A simple „elastic“ calculation would yield an average settlement between 200 and 250 cm.. IGS, University of Stuttgart. Oedometer tests give sometimes relatively low stiffness moduli by Tomlinson (1995): where :. κ cal s. s = κ cal s. = a coefficient (geological factor) which depends on the type of clay = settlement as calculated from oedometer tests κ. Type of clay Very sensitive clays (soft alluvial, estuarine and marine clays). 1.0 – 1.2. Normally consolidated clays. 0.7 – 1.0. Overconsolidated clays (London Clays, Weald, Kimmeridge, Oxford, and Lias Clays). 0.5 – 0.7. Heavily overconsolidated clays (glacial till, Keuper Marl). 0.2 – 0.5. Tomlinson: Although the geological factor has some theoretical basis it is generally regarded as a means whereby the apparently high settlements calculated from oedometer test results can be reconciled with the much smaller settlements as measured in foundations on stiff overconsolidated clays. It is possible that oedometer tests on good samples taken by pistondriven thin-wall tubes will give higher stiffness values than those obtained from conventional hammer-driven thick-wall tube samples and hence the geological factor will no longer be required. Tomlinson (1995): Foundation Design and Construction, Pitman Publishing Inc.. IGS, University of Stuttgart. 7.

(31) Settlement of high-rise buildings on predominantly stiff Frankfurt clay RF: raft foundation PRF: piled raft foundation PF: pile foundation s:. foundation pressure 400 – 600 kN/m². settlement at the end of construction. Ćommercial bank II high-rise building´ 1994-97 PF, s = 2.1 cm. ´MAIN TOWER´ 1996-99 PRF, s = 2.5 cm. Ćitibank´ ÉUROTHEUM´ 1985-86 1997-99 RF, PRF, s = 11 cm s = 3.2 cm. ´Helaba high-rise building´ 1975-77 RF, s = 10 cm. Éuro tower´ 1974-77 RF, s = 9 cm ´Japan Center´ 1994-96 PRF, s = 3.2 cm. Ćommercial bank I´ 1972-74 RF, s = 9 cm. Simple elastic calculations give reasonable predictions of the average settlements of raft foundations, but not the influence of new settlements on existing buildings.. IGS, University of Stuttgart. Concluding remarks on the use of linear elasticity in geotechnical engineering. - The practical use of linear elasticity for soils requires an appropriate linearization of real stress-strain curves. - Appropriate methods of linearization exist for estimating settlements of dams and foundations. - The accuracy of „elasticity“ methods can be increase by „sublayering“. - In this lecture we did not consider the use of linear elasticity beyond the field of foundation settlements, as there is no appropriate way to get suitable stiffnesses. - Beyond the field of foundation settlement, analytical elasticity solutions can be used for verification of computer codes. The direct practical use is very limited, as it is not easy to linearise stress-strain curves for problems of: excavations, tunnelling, etc.. IGS, University of Stuttgart. 8.

(32) Remarks on the use of the Mohr-Coulomb model. σ. For an element test, the MC-model gives a linear elastic behaviour up to failure.. ε. For structural problems, the MC-model will mostly produce a non-linear load-displacement curve, which might give an impression of accuracy. However, the model requires the same linearization for stiffness selection as “Linear Elasticity”.. Appropriate linearization of stress-strain behaviour requires knowledge of relevant stress paths and matching tests on samples in the lab. One would have to distinguish between loading and unloading, between low stress levels and high stress levels, between „straight ahead“ stressing and stress rotation. As linearization is difficult and in practice often impossible, one is forced to use non-linear soil models.. IGS, University of Stuttgart. Part 2 Exponential compression law (embedded in Hardening Soil model). σ´. Eoed = α ⋅ σm. 1. ε´. Es. IGS, University of Stuttgart. 9.

(33) Oedometer tests on loose and dense Hostun Sand. 0. 0.87. 0.01. dense ID = 0.91. loose approximation with m = 0.7. 0.85. void ratio e. axial strain ε´. U = 1.7 d50 = 0.35 mm nmin = 0.39 nmax = 0.5. 0.83 0.67. dense m = 0.55. loose ID = 0.32. 0.02. 0.65 0. 200. 400. 1. σ´ stress [kPa ]. 100. 10. 1000. σ´ stress [ kPa ]. IGS, University of Stuttgart. The exponential law ⎛ σ´ ⎞ Eoed = ve⋅ σat ⋅ ⎜⎜ ⎟⎟ ⎝ σat ⎠. Ohde (1939):. ve and we :. more general:. m ≈ 1.0. sands:. m ≈ 0.5. where σat = 100 kPa material constants. ⎛ σ ´+ a ⎞ ref ⎟⎟ Eoed = Eoed ⋅ ⎜⎜ ⎝ pref + a ⎠ E. clays:. We. ref oed. = v e ⋅ σat =. m. where pref = σat = 100 kPa a = c´ cotϕ´. reference oedometer modulus. Ohde (1939): Zur Theorie der Druckverteilung im Baugrund. Bauingenieur Nr. 20, 451-459.. IGS, University of Stuttgart. 10.

(34) Moduli for primary loading of NC-soils after von Sooss (2002). γ sat. E oed [MPa ]. kN / m 3. n %. σ′ = 100 kPa. very dense quartz sand very loose quartz sand. 21 18. 35 50. 50 20. 0.6. silt. primary loading of normally consolidated soils. m. with liquid limit. wL = 0.2. 19. 45. 5. 0.75. clay with liquid limit. wL = 0.6. 16. 65. 1. 1.0. von Sooss (2002) provides much more detailed information on many soil types Data from:. Geotechnical Engineering Handbook, Vol. 1: (Fundamentals), Publisher: Ernst & Sons. IGS, University of Stuttgart. Oedometer moduli for primary loading of NC-soils after Janbu (1963) Eoed [MPa] for NC-soils and σ´ = 100 kPa. 105 rock 104 Janbu : 103. Eoed = E. sandy gravel. ref oed. 102. ⎛ σ′ ⋅ ⎜⎜ ⎝ pref. ⎞ ⎟⎟ ⎠. m. sand 10. more general: Norwegian clays. 1. ⎛ σ′ + a ⎞ ⎜ ⎟⎟ Eoed = Eref oed ⋅ ⎜ ⎝ pref + a ⎠. Mexico City Clay. with 0. 50 porosity n [%]. m. a = c´ cotϕ´. 100. After Janbu ( 1963 ), Soil Compressibility as ´Determined by Oedometer and Triaxial Tests; Proceedings European Conference on Soil Mechanics and Foundation Engineering, Publisher: DGEG. IGS, University of Stuttgart. 11.

