COURSE ON COMPUTATIONAL GEOTECHNICS A Geotechnical Design Tool. Faculty of Civil Engineering UiTM, Malaysia

Transcription

1 COURSE ON COMPUTATIONAL GEOTECHNICS A Geotechnical Design Tool Faculty of Civil Engineering, Malaysia Name :

2 COURSE CONTENTS Use of Plaxis Getting Started Exercise 1: Elastic analysis of drained footing Exercise 2: Geotextile Reinforced Embankment Exercise 3: Excavation of Building pit in Limburg Exercise 4: Shield Tunnelling in Amsterdam Exercise 5: Finite Element on Embankment (Undrained Failure Analysis

3 ON THE USE OF PLAXIS (getting started)

4 1. STARTING THE PROGRAM General settings General tab sheet

5 General settings Dimensions tab sheet

6 Calculation program CREATING A GEOMETRY MODEL Main menu Toolbar(General) Toolbar(Geometry) ruler cluster point line DRAW AREA origin manual input Cursor position indicator 6

7 Open output program Zoom in Coordinate table output program Curve program New Save Print Zoom out output program Geometry line Node-to-node anchor Prescribed displacement Distributed Load system B Material sets Geogrid Fixed-end anchor Point Load system B Generate mesh Plate Hinge and Rotation Interface Tunnel designer Standard fixities Rotation fixity (plate) Point Load system A Distributed Load system A Drain Well Define initial conditions 7

8 EXERCISE 1 Elastic analysis of drained footing 8

9 INTRODUCTION This exercise illustrates the basic idea of a finite element deformation analysis. In order to keep the problem as simple as possible, only linear elastic behaviour is considered. Besides the procedure to generate the finite element mesh, attention is paid to the input of boundary conditions, material properties, the actual calculation and inspection of some output results AIMS Geometry input Initial stresses and parameters Calculation of vertical load Calculation of horizontal load (0,3.25) (0,3.0) B= 100 kn A= 100 kn clay

10 SCHEME OF OPERATIONS: a) Geometry Input i. General settings ii. Input of geometry lines iii. Input of boundary conditions iv. Input of material properties v. Mesh generation b) Initial Condition i. Generation of pore pressures ii. Initial geometry configuration iii. Generation of initial stress c) Calculation i. Construct footing (staged construction) ii. Apply vertical force iii. Apply horizontal force d) Inspect Output How to model a drained footing? Input Set to plane strain Use dimension as shown No need for large number of elements Load system A: vertical load Load system B: horizontal load Material data sets 10

11 Input for boundary conditions: Prescribed displacements: Standard fixities Vertical load: Point Load system A Horizontal load: Point Load system B (direction must be changed: enter x=1.0 and y=0) Input of material properties: Parameter Name Clay Concrete Unit Material model Model Linear elastic Linear elastic - Type of material behaviour Type Drained Non-porous - Dry soil unit weight γ dry kn/m 3 Wet soil unit weight γ wet 18 - kn/m 3 Permeability in k x 0 - m/day horizontal direction Permeability in k y 0 - m/day vertical direction Young s modulus E ref E6 kn/m 2 Poissson s ratio v Initial Condition Generation of pore pressures Go to initial condition and click ok for unit weight of water = 10 kn/m 3. Draw phreatic level at coordinate (0.0, 3.0) to (8.0, 3.0). Click on Generate water pressure Initial Condition Generation of Initial Stresses Click on generate initial stress button Switch cluster for strip footing. Enter Ko = 0.7 for cluster which represent clay geometry. Click Ok 11

12 Calculations: Phase 1: Construction of footing -general >> plastic calculation -parameters >> staged construction >> Define >> Switch on footing >> update Phase 2: Vertical Load -parameters >> Total multipliers >> Define >> Enter MloadA=100 Phase 3: Horizontal Load -parameters >> Total multipliers >> Define >> Enter MloadB=100. (Please note that the (load multiplier for MloadA needs to be remain at 100) After definition the last calculation phase (Phase 3), the calculation is started by clicking Calculate As no load-displacement curves will be generated, Press No to continue Output Inspect output results. Successful calculation execution will indicate for each phase. If during execution error would occur, Plaxis mark the stage with red cross Press Output button for Phase 3 12

