PLAXIS INTRODUCTORY COURSE 1012 JULY 2013 Danang, Vietnam The wellestablished Advanced Course on Computational Geotechnics for experienced PLAXIS users is organised every year as a continuation of the Standard Course on Computational Geotechnics. One of the aims of this course is to teach the application of advanced soil models. Whereas the standard course concentrates on using the Hardening Soil model, in the Advanced course attention is now fully focused on understanding the HSsmall model with smallstrain stiffness and also the Soft Soil Creep model for soft clay. Experts with a thorough theoretical background and an extensive experience in practical computer modelling have been invited to give lectures and to prepare exercises as well as case studies.
PLAXIS INTRODUCTORY COURSE 10-12 JULY 2013 Danang, Vietnam Plaxis Introductory Course, Danang, Vietnam PLAXIS DANANG 2013 Day 1: Wednesday 10.7.2013 Time Module Subject Lecturer 9:00 9:30 Lecture 9:30 10:15 Lecture 10:15 10:30 10:30 12:00 12:00 1:30 1:30 2:15 Lecture Non-linear Computation Dr Phung 2:15 3:00 Lecture Hardening Soil Model Dr Cheang 3:00 3:15 3:15 4:45 4:45 5:00 Introduction to Geotechnical Finite Element Analysis Dr Phung Mohr-Coulomb Soil Model Dr Cheang Break Exercise Simple Foundation on Elastoplastic Soil Dr Cheang Lunch Break Exercise Simulation of Laboratory Tests Dr Cheang Q/A Session Day 2: Thursday 11.7.2013 Time Module Subject Lecturer 9:00 9:30 Lecture 9:30 10:15 Lecture 10:15 10:30 10:30 12:00 12:00 1:30 1:30 2:15 Lecture Drained and Undrained Analysis Dr Cheang 2:15 3:00 Lecture Modelling of Groundwater Dr Cheang 3:00 3:15 3:15 4:45 4:45 5:00 Geometry, Elements & Descretization Dr Cheang Structural Elements Dr Phung Break Exercise Modelling of Anchored Excavation Dr Phung Lunch Break Exercise Dewatering of Excavation Dr Phung Q/A Session Day 3: Friday 12.7.2013 Time Module Subject Lecturer 9:00 9:30 Lecture 9:30 10:15 Lecture 10 10:15 10:30 10:30 12:00 12:00 1:30 1:30 2:15 Lecture 11 Overview of Soil Models Dr Phung 2:15 3:00 Lecture 12 Consolidation Analysis Dr Cheang 3:00 3:15 3:15 4:45 4:45 5:00 Initial Geo-static Stresses Dr Phung Safety of Factor Analysis through Phi'-C reduction Dr Cheang Break Exercise Stability of A Slope Reinforced with Soil Nails Dr Cheang Lunch Break Exercise Geotextile Reinforced Embankment & Consolidation Q/A Session of 375 Dr Phung LECTURERS Dr William Cheang Wai Lum Plaxis AsiaPac, Singapore William obtained his PhD from the National University of Singapore His interest is in Computational Geotechnics He has worked as a Geotechnical Engineer in Malaysia, Singapore and Thailand He is involved with many seminars and workshops around Asia for the promotion of good and effective usage of Plaxis Finite Element Codes Dr Phung Duc Long VSSMGE, Hanoi, Vietnam Dr Phung got PhD degree at Chalmers University of Technology, Sweden He has more than 30 years of international experience, including more than 20 years with Plaxis His expertise areas are: deep foundations, deep excavations, soil improvement, pile dynamics, tunnelling, and numerical analysis He has worked with projects in many countries, among other, Sweden, Norway, Denmark, USA, England, Russia, Germany, India, Hong Kong, China and Vietnam, etc ORGANIZERS Construction Informatics and Consultancy JSC (CIC) ADD: 37 Le Dai Hanh, Hai Ba Trung Dist., Hanoi, Vietnam, TEL#: (84.4) 39746798 FAX#: (84-4) 38216793 Contact: Mr Luong Thanh Hung Mobile: (84) 988 922 884 Email: Hunglt@cic.com.vn Skype : Hunglt07 Plaxis AsiaPac, Singapore 16 Jalan Kilang Timor, 05-08 Redhill Forum, Singapore University of Transport and Communications, Fecon Contact: Mr Le Quang Hanh Mobile: (84) 948 171 135 Email: hanhquangle@fecon.com.vn CONTENTS LECTURES & EXERCISES PAGE Lecture 1 Geotechnical Finite Element Analysis 5 Lecture 2 Mohr‐Coulomb Model 21 Exercise Exercise 1: Simple Foundation with Mohr‐Coulomb Model 43 Lecture 3 Non‐linear Calculations 74 Lecture 4 Hardening Soil & HS‐small Model 88 Exercise Exercise 2: Simulation of Triaxial and Oedometer Tests 124 Lecture 5 Geometry & Mesh Selection 169 Lecture 6 Structural Elements in