(35) ref. Correlation for Eoed of normally-consolidated fine-grained soils. One of the best known geotechnical correlations reads CC ≈ 0.9 (wL – 0.1) after Terzaghi and Peck (1967). In combination with the approximation (1+e)ln10 ≈ 4.5, it can now be ref ≈ 500 kPa / (wL-0.1). This new correlation fits data for 21 different NCderived that Eoed clays and NC-silts by Engel (2001) extremely well as shown in the figure on the right. IP = w L − w p. Data for 21 soft soils. λ * = pref / Eref oed. Eref oed =. 500 kPa w L − 0 .1. Liquid limit wL. Liquid limit wL. Engel (2002): Verfahren zur Festlegung von Kennwerten für bodenmechanische Nachweise. Report Nr. 10, Institute of Geotechnical Engineering, University of Dresden. Terzaghi & Peck (1961: Die Bodenmechanik in der Baupraxis. Publisher: Springer.. IGS, University of Stuttgart. Compressibility of OC-clays and NC-clays after Tomlinson (1995) Type. Qualitative description. Coefficient of volume compressibility mv [m2/MN]. Eoed [MPa]. Heavily overconsolidated boulder clays (e.g. many Scottish boulder clays) and stiff weathered rocks (e.g. weathered siltstone), hard London Clay, Gault Clay, and Oxford Clay (at depth). Very low compressibility. Below 0.05. > 20. Boulder clays (e.g. Teeside, Cheshire) and very stiff ´blue´ London Clay, Oxford Clay, Keuper Marl. Low compressibility. 0.05 – 0.10. 10 – 20. Upper ´blue´London Clay, weathered ´brown´ London Clay, fluvio-glacial clays, Lake clays, weathered Oxford Clay, weathered Boulder Clay, weathered Keuper Marl, normally consolidated clays (at depth). Medium compressibility. 0.10 – 0.30. 3 – 10. Normally consolidated alluvial clays (e.g. estuarine clays of thames, Firth of Forth, Bristol Channel, Shatt-al-Arab, Niger Delta, Chicago Clay), Norwegian ´QuickĆlay. High compressibility. 0.30 – 1.50. 0.7 - 3. Very high compressibility. Above 1.5. < 0.7. Very organic alluvial clays and peats. Note: Tomlinson does not indicate a stress level, but data seem to correspond to pref = 100 kPa. Tomlinson (1995): Foundation Design and Construction, Pitman Publishing Inc.. IGS, University of Stuttgart. 12.

(36) Cone Penetration Testing in Geotechnical Practice. Book by Lunne et al. (1997), Blackie Academic & Professional Quote from the CPT-book: Most correlations between CPT results and the drained constrained modulus, M, refer to the tangent modulus, as found from oedometer tests. The reference value of M is normally based on the effective vertical stress, σ′v 0 , before the start of the in situ test; this value is denoted M0. Based on a review of available calibration chamber tests, Lunne and Christophersen (1983) recommended that an estimate of M0 for NC unaged and uncemented predominantly silica sands can be obtained from:. M0 = 4qc. for qc < 10 MPa. M0 = 2qc + 20 (MPa). for 10 MPa < qc < 50 MPa. M0 = 120 MPa. for qc > 50 MPa. Lunne and Christophersen also included OC sands in their study and recommended as a rough guideline to use:. M0 = 5qc. for qc < 50 MPa. M0 = 250 MPa. for qc > 50 MPa. For an additional stress ∆σ′v , Lunne and Christophersen recommended Janbu´s (1963) formulation to compute M for the stress range σ′v 0 to σ′v 0 + ∆σ′v :. M = M0. σ´v 0 + ∆σv´ / 2 σv´0. Lunne, T. and Christophersen, H. P. (1983): Interpretation of cone penetrometer data for offshore sands. Proceedings of the Offshore Technology Conference, Richardson, Texas, Paper No. 4464.. IGS, University of Stuttgart. Part 3 The logarithmic compression law as a special case for m=1. m=1 :. Literature :. dε ≡. pref dσ dσ = Eoed Eref oed σ′. ∆e = − CC ∆ log σ′. ∆ε´ =. pref ∆ ln σ′ Eref oed. ∆ε´ =. CC ∆ ln σ′ 1 + e0 ln10. Eref oed = (1 + e 0 ) ln 10. pref CC. CC = Compression Index e0 = Initial Void Ratio. IGS, University of Stuttgart. 13.

(37) Results of an oedometer test on a reconstituted clay sample: m=1 e. e. 1,4. ε =. − ∆e 1 + eo. 1,4. Cc. 1,2. 1,2. 1,0. 1,0. 0. 200. 400. 600. 1. 800. 10. 100. σ´ [kPa ]. 1000. σ´ [kPa ]. Data from an oedometer test on a reconstituted clay sample (kaolin), wL = 69%, wP = 38%. after: Wood (1990), Soil Behaviour and Critical State Soil Mechanics, Cambridge University Press.. IGS, University of Stuttgart. The logarithmic law (m=1) is accurate for soft soils, but not for coarse grained soils and neither for heavily overconsolidated soils. normally consolidated clay from Drammen site. 1.4. logarithmic law. m=1. void ratio e. 1.2 0.9 loose Hostun sand m<1 0.7. heavily overconsolidated clay from Beaucaire site m<1 log σ´. 0.5 1. 10. 100. 1000. [kPa]. 10000. IGS, University of Stuttgart. 14.

(38) Compression Index for primary loading and a Swelling Index for unloading and reloading. 1.80 1 1.30. void ratio e. void ratio e. Cc = compression index. 0.80. Cs Cs = swelling index. 0.30 10. 100. 1000. 10000. log σ´. log σ´ [kPa]. In normally consolidated region: Results of oedometer tests on clay samples taken from the site of leaning tower in Pisa.. ∆e = − Cc ⋅ ∆ log σ´. In overconsolidated region: ∆e = − Cs ⋅ ∆ log σ´. IGS, University of Stuttgart. Compression and Unload-Reload Indices versus Plasticity Index. Cur = CS PI = IP. Kulhawy & Mayne (1990): Manual on Estimating Soil Properties for Foundation Design. IGS, University of Stuttgart. 15.