13 EXERCISE 2 Geotextile Reinforced Embankment 13

14 INTRODUCTION After determination of some model parameters the construction of an embankment on soft soil is simulated by means of a staged construction analysis. The use of undrained behaviour and the generation of pore pressures is reviewed in this exercise. As a suggestion of an extra exercise, the behaviour of the embankment can modelled without geotextile. AIMS Determination of soil stiffness parameters from CPT test results Simulation of embankment construction in stages Review of undrained behaviour and pore pressures Application of geotextile elements In 1979, a test embankment was constructed in the Netherlands near the town of Almere. The objective of this test was to measure the influence of geotextile reinforcement on the short term stability of an embankment on soft soil. Two test embankments were constructed on top of a layer, one with and one without geotextiles. The construction procedure was that a ditch was excavated in the clay layer while at the same time a retaining bank was made with the excavated clay. A cross-section of the reinforced test embankment is given in the figure below. retaining bank 5 geotextiles sand fill 4 sand fill soft clay Y X 1 14

15 Cone penetration test gave an average cone resistance of q c =150 kpa for the clay. The clay is considered to be normally consolidated. The behaviour is assumed to be undrained (the retaining bank should be drained, however). The wet weight of the clay is 13.5 kn/m 3. A plasticity index of I p = 50% is assumed. To obtain an undrained shear strength for the clay layer, it is suggested to use the correlation c u» q c / 15. Having no data for the effective cohesion and the effective friction angle, the undrained shear strength may be used directly as a strength property. For the determination of a stiffness parameter for the clay layer it is suggested to use correlation E u»15000 c u / I p% ). The shear modulus G is a third of the undrained Young s modulus E u. Poisson s ratio should be chosen such that a realistic K is obtained in one-dimensional compression ( K = v / (1-v)» 0.5 nc o The hydraulic fill was reported to be fully saturated loose sand with a wet weight of 18 kn/m 3. The behaviour is considered to be drained. The effective strength properties are nc estimated at j = 30 and c =3 kpa. K o is assumed at 0.5 (from v = 0.333). For the stiffness one should take E = 4000 kpa. nc o SCHEME OF OPERATIONS: a) Determination of Stiffness & Strength Properties (CLAY) b) Geometry Input i. Start a new project ii. Enter general settings iii. Enter fixities iv. Enter material properties for soil and geotextile v. Mesh generation + refine line c) Initial Condition i. Regeneration of pore pressures ii. Regeneration of initial stresses d) Calculations i. Switch on geotextile, excavate ditch + raise retaining embankment ii. Apply first hydraulic fill iii. Apply second hydraulic fill e) Safety Factor Analysis for Reinforced Situation f) Non Reinforced Embankment 15

16 Determination of Stiffness & Strength Properties (CLAY) Use the Mohr Coulomb model and enter the soil parameters as listed below. Parameter Name Clay Retaining bank Hydraulic fill Unit Material model Model Mohr Mohr Coulomb Mohr - Coulomb Coulomb Type of material behaviour Type Undrained Drained Drained - Dry soil unit weight γ dry kn/m 3 Wet soil unit weight γ wet kn/m 3 Young s modulus E ref kn/m 2 Poissson s ratio v Cohesion c ref kn/m 2 Friction angle j (phi) o Dilatancy y(psi) o Geometry Input- Geometry, boundary conditions, material properties (0, 3.5) (0, 1.5) (0, 0) Y 8 (4.5, 3.5) 9 10 (1, 1.5) (8,5.5) (9.5, 5.5) (12, 6.5) (12, 3.5) (26, 3.5) X 1 model width approx. 33 m (33, 6.5) (33, 5.5) (33, 3.5) (33, 0) 16

17 Input geometry Enter geometry as indicated Click Geotextile Input boundary condition Click Standard Fixities Input material properties Soil and Interfaces Enter the material properties for the three soil data sets as indicated in the first table of this exercise.. After entering all properties for the three soil types, drag and drop the properties to the appropriate clusters, as indicated below: retaining bank 5 geotextiles sand fill 4 soft clay soft clay Y X 1 Geotextile Select geotextiles and enter 2500 kn/m as stiffness. Note that this is the stiffness in extension. In compression no stiffness is used. 17

18 Geometry Input - Mesh Generation Click on the mesh generator button, which will present the following mesh: Coarse Generated mesh Select the geotextile (this consists of two lines, see also hint) and press Refine line from the Mesh menu. This will result in a refinement along the selected line as presented below: Mesh with local refinement 18