Plaxis 2D 186 Exercise Exercise 3: Anchored Excavation 199 Lecture 7 Undrained Analysis in Plaxis 222 Lecture 8 Modelling of Groundwater in Plaxis 238 Exercise Exercise 4: Excavation and Dewatering 264 Lecture 9 Initial Stresses 276 Lecture 10 Factor‐of‐Safety Analysis via Phi=C' Reduction 282 Exercise 310 Exercise 5: Stability Analysis of A Slope Stabilised by Soil Nails Lecture 11 Overview of Soil Models 323 Lecture 12 Consolidation Analysis 341 Exercise 357 Exercise 6:Geotextile Reinforced Embankment with Consolidation Plaxis Introductory Course, Danang, Vietnam CG1: GEOTECHNICAL FINITE ELEMENT ANALYSIS Antonio Gens Technical University of Catalunya, Barcelona some off the h slides lid were originally i i ll createdd by: b Cino Viggiani (Laboratoire 3S, Grenoble, France) Outline • Introduction • Finite Elements displacement analysis Elements for two-dimensional analysis Displacement interpolation Strains Constitutive equation Element stiffness matrix Global stiffness matrix Solution of the global stiffness equations • Elasticity as applied to soils Fundamentals, and elastic parameters Two-dimensional elastic analysis of 375 design requirements in geotechnical engineering Plaxis Introductory Course, Danang, Vietnam • Stability (local and general) • Admissible deformation and displacements p geotechnical analysis: basic solution requirements • Unknowns: 15 ((6 stresses,, strains,, displacements) p ) • Equilibrium (3 equations) • Compatibility (6 equations) • Constitutive C tit ti equation ti (6 equations) ti ) Potts & Zdravkovic (1999) of 375 geotechnical numerical analysis Plaxis Introductory Course, Danang, Vietnam • methods for numerical analysis Finite method Fi it difference diff th d Boundary element method (BEM) Discrete element method (DEM) Finite element method (FEM) Others (meshless methods, particle methods…) • while the FEM has been used in many fields of engineering practice for over 30 years, it is only recently that it has begun to be widely used for analyzing geotechnical problems • when properly used, this method can produce realistic results which are of value to practical soil engineering problems geotechnical finite element analysis • Objectives of the numerical (finite element) analysis Selection of design alternatives Quantitative predictions Backcalculations Understanding! Identification of critical mechanisms Identification d f off kkey parameters of 375 geotechnical finite element analysis Plaxis Introductory Course, Danang, Vietnam • • Advantages of numerical (finite element) analysis Simulation of complete construction history Interaction with water can be considered rigorously Complex geometries (2D-3D) can be modeled Structural elements can be introduced No failure mechanism needs to be postulated (it is an outcome of the analysis) (Nea l ) unavoidable (Nearly) na oidable uncertainties nce tainties Ground profile Initial conditions (initial stresses stresses, pore water pressure pressure…)) Boundary conditions (mechanical, hydraulic) pp op ate model ode for o soil so behaviour be a ou Appropriate Model parameters geotechnical finite element analysis • Some requirements for successful numerical modelling q p Construction of an adequate conceptual model that includes the basic features of the model The model should be as simple as possible but not simpler Selection of an appropriate constitutive model model It depends on: type of soil or rock goal of the analysis quality and quantity of available information patterns of behaviour and mechanisms rather than Payy attention to p just to quantitative predictions Perform sensitivity analyses Check robustness of solution Model calibration (using field results) should be a priority, especially of quantitative predictions are sought Check against alternative computations if available (even if simplified) of 375 three final remarks Plaxis Introductory Course, Danang, Vietnam g g is complex p y ggeotechnical engineering It is not because you’re using the FEM that it becomes simpler the quality of a tool is important important, yet the quality of a result also (mainly) depends on the user’s