(39) Correlations for Compression Index and Swelling Index of NC-clays and NC-silts. Wroth & Wood (1987):. CC ≈. 4 IP ≈ w L − 0.1 3. CC = 0.1 − 1.5. Kulhawy & Mayne (1990):. CS ≈. 1 CC 5. CS = 0.02 − 0.3. primary loading: unloading-reloading:. N.B.. E oed =. (1 + e 0 ) ln10 500 kPa ⋅ σ´ ≈ ⋅ σ´ CC w L − 0. 1. Eur oed ≈ 5 E oed. (Vermeer). (Kulhawy & Mayne). ur. Cs correlation is very crude. As a consequence the correlation for Eoed is ur also very crude. Please note that Eoed can be used as a rough estimate of the stiffness of overconsolidated clays and silts. For small-strain problems unloading-reloading stiffnesses are needed that exceed by far the above ur indications of Eoed. Wroth & Wood (1987): The correlation of index properties with some basic engineering properties of soils. Canadian Geotechnical Journal, Vol.15, No.2, pp 137-145.. IGS, University of Stuttgart. Conclusions and Remarks. -. Exponential law has an extremely strong empirical basis.. -. For non-cemented NC-sands, there is the nice correlation. .] Eref oed ≈ 60 ⋅ Id [MPa. Moreover, this stiffness can be estimated by using CPT data. Eref oed ≈ (500 kPa ) / ( w L − 0..1). -. For NC-clays and NC-silts, there is the nice correlation. -. For overconsolidated fine-grained soils, accurate correlations are not available. There only is the not easy rough indication. -. Eref oed ≈ ≈ ( 2.5 MPa ) / ( w L − 0..1). As yet unloading-reloading, preconsolidation stress, etc have not been discussed. This will be done in a subsequent lecture.. IGS, University of Stuttgart. 16.

(40) Part 5: Questions and Exercises Question 1 The height of an oedometer sample is 19.73 mm under a vertical effective stress of 60 kPa and 19.45 mm at an effective stress of 120 kPa. Determine the secant oedometer modulus Eoed for a oedometer loading range from 60 kPa to 120 kPa. What is the the corresponding Young‘s modulus E for a Poisson‘s ratio ν = 1/3? Note that the oedometer depends to some extend on the choice of the initial height h0, as h we have the definition є = ∆h/h0. For this question you may use h0 = 19.73 mm. Question 2 A normally consolidated clay sample has a porosity n = 0.53 and a height of 20 mm under an effective vertical stress of 10 kPa in an oedometer test. Determine the necessary vertical stress to compress the sample to a height of 10 mm. The Compression Index Cc is equal to 0.5. Use h0 = 20 mm. Question 3 An oedometer sample with a height of 2 cm has a porosity n = 0.4. Determine the height of the sample to which the sample has to be compressed in order to get a porosity n = 0. Also, calculate the required vertical ref stress for Eoed = 10 MPa, σref = 100 kPa and m = 0.5. Please use the formula: Eoed =. m Eref oed ⋅ ( σ´ / σref ). Question 4 The settlement due to the construction of an embankment has to be determined. Under the embankment is a compressible soil layer of 10 m thickness resting on a rock horizon. The soil layer is normally consolidated and has an submerged unit soil weight of γ´ = 12 kN/m3 and a porosity of n = 0.3. The surcharge load imposed by the embankment is 20 kN/m2. The Compression Index Cc as determined from an oedometer test is 0.23. Please calculate the settlement of the compressible soil layer assuming that the embankment is wide as compared to the soil layer thickness of 10 m.. IGS, University of Stuttgart. 17.

(41) 1ST Asian Course for. EXPERIENCED PLAXIS USERS 31ST JULY to 2ND AUGUST 2003. THURSDAY, 31ST JULY 2003. CG04 Foundation.

(42) Eindhoven Warehouse. EINDHOVEN WAREHOUSE. (Determination of soil stiffness parameters). Course for Experienced PLAXIS Users. Course for Experienced PLAXIS Users. 1.

(43) Eindhoven Warehouse. BACKGROUNDS ON EXERCISE This exercise is based on a practical situation, the excavation and loading of a real foundation. In addition to soil, structural elements are included in the model. The possibility of staged excavation and construction is shown by switching elements on and off. Attention is focused on output options for structural elements. It is shown how the stiffness modulus is determined from results of oedometer tests.. 3.00 P1 = 200 kN/m. 2.00 m. 3.00 m. P2 = 300 kN/m. P1. 2.30 m. 0.20 m. d = 4.80 m. 0.40 m. d = 2.70 m. 0. 0.20 m loam. -7.50 m gravel. Figure 1: Geometry of the problem. •. Determination of effective plate weights and stiffnesses.. •. Determination of soil stiffnesses for next exercise.. Course for Experienced PLAXIS Users. 3.

(44) Eindhoven Warehouse. DETERMINATION OF WEIGHT FOR WALLS, PLATES AND SHELLS. IN GENERAL: d real. w = ( γ concrete - γ soil ) ⋅ d real. For soil weight, γsoil, use:. γunsat above phreatic line γsat below phreatic line. TUNNELS:. dreal rinside. routside. r. lining soil. r = 1 ( rinside + routside ) 2 w = ( γ concrete ⋅ d real ) - ( γ soil ⋅ 1 d real ) 2 P.S. this also applies to the weight of other structures besides excavated soil !. 4. Course for Experienced PLAXIS Users.

(45) Eindhoven Warehouse. DETERMINATION OF EFFECTIVE PLATE WEIGHTS E = 20·106 kPa υ = 0.2 γ = 24 kN/m3 Floor: d = 0.4 m I = b d3 / 12 = 1 ·(0.4)3 / 12 = 5.33 ·10-3 m4 A = b d = 1 ·0.4 = 0.4 m2 EI =1 ·105 kNm2/m EA =8 ·106 kN/m wnet = wgross - ½·γsoil ·d = 0.4 ·24 - ½·18 ·0.4 = 6.0 kN/m2. Wall: d = 0.2 m I = 1 ·(0.2)3 / 12 = 6.67 ·10-4 m4 A = 1 ·0.2 = 0.2 m2 EI =0.13 ·105 kNm2/m EA =4.0 ·106 kN/m wnet = wgross - ½·γsoil ·d = 0.2 ·24 - ½·18 ·0.2 = 3.0 kN/m2. Course for Experienced PLAXIS Users. 5.