19 Initial Condition Generation of pore pressures Enter phreatic level line by two coordinates (0, 3.5) and (33, 3.5) Generate water pressure button Initial Condition Generation of Initial Stresses Deselect all material clusters and geotextile elements that are not present at the start of analysis. Switch off: -Geotextile elements -Material clusters for the hydraulic fill -Material cluster for retaining bank Click on Generate initial stress button and enter a K o value for the Clay clusters of 0.5. By default, Plaxis proposes K o values that are calculated from the relation: 1- sinj. This result in a default value of 1.0 for the clay layer (j = 0). As we have used in the undrained shear strength no input value for j is used. But as suggested in the introduction of this exercise, we should enter K o value calculated from another relation: v K NC» (1 - v)» Calculations In the calculation list, three phases are needed. For each calculation phase, Plastic calculation is involved. For each calculation phase the loading type Staged Construction is selected, other settings are taken at their default values: Phase 1 Switch on: 1) Construction geotextile 2) Construction of retaining bank 3) Excavation of the ditch (left of the embankment)-switch off Phase 2 Switch on: 1) Construction of 1 st hydraulic fill Phase 3 Switch on: 1) Construction of 2 nd hydraulic fill 19

20 Inspect Output In order to get a good idea of failure mechanism, one can view the contour lines of incremental displacements. This plot of the final calculation step clearly shows the effect of the geotextile reinforcement (presented below). Incremental displacements contour lines (final step) The axial force of the geotextile can be visualised by double clicking the geotextile. This will first present the displacement of the geotextile. On using the menu item Forces, one can select Axial Forces Axial forces in geotextile (final step) 20

21 F) SAFETY FACTOR ANALYSES SCHEME OF OPERATIONS: A) Safety factor analysis Safety Factor Analysis Start the calculation program and select the reinforced embankment project. In the existing calculation list, press the Next button to add the fourth calculation phase. This will add <Phase 4>. Please note that the previous calculation phases must be indicated by check mark Ö. In contrast to most other calculation, a number of steps calculation is needed for safety factor analysis. On the first tab sheet, select Calculation type as Phi/c reduction. On the second tab select press the Define button and Plaxis has introduced a default value for the incremental multipliers Ms f (0.1). This value may be used in most situations. Click on the Calculation button to start the safety factor analysis. Note that the calculation process will skip all calculation phases that were successfully finished, and that are indicated by Ö. Phase 4 is the only calculation phase that is processed. Inspect Output Note that displacements resulting from a Phi/c reduction are non physical. Hence, the total displacements are not relevant. An incremental displacements plot of the last step, however, shows the failure mechanism that corresponds to the calculated value of åm sf. 21

22 Incremental displacement vectors (final step) Incremental displacement contour lines (final step) 22

23 G) NON-REINFORCED EMBANKMENT SCHEME OPERATIONS: a) Delete the geotextiles elements from the previous analysis b) Repeat the first three calculation phases. Note that the calculation process finishes with the message that the soil body collapses. Hence, the total load (the second hydraulic fill in this case) could not be loaded. Only 80% is applied when failure occurs. Presented below is the incremental displacement plot of the final calculation step. This plot shows the failure mechanism. Incremental displacement as vectors (final step) 23

24 Incremental displacements as contour lines (final step) 24

25 EXERCISE 3 Excavation of building pit in Limburg 25

26 INTRODUCTION A building pit was constructed in the south of the Netherlands. The pit is 15 m and 30 m wide. A diaphragm wall is constructed by 60 cm diameter bored piles, the wall is anchored by two rows of pre-stressed ground anchors. In this exercise the construction of the building pit is simulated and the deformation and bending moments of the wall are evaluated. The upper 40 m of the subsoil consists of a more or less homogeneous layer of medium dense fine sand with a unit weight of 18 kn/m 3. Triaxial test data of a representative soil sample given. Underneath this layer is very stiff layer of gravel, which is not to be included in this model. The groundwater table is very deep and does not play a role in this analysis. AIMS - Using interface elements - Using ground anchors - Pre-stressing of anchors - Combination of structural elements Upper sand Middle sand node-to-node anchor Geotextiles (25,25) (17.5,20) (17.5,15) Beam (40,40) (25,20) Stage 1 (40,35) Stage 2 (40,30) Stage 3 (40,25) (40,15) (40,13) Lower sand (55,40) (55,35) (55,30) (55,25) (55,15) Y 0 X 3 (55,0) Figure 1: Geometry for excavation 26

27 Enter fixities Click the standard fixities for the standard boundary condition Input of material properties: Parameter Name Units Upper sand Middle sand Lower sand Material model Model Mohr-Coulomb Mohr-Coulomb Mohr-Coulomb Type of material behaviour Type Drained Drained Drained Dry soil unit weight γdry kn/m Wet soil unit γwet kn/m weight Permeability in kx m/day horizontal direction Permeability in ky m/day vertical direction Young s modulus Eref kn/m Poissson s ratio v Cohesion c ref kn/m Friction angle φ o Dilatancy angle ψ o EA(kN/m) EI(kNm 2 /m) w(kn/m 2 ) L S Beam Anchor Geotextile (Note: all material types are elastic ) R inter [-] 0.6 (sand/concrete inter) INTERFACES 0.6 (sand/concrete inter) 1.0 (soil/soil interaction) 27