understanding of both the problem and the tool the design process involves considerably more than analysis Borrowed from C Viggiani, with thanks introduction: the Finite Element Method the FEM is a computational procedure that may be used to obtain an approximate value i t solution l ti to t a boundary b d l problem bl the governing mathematical equations are approximated by a series of algebraic equations involving quantities that are evaluated at discrete points within the region of interest The FE equations are formulated and solved in such a wayy as to minimize the error in the approximate pp solution this lecture presents only a basic outline of the method the discussion is restricted to: linear elasticity two-dimensional plane strain attention is focused on the "displacement based" FE approach of 375 introduction: the Finite Element Method Plaxis Introductory Course, Danang, Vietnam the first stage in any FE analysis is to generate a FE mesh Footing width = B Node Gauss point a mesh consists of elements connected together at nodes examples: embankment 10 of 375 Plaxis Introductory Course, Danang, Vietnam Geotextile reinforced embankment Note: The main purpose of the exercise is to assess the failure mechanism and the factor of safety, which has the following consequences for the model: • There is no need to use an advanced soil model as the main advantage of advanced models is a better prediction of displacements • The geometry size is chosen such that the failure mechanism fits within the model boundaries This means the geometry can be fairly small If a deformation analysis has to be performed for this case it is recommended to use an advanced soil model, for instance the Hardening Soil or HSsmall model, and to choose the geometry considerably larger to avoid influence from the boundary conditions on the results Computational Geotechnics 361 of 375 Plaxis Introductory Course, Danang, Vietnam Geotextile reinforced embankment GEOMETRY INPUT General settings Start a new project and select appropriate General settings Use 15-node elements as basic element type since in this exercise we will deal with failure behaviour Geometry and boundary conditions (9.5,7.5) (4.5,5.5) (0,5.5) (0,3.5) (0,2) (12,8.5) 10 (8,7.5) (33,8.5) (33,7.5) (33,5.5) 11 (12,5.5) 12 (26,5.5) 13 (1,3.5) (33,2) 14 15 y (0,0) x (33,0) Figure 2: Geometry model with coordinates • Enter the geometry as indicated in the previous graph The order in which geometry points are created is arbitrary • Click the Geogrid button to introduce the geotextile (from (4.5, 5.5) to (26.0, 5.5)) • Click the Standard fixities button for the standard boundary conditions Material properties (clay) Determine the Mohr-Coulomb strength parameters (ϕ and c) as well as the elastic parameters (E’ and ν’) for the clay layer from the data as given in the introduction of this exercise The procedure on how to determine the parameters for clay are provided at the end of this exercise For this exercise, we will continue with the parameters as given in table Soil and interfaces • Enter the material properties for the three soil data sets, as indicated in table • After entering all properties for the three soil types, drag and drop the properties to the appropriate clusters, as indicated in figure Computational Geotecnics 362 of 375 Plaxis Introductory Course, Danang, Vietnam Geotextile reinforced embankment Table 1: Soil parameters Parameter Symbol Clay Material model Model Type of behaviour Unsaturated weight Saturated weight Young’s modulus Poisson’s ratio Cohesion Friction angle Dilatancy angle Permeability x-dir Permeability y-dir K0 Type γunsat γsat E ν c ϕ ψ kx ky MohrCoulomb Undrained A 13.5 13.5 2667 0.33 8.0 20.0 0.0 1.0·10−3 1.0·10−3 Automatic Retaining Fill Stiff layer bank MohrMohrMohrCoulomb Coulomb Coulomb Drained Drained Drained 13.5 18.0 18.0 13.5 18.0 18.0 2667 4000 40000 0.33 0.33 0.33 8.0 3.0 3.0 20.0 30.0 32.0 0.0 0.0 2.0 1.0 1.0 1.0 1.0 1.0 1.0 Automatic Automatic Automatic Unit – – kN/m3 kN/m3 kN/m2 – kN/m2 ◦ ◦ m/day m/day – 3 1 Figure 3: Geometry model with soil material sets (1) Clay, (2) Retaining bank, (3) Fill