(46) Eindhoven Warehouse. DETERMINATION OF SOIL STIFFNESSES Calculation of equivalent Young's modulus from oedometer test results.. 8 m.. 2.5 2.5. Reference point. 2.5. loam gravel. Stresses at reference point: INITIAL STRESS: σ' = 5 ·18. =. 90 kPa (initial stress). INITIAL PRE-CONSOLIDATION STRESS: σc = 5 ·18 + 20 = 110 kPa σc 5m 18 kPa 20 kPa. (σpre-consolidation). = maximum stress that reference point has ever experienced in the past = depth of reference point = specific soil weight = this is an assumed pre-overburden pressure at soil surface, characteristic for the region considered. AFTER EXCAVATION: σ0 = 2.5 ·18 = 45 kPa σ0 2.5 m 18 kPa. = real vertical stress after excavation in reference point = depth of reference point after excavation = specific soil weight. AFTER LOADING: σ2 = 45 + 6.0 + 125 = 176 kPa σ2 45 kPa 6.0 kPa 125 kPa. 6. = real vertical stress after loading = (σ0 see above) = is weight of floor = 2 ·200 kN + 2 ·300 kN (point loads) / 8 m (width of floor). Course for Experienced PLAXIS Users.

(47) Eindhoven Warehouse )kPa 0. 50. 90 110 150 180. 250. 350. 1.0. 1.5 2.0. 2.5 primary loading 3.0. 3.4 )’. 4.0. 5.0. N[%]. unloading/reloading. 6.0. Unloading from σ' to σ0 and reloading from σ0 to σ' does not give deformation (elastic behaviour) From unloading/reloading curve from σ' to σc (from ~90 kPa to 110 kPa):. ∆ ε 1 = 1.5 % - 1.4 % = 0.1 % From primary loading curve from σc to σ2 (from 110 kPa to ~180 kPa):. ∆ ε 2 = 2.5 % - 1.5 % = 1.0 %. PARAMETERS FOR THE MOHR-COULOMB MODEL. ∆ ε = ∆ ε 1 + ∆ ε 2 = 1.1 % ∆ σ = 176 - 90 = 86 kPa E oed =. 86 ∆σ = = 7800 kPa ∆ε 1.1 %. ν= 0.4 E=. 1+ν 1.4 (1 - 2 ν ) E oed = 0.2 ⋅ 7800 ≈ 3640 kPa 1 -ν 0.6. Course for Experienced PLAXIS Users. 7.

(48) Eindhoven Warehouse. PARAMETERS FOR HARDENING SOIL MODEL Primary loading. ∆ ε = ∆ ε 2 = 1.0 % ∆ σ = 176 - 110 = 67 kPa E oed =. 67 ∆σ = = 6700 kPa ∆ε 1.0 %. E oed = E oed ( ref. pref. σ1 ,. 0.5. 0.5. ) = 6700 (. 100 ) 143. ≈ 5600 kPa. σ'1 is the average vertical stress, that is σ , = (176 + 110) = 143 kPa 1 2 ref. Assuming E50. = Eoedref, we have E ref 50 = 5600 kPa. Unloading-Reloading ref. We can make a good estimate with Eur = 3E50 E. ref ur. = 16800 kPa. K0nc = 1 – sin(20) = 0.658 υ = 0.2 (Standard setting). 8. Course for Experienced PLAXIS Users.

(49) Eindhoven Warehouse. EINDHOVEN WAREHOUSE. (Calculation with HS model). 3.00 P1 = 200 kN/m. 2.00 m. 3.00 m. P2 = 300 kN/m. P1. 2.30 m. 0.20 m. d = 4.80 m. 0.40 m. d = 2.70 m. 0. 0.20 m loam. -7.50 m gravel. Course for Experienced PLAXIS Users. Course for Experienced PLAXIS Users. 1.

(50) Eindhoven Warehouse. INTRODUCTION This exercise concerns a simple practical situation, the excavation and loading of a foundation. The purpose of this exercise is to get familiar with the Hardening Soil model and to discover the advantages over the Mohr-Coulomb model.. INPUT 3.00 P1 = 200 kN/m. 2.00 m. 3.00 m. P2 = 300 kN/m. P1. 2.30 m. 0.20 m. d = 4.80 m. 0.40 m. d = 2.70 m. 0. 0.20 m loam. -7.50 m gravel. •. As the problem is fully symmetric, it will be sufficient to model only one symmetric half of the entire geometry. In this example we choose to model the right hand side.. •. At a depth of 7.5 meter a stiff gravel layer is present. It can be assumed that no significant deformations occur in this material. To this end the gravel is excluded from the FE model. Hence we choose the bottom of the geometry at the level of -7.5 m. As no deformations are assumed to occur, the displacements along this boundary are fully fixed (default option Standard fixities).. •. The line loads, indicated as P2 are transfered to the basement bottom by a wall. Hence the point loads can also be positioned directly on the basement bottom.. Course for Experienced PLAXIS Users. 3.

(51) Eindhoven Warehouse. GEOMETRY MODEL. (0, 7.5). (4.0, 7.5) (10, 7.5). (1.0, 5.0). (0, 5.0). (0, 0). •. (4.0, 5.0). (10, 0). • •. Create a project with dimensions 10m horizontal. x 7.5 m vertical. Use 15-noded elements in plane strain. Use standard fixities. Use the Load system A to apply the following loads On point 6, enter a vertical load downwards of 200 kN/m. On point 7, enter another load of 300 kN/m, downwards.. 4. Course for Experienced PLAXIS Users.

(52) Eindhoven Warehouse. MATERIAL PROPERTIES SOIL Loam Model. HS. Type. Drained. γunsat (kN/m3). 18. γsat (kN/m3). 18. kx (m/day). 0. ky (m/day). 0. E50ref (kN/m2). 5600. Eoedref (kN/m2). 5600. Eurref (kN/m2). 16800. cref (kN/m2). 1. φ' (Β). 20. ψ (Β). 0. νur. 0.2. pref (kN/m2). 100. power. 0.5. K0nc. 0.658. PLATES. Type. EA (kN/m). EI (kNm2/m). w (kN/m2). ν. Floor. Elastic. 8E6. 1E5. 6.0. 0.2. Wall. Elastic. 4E6. 1.3E4. 3.0. 0.2. Course for Experienced PLAXIS Users. 5.