28 GEOMETRY INPUT Enter general settings Enter geometry + enter beam, interfaces, anchors and geotextiles - Chick Beam button to introduce diaphragm wall - Click Geotextile button to introduce the geotextile elements that represent the grout body - Click interface button, which will present the cursor in the Interface mode. As interfaces can be introduced on both sides of a geometry line, one should pay attention of the arrows o the cursor. - Click Node-to-node anchor button and introduce the two anchors. These anchors connect the beginning of the grout-body to wall. MESH GENERATION Click on the mesh generator button, which will present to following FE mesh: 28

29 Select the geotextiles and beam elements and press Refine line from the Mesh menu. This will result in a refinement around the selected lines as presented below: INITIAL CONDITIONS As the phreatic line is located below the geometry, the generation of pore pressures can be skipped. Click on switch in the toolbar to continue. The program is now in the Geometry configuration mode. Switch off all structural elements as they are not present before construction (initial situation) Click on the Generate initial stresses button and accept K 0 -values Plaxis proposes. The K 0 values are calculated from the relation 1-sinφ 29

30 CALCULATIONS There entire construction process consists of five phases Phase 1: activation of diaphragm wall, ignore undrained behaviour, reset displacement to zero -parameters >> Plastic calculation >> Staged Construction >> Define >> Switch on diaphragm wall >> update Phase 2: Excavation Stage 1 (-5.00 m) -parameters >> plastic calculation >> Staged Construction >> Define first cluster >> update Phase 3: Pre-stress first anchor row with 300 kn/m --parameters >> plastic calculation >> Staged Construction >>activate anchor pre-tension 300 kn/m and geotextiles >> update Phase 4: Excavation Stage 2 ( m) -parameters >> plastic calculation >> Staged Construction >> Define second cluster >> update Phase 5: Pre-stress second anchor row with 300 kn/m -parameters >> plastic calculation >> Staged Construction >>activate anchor pre-tension 300 kn/m and geotextiles >> update Phase 6: Excavation Stage 3 ( m) -parameters >> plastic calculation >> Staged Construction >> Define third cluster >> update 30

31 INSPECT OUTPUT By double clicking on the node-to-node anchors, Plaxis will present a box, in which the stress in the anchor may be inspected. Double clicking on the anchors will present a box with the anchor force. Check on deformed mesh(final situation) Deformed mesh (final situation) 31

32 EXERCISE 4 Shield Tunnelling in Amsterdam 32

33 INTRODUCTION This exercise comprises the generation and excavation of a circular shield tunnel. The Plaxis tunnel designer is used in this exercise. The excavation of the tunnel consists, in principle, of three stages: Excavation of the soil, removal of the water in the tunnel and simulation of the volume loss due to tunneling. The volume loss is simulated by prescribing a contraction of the tunnel lining. AIMS Generation of a finite element mesh including a circular tunnel Calculating settlements due to tunneling. GEOMETRY INPUT Start a new project General setting: enter title and description Use 15 nodes elements Enter geometry dimensions ENTER GEOMETRY Enter geometry as proposed in Figure 2 33

34 (0, 0) Y 0 X 1 (25, 0) Upper sand Deep sand Upper clay Deep clay (0, -13) (0, -15) (0, -20) (0, -25) (25, -13) (25, -15) (25, -20) (25, 25) Figure 2: Geometry of the model with coordinates in meters ENTER TUNNEL Click on tunnel button. The tunnel designer window is opened. In the presented Tunnel designer window select the right half tunnel button. Please note that as a result the tunnel shape changes on-line. Bored tunnel is already selected as Type of tunnel By default the first section of the tunnel is selected. Enter a radius of 2.5 m. The tunnel designer allows for the creation of tunnels, composed of different archs. As a bored tunnel circular by default, the other sections will have the same radius A lining(shell) and interface are added by default. 34

35 Click the Ok button to finish the design of the tunnel. Move on the cursor to the coordinate (0,-20). On clicking the left mouse button, the tunnel is integrated in the geometry. ENTER FIXITIES Click the standard fixities button, for the standard boundary conditions (Note: that rotation fixities at the intersection of the tunnel lining and the (symmetry) boundary) 35