and (4) Stiff layer Geotextile • In the project database select the data type Geogrids and create a new material set In this material set, enter 2500 kN/m as stiffness Note that this is the stiffness in extension In compression no stiffness is used • Drag the geogrid data set to the geotextile in the geometry and drop it there The geotextile should flash red once, indicating the properties have been set Mesh generation • From the Mesh menu select the option Global coarseness In the window that appears, set the mesh coarseness to Medium and click on the Generate button, which will present the following FE mesh composed of 15-node elements Computational Geotechnics 363 of 375 Plaxis Introductory Course, Danang, Vietnam Geotextile reinforced embankment Figure 4: Medium coarse generated mesh • Select the clay layer (this consists of two clusters, see also hint) and press Refine cluster from the Mesh menu This will result in a refinement in the clay layer that will be needed for the consolidation analysis See figure Close the window showing the generated mesh and continue to the Calculations program Figure 5: Mesh with cluster refinement Computational Geotecnics 364 of 375 Plaxis Introductory Course, Danang, Vietnam Geotextile reinforced embankment CALCULATION The calculation consists of two alternatives for the construction of the embankment: without and with consolidation taken into account After both alternatives the factor of safety is determined In the calculations list phases are needed, phases for each alternative First start with the fully undrained construction, that is without taking consolidation into account When starting Plaxis Calculations, choose Classical mode Initial conditions • Select the initial phase in the phase list and then press the Define button on the Parameters tabsheet in order to define the initial phase The input window now opens in Staged Construction mode • Deselect all material clusters and geotextile elements that are not present at the start of the analysis As we want to model the entire construction sequence from the beginning, switch off: – Geotextile elements – Material clusters for the fill – Material cluster for retaining bank • Now continue to the Water conditions mode by clicking the equally named button • Enter a phreatic level at ground level by two coordinates (0, 5.5) and (33, 5.5) Click on the Water pressures button to generate the pore pressures Phase 1: Excavation of the ditch and construction of the retaining bank This calculation phase is a Plastic analysis, with loading type Staged construction For all the other settings the defaults should be used In this phase: • Activate the full geotextile • Construct the retaining bank • Excavate the ditch (left of the embankment) Phase 2: First fill • This calculation phase is also a Plastic analysis with the Staged construction loading type For all the other settings the defaults should be used In this phase the first layer of fill must be switched on Computational Geotechnics 365 of 375 Plaxis Introductory Course, Danang, Vietnam Geotextile reinforced embankment Phase 3: Second fill • This calculation phase is again a Plastic analysis, loading type Staged construction For all the other settings the defaults should be used Switch on the second layer of fill Phase 4: Safety factor determination • This calculation phase is a Safety phase The loading type will be set automatically Keep all default settings After this, we will construct the embankment taking into account consolidation: Phase 5: Consolidated construction of the ditch and retaining bank This phase starts an alternative calculation, so phase should NOT follow on phase as is the default, but it should follow on the initial phase To so, on the General tabsheet set Start from phase to the Initial phase This calculation phase is a Consolidation analysis, loading type Staged construction We assume that construction of the ditch and retaining bank will take days Hence, in the Loading Input box fill in a Time Interval of days During this time interval construction will take place, as well as consolidation For all the