(53) Eindhoven Warehouse. MESH GENERATION Generate the mesh, using refinements along the floor and wall.. INITIAL CONDITIONS • • •. The water table is below the area of study. Therefore no water pressure generation is needed. Deactivate the plate elements (floor and wall). To generate the initial stresses use K0 = 0.75 and POP = 20 kPa.. CALCULATIONS Phase 1 • •. Activate the wall and floor. Remove the soil inside.. Phase 2 • Apply vertical forces Select a point in the 'center' of the floor and one point on top of the wall, to be used in the Curves program.. 6. Course for Experienced PLAXIS Users.

(54) Eindhoven Warehouse. OUTPUT PHASE 1: EXCAVATION The heave of the basement is around 0.011 m.. PHASE 2: APPLICATION OF VERTICAL FORCES The settlement of the basement is equal to 0.053 m.. Course for Experienced PLAXIS Users. 7.

(55) Eindhoven Warehouse. PHASE 1: EXCAVATION HS Model Bending moments on plates. 29 kNm/m. 23 kNm/m Shear forces on plates. 34 kN/m. 24 kN/m Axial forces on plates. 22 kN/m. 30 kN/m 8. 36 kN/m Course for Experienced PLAXIS Users.

(56) Eindhoven Warehouse. PHASE 2: APPLICATION OF VERTICAL FORCES HS Model Bending moments on plates. 42 kNm/m 68 kNm/m. 56 kNm/m 112 kNm/m. Shear forces on plates. 188 kN/m 73 kN/m. -112 kN/m. -167 kN/m. Axial forces on plates. 200 kN/m. 178 kN/m 69 kN/m Course for Experienced PLAXIS Users. 9.

(57) 1ST Asian Course for. EXPERIENCED PLAXIS USERS 31ST JULY to 2ND AUGUST 2003. THURSDAY, 31ST JULY 2003. CG05 Hardening Soil Model.

(58) 1.

(59) 2.

(60) 3.

(61) 4.

(62) 5.

(63) 6.

(64) 7.

(65) 8.

(66) 9.

(67) 10.

(68) 11.

(69) 12.

(70) 13.

(71) 14.

(72) 15.

(73) 16.

(74) 17.

(75) 18.

(76) 19.

(77) 20.

(78) 21.

(79) 1ST Asian Course for. EXPERIENCED PLAXIS USERS 31ST JULY to 2ND AUGUST 2003. THURSDAY, 31ST JULY 2003. CG06 Drained and Undrained Soil Behaviour.

(80) PLAXIS Experienced Users Course, August 2003. Drained and Undrained Behaviour presented by Tan S A National University of Singapore Helmut F. Schweiger Institute for Soil Mechanics and Foundation Engineering Graz University of Technology, Austria. CONTENTS . Definition drained / undrained. . Drained / undrained soil behaviour • •. . Modelling undrained behaviour with Plaxis • • •. . In terms of effective stresses with drained strength parameters In terms of effective stresses with undrained strength parameters In terms of total stresses. Influence of constitutive model and parameters • • •. . Typical results from drained and undrained triaxial tests Skempton‘s parameters A and B. Influence of dilatancy Undrained behaviour with Mohr-Coulomb Model Undrained behaviour with Hardening Soil Model. Summary. 1.

(81) DRAINED / UNDRAINED . Drained analysis appropriate when • • •. . permeability is high rate of loading is low short term behaviour is not of interest for problem considered. Undrained analysis appropriate when • •. permeability is low and rate of loading is high short term behaviour has to be assessed. Suggestion by Vermeer & Meier (1998) for deep excavations: T < 0.1 use undrained conditions T > 0.40 use drained conditions. T=. k E oed t γ w D2. k Eoed γw D t Tv. = = = = = =. permeability oedometer modulus unit weight of water drainage length construction time dimensionless time factor. UNDRAINED BEHAVIOUR . Implications of undrained soil behaviour • •. excess pore pressures are generated no volume change in fact small volumetric strains develop because a finite (but high) bulk modulus of water is introduced in the finite element formulation. • •. predicted undrained shear strength depends on soil model used assumption of dilatancy angle has serious effects on results. Fig.1 Results from undrained triaxial tests using the Mohr-Coulomb and Hardening Soil Model. 2.

(82) TRIAXIAL TEST (NC) – DRAINED / UNDRAINED. a). b). Fig.2 Typical results from drained (a) and undrained (b) triaxial tests on normally consolidated soils (from Atkinson & Bransby, 1978). TRIAXIAL TEST (OC) – DRAINED / UNDRAINED. a). b). Fig.3 Typical results from drained (a) and undrained (b) triaxial tests on overconsolidated soils (from Atkinson & Bransby, 1978). 3.

(83) TRIAXIAL TEST UNDRAINED – NC / OC ∆pw. ∆pw. Fig.4 Typical results from undrained triaxial tests on (a) normally consolidated and (b) overconsolidated clay (from Ortigao, 1995). PORE PRESSURE PARAMETERS A AND B Skempton 1954:. ∆pw = B [∆σ 3 + A(∆σ 1 − ∆σ 3 )]. - fully saturated soil - no inflow / outflow of pore water - bulk modulus of soil grains >>> - isotropic linear elastic material behaviour (Hooke´s law). ∆ε vol , skeleton = ∆ε vol , pore water ∆ε vol , skeleton =. ∆p' K'. ∆ε vol , pore water =. n ∆p w Kw. K' =. E´ 3(1 − 2ν´ ). 4.

(84) PORE PRESSURE PARAMETERS A AND B assuming triaxial compression:. ∆σ 1 ; ∆σ 2 = ∆σ 3 ∆p w =. ∆ σ 1 + 2 ∆ σ 3 − 3 ∆ pw K w ⋅ 3K ' n. leading to. ∆ pw =. 1 nK ' 1+ Kw. 1 ⎤ ⎡ ⎢ ∆σ 3 + 3 (∆σ 1 − ∆σ 3 )⎥ ⎦ ⎣. ∆pw = B [∆σ 3 + A(∆σ 1 − ∆σ 3 )] with. B=. 1 nK ' 1+ Kw. A=. 1 3. PORE PRESSURE PARAMETERS A AND B. notes on parameters A and B: for Kw large compared to K´, parameter B ~ 1.0 (corresponds to ∆pw = ∆p > ∆p´ = 0) small amount of drapped air reduces parameter B significantly (Figure 4) parameter A depends on stress path, even for elastic material behaviour parameter A cannot be determined a priori for complex elastic-plastic constitutive models > is a result of the model behaviour for the stress path followed. 5.