36 MATERIAL PROPERTIES Enter the material properties for the four soil data sets as determined in Table below. Table 1: Geotechnical parameters for the four layers. Parameter Symbol Deep sand Deep clay Upper sand Upper clay Unit Material Model Mohr Mohr Mohr Mohr - model Coulomb Coulomb Coulomb Coulomb Type of Type drained drained drained drained - behaviour Dry weight g dry (kn/m 3 ) Wet weight g wet (kn/m 3 ) Horizontal k x (m/d) Permeability Vertical k y (m/d) Permeability Young s E ref (kn/m 2 ) moduli Cohesion c ( o ) Friction j ( o ) angle Dilatancy y ( o ) angle Poisson s v (-) ratio Interface strength reduction R inter (-) Table 2: Parameters for the tunnel lining EA(kN/m) EI(kN/m 2 /m) w(kn/m 2 ) v (-) Beam 1.4E7 1.43E

37 MESH GENERATION It is advisable to refine the area where deformations are expected, in this current example this will be the tunnel area. To limit the refinements to the tunnel area only line is drawn from (8,-15) to (8,-25) Generate a coarse finite element mesh Select two clusters inside the tunnel and two clusters outside the tunnel. Select option Refine cluster from the Mesh menu. This will result in a refinement of the tunnel area. 37

38 INITIAL CONDITIONS Initial pore pressures Enter general phreatic line at the top of the mesh (0,0) to (25,0) Generate water pressure button Initial geometry configuration Click on switch Initial stress Generate initial stress button and accept K 0 values. CALCULATIONS Phase 1 - parameters >> staged construction >> Define >> Switch off tunnel soil inside >> Switch on tunnel lining >> -switch to pore pressure mode >> Right click on one of the clusters inside the tunnel >> click cluster dry in cluster pore pressure distribution window >> Press ok >> do the same for other cluster inside. -Click generate water pressure button. Please note that no water pressures are active inside the tunnel. 38

39 Phase 2 Staged construction >> Double click on the center point of the tunnel >> Tunnel contraction window appears >> Enter value 1% 39

40 INSPECT OUTPUT Deformed mesh (last phase) Relative shear stresses Total displacements Arching around tunnel effective stresses Bending moments in the tunnel lining Shear forces at the tunnel lining a) Deformed mesh (last phase) 40

41 b) Arching around tunnel, effective stresses c) Total displacements 41

42 e) Plastic zone around tunnel 42

43 Bending moments in tunnel lining Shear Forces 43

44 EXERCISE 5 Finite Element on Embankment (Undrained Failure Analysis) 44

45 INTRODUCTION In this exercise the Muar trial embankment in Johore (Malaysia) is presented. This is well-documented case history with high quality instrumentation of a test embankment build to failure on a soft marine clay foundation. The undrained soil properties can be determined from vane shear test, CPT tests, as well as UU triaxial test results given in the paper. It is established from the instrumentation as well as limit equilibrium back analysis that failure occurred at embankment height of about 5.5 m. PLAXIS GEOMETRY (0,5.5) (10,5.5) 9 10 (0,0) (0,-2) Y 0 X Fill (20,0) (50, 0) Crust 2 (50,-2) Upper clay (0,-8) (50,-8) 7 Lower clay 3 (0,-18) 5 (50,-18) 4 45

46 INPUT PROPERTIES Parameter Name Fill Crust Upper clay Lower clay Material model Model MC MC MC MC Type of material behaviour Type Undrained Undrained Undrained Undrained Dry soil unit γdry weight Wet soil unit γwet weight Permeability in kx E E-4 9.5E-5 horizontal direction Permeability in ky E E E-5 vertical direction Young s Eref modulus Poissson s ratio v Cohesion c ref Friction angle φ Dilatancy angle ψ Identification E inc c inc g ref Fill Crust Upper Clay Lower Clay INITIAL CONDITIONS Initial pore pressures Phreatic surface is set at 1m below GL Initial stresses Switch off embankment and generate initial stresses based on Ko conditions. 46

47 CALCULATIONS Phase 1 - parameters >> staged construction >> Define >> Activate embankment cluster Phase 2 - Phi/c reduction analysis to obtain FOS for undrained condition. Select node displacement point at the crest of embankment for curve plot of FS vs. displacement. 47

48 INSPECT OUTPUT Check deformed mesh Check total displacement Total displacement pattern shows the mode of failure. 48

49 Plot Sum-Msf vs. U to check FOS Sum-Msf 1.16 Chart 1 Curve e3 2e3 3e3 4e3 5e3 U [m] 49