other settings the defaults should be used In this phase again: • Switch on the full geotextile • Construct the retaining bank • Excavate the ditch (left of the embankment) Phase 6: First fill - consolidated This calculation phase is also a Consolidation analysis, loading type Staged construction We assume that making the hydraulic fill will take days, so the Time interval should be set on days For the rest this phase is equal to phase 2; hence the first layer of fill must be switched on Phase 7: Second fill - consolidated This calculation phase is again a Consolidation analysis, loading type Staged construction This second fill will take days, so the Time interval should be set on days For all the other settings the defaults should be used In staged construction, switch on the second layer of fill 10 Computational Geotecnics 366 of 375 Plaxis Introductory Course, Danang, Vietnam Geotextile reinforced embankment Phase 8: Safety factor determination This calculation phase is a Safety phase The loading type will be set automatically Keep all default settings Select points for load-displacement curves As node for load-displacement curves, select the toe of the embankment and start the calculation Computational Geotechnics 11 367 of 375 Plaxis Introductory Course, Danang, Vietnam Geotextile reinforced embankment INSPECT OUTPUT In order to get a good idea of the displacement mechanism, one can view the contours of incremental displacements Figure shows this plot of the final calculation step for the undrained construction It clearly shows the effect of the geotextile reinforcement Figure shows the incremental displacement for the consolidated construction Here the embankment has a more gradual settlement without showing an upcoming failure mechanism Figure 6: Incremental displacements contours, undrained (phase 3) Figure 7: Incremental displacement contours, consolidated (phase 7) The axial forces of the geotextile can be visualised by double clicking on the geotextile This will first present the displacement of the geotextile On using the menu item Forces, one can select Axial forces N Figure 8: Axial forces in geotextile, undrained (phase 3) At the ends of the geotextile the axial force must be zero, but due to the discretisation and some numerical inaccuracy this is not completely achieved The maximum axial forces is approx kN/m figure shows the axial forces for the consolidated construction The maximimum axial force here is only 5-6 kN/m Finally, the factors of safety are checked In order to so follow these steps: • Start the curves manager by selecting the Curves manager option from the Tools menu 12 Computational Geotecnics 368 of 375 Plaxis Introductory Course, Danang, Vietnam Geotextile reinforced embankment Figure 9: Axial forces in geotextile, consolidated (phase 7) • In the curves manager (see figure 10) select New in the Charts tabsheet This presents the Curve Generation window as shown in figure 11 • On the x-axis we want to show the displacements of the point at the toe of the embankment, hence choose Point A and Deformations → Total displacements → |u| • On the y-axis we want to show the strength reduction factor, hence select Project and Multiplier → ΣM sf on the y-axis Figure 10: Curves manager The created curve indicates a safety factor around 1.4 for the undrained construction and a a safety factor of 2.1 for the consolidated construction of the embankment, as can be seen in figure 12 From the graph above, the factor of safety can be determined Always look for a steady state solution (slight variations in the load multipliers, increasing displacements) In most case, the phi/c reduction calculation shows some variation at the beginning of the calculation Note that the displacements resulting from a Safety analysis are non-physical Hence the total displacements are not relevant An incremental displacement plot of the last step, however, shows the failure mechanism that corresponds the calculated value for ΣM sf Addicionally, figures 13 and 14 show the failure mechanisms with the lowest factor or safety for both the undrained and consolidated case