(85) PORE PRESSURE PARAMETER B. Fig.5 Dependence of pore pressure parameter B on degree of saturation. UNDRAINED BEHAVIOUR WITH PLAXIS PLAXIS automatically adds stiffness of water when undrained material type is chosen using the following approximation. K total = K ' +. K total =. Kw Eu 2 G (1 + ν u ) = = n 3(1 − 2ν u ) 3(1 − 2ν u ). E' (1 + ν u ) 3(1 − 2ν u ) (1 + ν'). assuming νu = 0.495. Note: - this procedure gives reasonable B-values only for ν´ < 0.35 ! - real value of Kw/n ~ 1.106 kPa (for n = 0.5) - NB: in Version 8 B-value can be entered explicitely. 6.

(86) UNDRAINED BEHAVIOUR WITH PLAXIS Example 1: ν´ = 0.3,. E´ = 3 000 kPa, → K´ = 2 500 kPa, with. B=. νu = 0.495. Ktotal = 115 000 kPa. → Kw/n = 112 500 kPa. 1 = 0.978 > reasonable value for saturated soil nK ' 1+ Kw. Example 2: E´ = 3 000 kPa,. ν´ = 0.45,. → K´ = 10 000 kPa,. νu = 0.495. Ktotal = 103 103 kPa → Kw/n = 93 103 kPa. B = 0.903 > poor value for saturated soil. UNDRAINED BEHAVIOUR WITH PLAXIS Method A (analysis in terms of effective stresses): type of material behaviour: undrained effective strength parameters c´, ϕ´, ψ´ effective stiffness parameters E50´, ν´ Method B (analysis in terms of effective stresses): type of material behaviour: undrained undrained strength parameters c = cu, ϕ = 0, ψ = 0 effective stiffness parameters E50´, ν´ Method C (analysis in terms of total stresses): type of material behaviour: drained total strength parameters c = cu, ϕ = 0, ψ = 0 undrained stiffness parameters Eu, νu = 0.495. 7.

(87) UNDRAINED BEHAVIOUR WITH PLAXIS Notes on different methods: Method A: recommended soil behaviour is always governed by effective stresses increase of shear strength during consolidation included essential for exploiting features of advanced models such as the Hardening Soil model, the Soft Soil model and the Soft Soil Creep model Method B: only when no information on effective strength parameters is available cannot be used with the Soft Soil model and the Soft Soil Creep model Method C: NOT recommended no information on excess pore pressure distribution (total stress analysis). UNDRAINED STRENGTH FROM MOHR CIRCLE Consider fully undrained isotropic elastic behaviour (Mohr Coulomb in elastic range) ∆pw = ∆p > ∆p´ = 0 → centre of Mohr Circle remains at the same point cu =. (. ). 1 'o σ x + σ 'yo sin ϕ' + c' cos ϕ' 2. Fig.6 Mohr Circle for evaluating undrained shear strength (plane strain). 8.

(88) INFLUENCE OF CONSTITUTIVE MODEL ref. Model Number. Eur. E50. kN/m. 2. ref. kN/m. ref. φ. Ψ. c. 2. °. °. kN/m. Eoed. 2. kN/m. nc. υur. p. -. kN/m. 0.0. 0.2. 100. 0.75 0.426 0.9. 2. ref. 2. m. K0. -. -. Rf -. HS_1. 30 000 90 000. HS_2. 50 000 150 000 50 000 35. 0. 0.0. 0.2. 100. 0.75 0.426 0.9. HS_3. 15 000 45 000. 15 000 35. 0. 0.0. 0.2. 100. 0.75 0.426 0.9. HS_4. 30 000 90 000. 40 000 35. 0. 0.0. 0.2. 100. 0.75 0.426 0.9. HS_5. 30 000 90 000. 15 000 35. 0. 0.0. 0.2. 100. 0.75 0.426 0.9. HS_6. 50 000 150 000 30 000 35. 0. 0.0. 0.2. 100. 0.75 0.426 0.9. 30 000 35 0 / 10. Table 1 Parameter sets for Hardening Soil model. Parameters for MC Model E = 30 000 kN/m. 2. υur = 0.2 φ = 35° Ψ = 0° and 10°. see also Schweiger (2002). COMPARISON MC – HS / INFLUENCE ψ 300 275 250 225. 2. q [kN/m ]. 200 175 150 125 100 75. MC non dil MC dil HS_1 non dil HS_1 dil. 50 25 0 0.00. 0.25. 0.50. 0.75. 1.00. 1.25. 1.50. 1.75. 2.00. 2.25. 2.50. 2.75. 3.00. ε1 [%] Fig.7 Simulation of undrained triaxial compression test – MC / HS model - q vs ε1. 9.

(89) COMPARISON MC – HS / INFLUENCE ψ 300 MC non dil MC dil HS_1 non dil HS_1 dil total stress path. 275 250 225. 2. q [kN/m ]. 200 175 150 125 100 75 50 25 0 0.00. 25.00. 50.00. 75.00. 100.00 125.00 150.00 175.00 200.00 225.00 250.00 2. p' [kN/m ] Fig.8 Simulation of undrained triaxial compression test – MC / HS model - q vs p´. COMPARISON MC – HS / INFLUENCE ψ 100 90. MC non dil MC dil HS_1 non dil HS_1 dil. 2. excess pore pressure [kN/m ]. 80 70 60 50 40 30 20 10 0 -10 -20 0.00. 0.25. 0.50. 0.75. 1.00. 1.25. 1.50. 1.75. 2.00. 2.25. 2.50. 2.75. 3.00. ε1 [%] Fig.9 Simulation of undrained triaxial compression test – MC / HS model - ∆pw vs ε1. 10.

(90) COMPARISON MC – HS / INFLUENCE ψ 1.0 0.9. MC non dil MC dil HS_1 non dil HS_1 dil. 0.8 0.7 0.6. parameter A. 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 0.00. 0.25. 0.50. 0.75. 1.00. 1.25. 1.50. 1.75. 2.00. 2.25. 2.50. 2.75. 3.00. ε1 [%] Fig.10 Simulation of undrained triaxial compression test – MC / HS model - A vs ε1. PARAMETER VARIATION – HARDENING SOIL 150. 125. 2. q [kN/m ]. 100. HS_1 HS_2 HS_3 HS_4 HS_5 HS_6 total stress path. 75. 50. 25. 0 0.00. 25.00. 50.00. 75.00. 100.00. 125.00. 150.00. 2. p' [kN/m ] Fig.11 Simulation of undrained triaxial compression test – HS model - q vs p´. 11.

(91) PARAMETER VARIATION – HARDENING SOIL 150. 125. 2. q [kN/m ]. 100. 75. 50. HS_1 HS_2 HS_3 HS_4 HS_5 HS_6. 25. 0 0.00. 1.00. 2.00. 3.00. 4.00. 5.00. 6.00. ε1 [%] Fig.12 Simulation of undrained triaxial compression test – HS model - q vs ε1. PARAMETER VARIATION – HARDENING SOIL 80. 2. excess pore pressure [kN/m ]. 70 60 50 40 30 HS_1 HS_2 HS_3 HS_4 HS_5 HS_6. 20 10 0 0.00. 1.00. 2.00. 3.00. 4.00. 5.00. 6.00. ε1 [%] Fig.13 Simulation of undrained triaxial compression test – HS model - ∆pw vs ε1. 12.

(92) PARAMETER VARIATION – HARDENING SOIL 0.8 0.7. parameter A. 0.6 0.5 0.4 0.3 HS_1 HS_2 HS_3 HS_4 HS_5 HS_6. 0.2 0.1 0.0 0.00. 1.00. 2.00. 3.00. 4.00. 5.00. 6.00. ε1 [%] Fig.14 Simulation of undrained triaxial compression test – HS model - A vs ε1. Factor of Safety of Embankments Critical FS is Shortterm loading condition, undrained strength is key parameter for safe design. 13.

(93) Factor of Safety of Cuts/Excavations Critical FS is Longterm unloading condition, For permanent cuts drained strength is key parameter for safe design For temporary cuts, need to consider if undrained or partially drained condition. SUMMARY. . Undrained analysis should be performed in effective stresses and with effective stiffness and strength parameters. . Undrained shear strength is result of the constitutive model. . Care must be taken with choice of value for dilatancy angle. . Note that for NC-soils in general factor of safety against failure is lower for short term (undrained) conditions for loading problems (e.g. embankments) factor of safety against failure is lower for long term (drained) conditions for unloading problems (e.g. excavations). 14.

(94) REFERENCES Atkinson, J.H., Bransby, P.L. (1978) The Mechanics of Soils, An Introduction to Critical State Soil Mechanics. McGraw Hill Ortigao, J.A.R. (1995) Soil Mechanics in the Light of Critical State Theories – An Introduction. Balkema Schweiger, H.F. (2002) Some remarks on pore pressure parameters A and B in undrained analyses with the Hardening Soil Model. Plaxis Bulletin No.12 Skempton, A.W. (1954) The Pore-Pressure Coefficients A and B. Geotechnique, 4, 143-147 Vermeer, P.A., Meier, C.-P. (1998) Proceedings Int. Conf. on Soil-Structure Interaction in Urban Civil Engineering, Darmstadt, 177-191. 15.

(95) 1ST Asian Course for. EXPERIENCED PLAXIS USERS 31ST JULY to 2ND AUGUST 2003. THURSDAY, 31ST JULY 2003. CG07 Pile Loading Test.

(96) Simulation of a Pile load test. CG07 SIMULATION OF A PILE LOAD TEST. Course for Experienced PLAXIS Users. Course for Experienced PLAXIS Users. 1.

(97) Simulation of a Pile load test. INTRODUCTION An extensive research program related to bored piles in overconsolidated clay was conducted by Sommer & Hambach (1974) to optimize the foundation design of a highway bridge in Germany. Load cells were installed at the pile base to measure the loads carried directly by pile base. Figure 1 gives the layout of the pile load test arrangement. The upper 4.5 m subsoil consist of silt (loam) followed by tertiary sediments down to great depths which are more or less overconsolidated stiff plastic clay similar to the so-cal1ed Frankfurt clay. Therefore this pile load test is often used to verify the numerical modeling of the pile behavior in Frankfurt overconsolidated clay. The groundwater table is about 3.5 m below the ground surface. The considered tested pile has a diameter of 1.3 m and a length of 9.5 m. It is located completely in the overconsolidated clay. The loading system consists of two hydraulic jacks working against a reaction beam. The reaction beam was supported by 16 anchors. The anchors were installed vertically at a depth between 15 and 20 m below the ground surface at a distance of about 4 m from the tested pile to minimize the effect of the mutual interaction between the tested pile and the reaction system (Fig 1.a). Vertical and horizontal loading tests were carried out. The loads were applied in increments and maintained constant till the settlement rate was negligible. Both the applied loads and the corresponding displacements at the tested pile head were measured. Additionally the soil displacements near the pile in different depths were measured using deep settlement points (Fig 1.b).. Figure 1: Lay of the pile load test and the measured points. AIM The purpose of this case study is to simulate the pile-loading test, create about the same amount of settlement and compare the simulation results with the results of Sommer & Hambach (1974).. Course for Experienced PLAXIS Users. 3.

(98) Simulation of a Pile load test. GEOMETRY OF THE MODEL • • • • •. Create an axisymmetric geometry with 15-noded elements. The dimensions are 4 m width x 15 m depth. The first 4.5 m of the soil consists of silt (loam) The following layer consists of overconsolidated stiff plastic clay, similar to the socalled Frankfurt clay, which extends to great depths. The groundwater table is located at a depth of 3.5 m below the ground surface. The boundaries are sufficiently far away to apply the standard fixities.. A A. (0.65,15) (0,15). (4,15) loam. concrete pile water table (4,10.5). (0,10.5). clay. (0,5.5). (0.65,5.5) (0.65,5.0) y. (4,0). (0,0) 0. • • •. 4. x. The pile has a diameter of 1.3 m and a length of 9.5 m. Create an interface at the right side of the pile. Extend the interface for half a meter to allow for sufficient flexibility around the pile tip. Apply a distributed load (system A) to the pile or a prescribed displacement. When accurately modelled, both should give the same results.. Course for Experienced PLAXIS Users.

(99) Simulation of a Pile load test. MATERIAL PROPERTIES The required soil parameters were determined based on the conducted laboratory and in-situ tests as well as on experience gained in similar soil conditions (see Table 1). The parameters for the concrete pile are also given in Table 1. Parameter. Symbol. Material model. Model. Silt (Loam). OCR Clay. MohrCoulomb Drained 19 19 10E+3 0.3 5 27.5 0. HardeningSoil Drained 20 20 ?** ?** 0.7 0.2 100 20 20 2. Concrete Pile Linear Elastic Non-Porous 25 30E+6 0.2 -. Type of behaviour Type Dry weight γunsat Wet weight γsat Young's modulus Eref/50 Oedometer modulus Eoed Power M Unloading modulus Eur Poisson's ratio ν Reference stress pref Cohesion c Friction angle ϕ Dilatancy angle ψ Interface strength 1.0 (rigid) 1.0 (rigid) 1.0 (rigid) Rinter reduction POP POP 200 OCR OCR Table 1: Geotechnical parameters for the 2 layers and the concrete pile.. Unit kN/m3 kN/m3 kN/m2 kN/m2 kN/m2 kN/m2 kN/m2 ° ° kN/m2 -. The remaining parameters for the clay (E50ref and Eurref) shall be determined from the following results of Triaxial tests by Amann (1975).. **. Course for Experienced PLAXIS Users. 5.

(100) Simulation of a Pile load test. 1 kp/cm² = 100 kPa. Figure 2: Triaxial Tests with Frankfurt clay (σ3 = const.). 6. Course for Experienced PLAXIS Users.

(101) Simulation of a Pile load test •. Do not assign the concrete material properties to the pile yet, but instead assign the loam and clay material properties to the clusters of the pile. Initial stresses are not correctly calculated if the pile is alread in place. The material properties of the pile will be assigned in the first calculations phase. Create a water table at a depth of 3.5 m and generate water pressures. Generate initial stresses (assign a value for POP to the clay layer).. • •. CALCULATIONS •. In the first phase, ‘activate’ the pile by assigning the material property of concrete to the pile clusters. In the second phase the pile load is activated or a prescribed displacement of 35 mm is applied. In the third phase the pile load is increased until a settlement of about 35 mm is observed (ignore this phase if prescribed displacement is used).. • •. OUTPUT Figure 3 shows the results of the observed pile load settlement behavior by Sommer & Hambach (1974). Load [kN] 0. 250. 500. 750. 1000. 1250. 1500. 1750. 2000. 2250. 2500. 2750. 3000. 3250. 3500. 0.00 Total load Skin friction. 5.00. Base load. Settlement [mm]. 10.00 15.00 20.00 25.00 30.00 35.00 40.00. Figure 3: Observed pile load settlement behavior. •. In addition to the total load, check the skin friction (total amount of friction along the surface of the pile) and the base load of the pile (total load at the base-surface op the pile).. Course for Experienced PLAXIS Users. 7.

(102) Simulation of a Pile load test. Plate element with negligible stiffness for the determination of normal force in pile.. Figure 4a: Effective Stresses. Figure 4b: Deformed Mesh. REFERENCES Amann, P., Breth, H., Stroh, D. (1975) „Verformungsverhalten des Baugrundes beim Baugrubenaushub und anschließendem Hochhausbau am Beispiel des Frankfurter Tons.“ Mitteilungen der Versuchsanstalt für Bodenmechanik und Grundbau der TH Darmstadt, Heft 15 El-Mossallamy, Y. (1999) “ Load settlement behavior of large diameter bored piles in overconsolidated clay.” Proceedings NUMOG VII Graz, Balkema Rotterdam Sommer, H. & Hambach, P. (1974) „Großpfahlversuche im Ton für die Gründung der Talbrücke Alzey.“ Der Bauingenieur, Vol. 49, pp. 310-317. 8. Course for Experienced PLAXIS Users.

(103) Simulation of a Pile load test. SOLUTIONS TO THE SIMULATION OF A PILE LOAD TEST. Course for experienced PLAXIS users. Course for Experienced PLAXIS Users. 9.

(104) Simulation of a Pile load test. From the Triaxial tests on the Frankfurt clay in figure 2 an E50ref of 20.000 kN/m2 and an Eurref of 72.000 kN/m2 was found. A Triaxial test of the Frankfurt clay was simulated with PLAXIS to compare and test the chosen parameters with the Triaxial tests of Amann (1975). The results are shown in figure 5 and match with the results of Amann (figure 2). (sig'yy - sig'xx)/2 [kN/m2] -200. -160. -120. -80. p=300 kN/m2. -40. p=200 kN/m2 p=100 kN/m2 0 0. -0.01. -0.02. -0.03. -0.04. eps-1. Figure 5: Results of the Triaxial test in PLAXIS of the Frankfurt Clay. With the chosen E50ref and Eurref the pile load test was calculated with a prescribed displacement of 35 mm applied to the top of the pile. The Total load – settlement curve is shown in figure 6. When using Traction loads, the Total load is obtained by multiplying the traction loads in Load System A by πr2, i.e. the cross section area of the pile. When Prescribed displacements were used, the total load is obtained by multiplying the vertical reaction force of the axisymmetric analysis (Force-Y) by 2π, i.e. the full circle. For an axissymmetric problem the Base Load can be calculated as follows: In output a cross-section of the total stresses is made just below the base of the pile (figure 6). This cross-section represents the total stresses over the radius of the pile. To obtain the total base load we need to integrate the total stresses over the total cross section of the pile (~ average total stress * πr2). To obtain a correct Base Load value we need to substract the Initial Load of the pile. The calculated Base Load is plotted in figure 8.. 10. Course for Experienced PLAXIS Users.

(105) Simulation of a Pile load test x 0.341. 0 0.033. 0.65. X [m]. Y [m]. )n [kN/m2]. 0.000 0.033 0.341 0.650. 5.475 5.475 5.475 5.475 Average σ'n Base Load [kN] Initial Load [kN] Base Load – Initial Load[kN]. -898 -911 -1004 -1442 -1064 1412 248. )n. Figure 6 and Table 1: Total stresses 2.5 mm below the base of the pile.. 1164. The Skin Friction of an axissymmetric problem can be calculated from the shear stresses in the interface of the pile (figure 7). The shear stresses shown in figure 7 and table 2 are the shear stresses along the perimeter of the pile. To obtain the skin friction of the pile the shear stresses have to be integrated over the total skin surface of the pile (skin surface=length*circumference=L*2πr). The calculated Skin Friction is plotted in figure 8. 0 )s. y. X [m]. Y [m]. )s [kN/m2]. 0.650005 0.650005 0.650005 : : 0.650005 0.650005 0.650005 0.650005. 5.50 5.64 5.78 : : 14.58 14.72 14.86 15.00 Average σs Skin Friction [kN]. -89 -91 -98 : : -20 -13 -12 -14 56 2183. Figure 7 and Table 2: Shear stresses at the interface of the pile.. Course for Experienced PLAXIS Users. 11.

No results found