Computational Geotechnics 13 369 of 375 Plaxis Introductory Course, Danang, Vietnam Geotextile reinforced embankment Figure 11: Curve generation window Consolidated: ΣMsf=2.1 Undrained: ΣMsf=1.4 Figure 12: Safety factor curve for reinforced embankment 14 Computational Geotecnics 370 of 375 Plaxis Introductory Course, Danang, Vietnam Geotextile reinforced embankment Figure 13: Incremental displacements, undrained (phase 4) Figure 14: Incremental displacements, consolidated (phase 8) Computational Geotechnics 15 371 of 375 Plaxis Introductory Course, Danang, Vietnam Geotextile reinforced embankment SUGGESTION FOR EXTRA EXERCISE: NON-REINFORCED EMBANKMENT SCHEME OF OPERATIONS • For the undrained construction of an embankment, now introduce phase (9) In the Start from phase list box select This phase as well as phases 10 and 11 are Plastic analyses Excavate the ditch and construct the embankment, but NOT activate the geotextile • In the next phase (10) the first part of the fill is activated • In the next phase (11) the second part of the fill is activated • In the next phase (12) perform a safety analysis In principle we can keep the 100 additional steps for this calculation However, 50 additional steps is already sufficient here • For the consolidated construction of the embankment, now introduce phase (13) In the Start from phase list box select This phase as well as phases 14 and 15 are Consolidation analyses Set the Time interval to days, excavate the ditch and construct the embankment, but NOT activate the geotextile • In the next phase (14) the first part of the fill is activated Set the Time interval to days • In the next phase (15) the second part of the fill is activated Set the Time interval to days • Finally, in the last phase (16) perform a Safety analysis again In principle we can keep the 100 additional steps here as well However, 30 additional steps is already sufficient to obtain a reliable value Presented below is both the incremental displacement plot as well as the incremental shear strain plot of both the drained and consolidated non-reinforced embankment after safety analysis Hence, the plots show the failure mechanisms Figure 15: Incremental displacements, undrained (phase 12) FACTORS OF SAFETY The factors of safety are checked with the Curves program, see figure 19 16 Computational Geotecnics 372 of 375 Plaxis Introductory Course, Danang, Vietnam Geotextile reinforced embankment Figure 16: Incremental shear strains, undrained (phase 12) Figure 17: Incremental displacements, consolidated (phase 16) Figure 18: Incremental shear strains, consolidated (phase 16) Consolidated: ΣMsf=1.4 Undrained: ΣMsf=1.1 Figure 19: Safety factor curve for non-reinforced embankment Computational Geotechnics 17 373 of 375 Plaxis Introductory Course, Danang, Vietnam Geotextile reinforced embankment 18 Computational Geotecnics 374 of 375 Plaxis Introductory Course, Danang, Vietnam Geotextile reinforced embankment SUGGESTIONS FOR THE DETERMINATION OF THE CLAY PARAMETERS qc su ≈ 15 = 150 = 10 kPa 15 ,0 ,0 su = 12 σx,0 + σ ,0 y sin(ϕ) + c cos(ϕ) with σx = K0 · σy ≈ (1 − sin(ϕ)) · σ y In the middle of the clay layer at about 2m below ground level: σy,0 = h · (γsat − γwater ) = · 3.5 = kPa =⇒ σx,0 = (1 − sin(20)) · σy,0 = 4.6 kPa For this clay estimate ϕ = 20º, then c ˜ kPa u Eu ≈ 15000·s = 15000·10 = 3000 kPa 50 50 1 G = Eu = · 3000 = 1000 kPa E = 2G(1 + ν) = 83 · G = 2667 kPa K0 ν = 1+K = 0.5 = 0.33 1.5 Use ‘Undrained A’ as the type of material behaviour Computational Geotechnics 19 375 of 375 ... angle Plaxis Introductory Course, Da Nang 10 - 12 July 2013 The Mohr Mohr-Coulomb Coulomb failure criterion c cos t* c -? ?? 3 -s* sin 1 -? ?? -s* Plaxis Introductory Course, Da Nang 10 - 12... '' -? ??1 v sin sin 1-2 ’ 2 Plaxis Introductory Course, Da Nang 10 - 12 July 2013 37 of 375 -? ??1 Plaxis Introductory Course, Danang, Vietnam MC approximation of a compr test -? ??1 Eoed -? ??1... Nang 10 - 12 July 2013 35 of 375 xy Plaxis Introductory Course, Danang, Vietnam The LEPP Mohr-Coulomb model Linear-elastic perfectly-plastic stress-strain relationship - Elasticity: - Plasticity: