# Dynamics Manual. Version 7

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Dynamics Manual Version 7

2

4 PLAXIS Load multiplier from data file Modelling block loads Output Curves Validation and verification of the dynamic module One-dimensional wave propagation Simply supported beam Determination of the velocity of the Rayleigh wave Lamb s problem Surface waves: Comparison with boundary elements Pulse load on a multilayered soil; comparison with spectral elements Theory Basic equation dynamic behaviour Time integration Wave velocities Critical time step Model boundaries Absorbent boundaries Initial stresses and stress increments References IV

6 PLAXIS Reference Chapters The second part of the Dynamics manual consists of four chapters. These chapters describe the four parts of the PLAXIS Program in view of the functionality of the Dynamics module. Validation/Verification Chapters The third part of the manual describes some of the test cases that were used to validate the accuracy and performance of the dynamics module. Theory Chapters In the fourth part of the manual you will find an explanation of the theory on Dynamic analysis as used in PLAXIS. 1-2

7 DYNAMICS MANUAL 2 TUTORIAL This tutorial is intended to help users to become familiar with the possibilities of the PLAXIS dynamics module. New users of PLAXIS are referred to the Tutorial section in the complete manual (PLAXIS Version 7). The lessons in this part of the manual deal with three specific applications of the program. Generator on elastic foundation an axisymmetric model for single source vibrations dynamic soil-structure interaction standard absorbent boundaries Pile driving plastic behaviour influence of water Building subjected to an Earthquake a plane strain analysis for earthquake problems SMC file used for acceleration input standard earthquake boundaries 2.1 DYNAMIC ANALYSIS OF A GENERATOR ON AN ELASTIC FOUNDATION Apart from the dynamic aspects like inertia and dynamic loads, it is possible to model dynamic soil-structure interaction with PLAXIS. Here the influence of a vibrating source over its surrounding soil is studied. Due to the three dimensional nature of the problem, an axisymmetric model is the best approach. The spatial spreading of the waves or 'geometric damping' as well as the physical damping due to the viscous behaviour of the soil is taken into account. The modelling of the boundaries is one of the key points. In order to avoid spurious wave reflections at the model boundaries (which are not there in reality), special conditions have to be applied in order to absorb waves reaching the boundaries INPUT The vibrating source is a generator founded over a 0.2 m thick concrete footing of 1 m in diameter. The rotations caused by the generator are transmitted through the footing into the subsoil. These oscillations can be schematised as a uniform harmonic loading, 2-1

9 DYNAMICS MANUAL 3. Proceed to the lower right point and click again; 4. Proceed to the upper right point and click again; Only the right and bottom boundaries are absorbent boundaries. The left boundary is an axis of symmetry and the upper boundary is a free surface. You have to add Standard fixities to the model as well (Standard fixities option from the Loads menu). A 10 x = 0.5 standard fixities absorbent boundaries y 0 x 20 Figure 2.2 Generator model with absorbent boundaries MATERIAL PROPERTIES The properties of the subsoil are given in Table 2.1. It consists of sandy clay, which is assumed to be elastic. The dynamic stiffness of the ground is generally considerably larger than the static stiffness, since dynamic loadings are usually fast and cause very little deformations. The unit weight suggests that the soil is saturated; however the presence of the groundwater is neglected. The footing itself has a weight of 5 kn/m 2 and is also assumed to be elastic. The properties are listed in Table 2.2. Table 2.1 Material properties of the subsoil Parameter Name Value Unit Material model Model Elastic - Type of material behaviour Type Drained - Soil weight γ 20.0 kn/m 3 Young's modulus (constant) E ref kn/m 2 Poisson's ratio ν

10 PLAXIS Hint: When using Mohr-Coulomb or linear elastic models the wave velocities V p and V s are calculated from the elastic parameters and the soil weight. V p and V s can also be entered as input; the elastic parameters are then calculated automatically. See also Elastic parameters page 3-4 and the theory on Wave Velocities on page 5-4. Table 2.2 Material properties of the footing Parameter Name Value Unit Normal stiffness EA kn/m Flexural rigidity EI knm 2 /m Weight w 5.0 kn/m/m Poisson's ratio ν MESH GENERATION Because of the high concentration of stresses expected in the area below the footing a local refinement is proposed there. The mesh is generated with the global coarseness set to very coarse and then the line of the footing is refined three times. The result is plotted in Figure A x=0.5 y 0 x 20 Figure 2.3 Geometry and mesh 2-4

11 DYNAMICS MANUAL INITIAL CONDITIONS Water pressures: The generation of water pressures can be skipped, since water is not considered in this example. Initial stresses: The last step is the generation of initial stresses by means of the K 0 procedure using a K 0 value of 0.5. In the initial situation the footing is not present yet; therefore it must be deactivated CALCULATIONS There are four calculation phases. In the first phase the footing is built. In the second the generator weight is applied on the footing. The third phase is the situation when the generator is running. In the fourth phase the generator is turned off, and the soil vibrates freely. The last two phases involve dynamic calculations. Phase 1: 1. Select Plastic calculation - Load Advancement Ultimate Level in the General tab sheet. 2. Select Staged construction in the Parameter tab sheet. 3. Click on Define. 4. Activate the footing with its weight of 5kN/m 2. Phase 2: 1. Select Plastic calculation - Load Advancement Ultimate Level in the General tab sheet. 2. Select Total multipliers in the parameter tab sheet. 3. Enter ΣMloadA = 8 in the multiplier tab sheet to apply the weight of the generator (8 kn/m 2 ). Hence, the total weight on the sub-soil amounts 13 kn/m 2. Phase 3: A vertical harmonic load simulates the vibrations transmitted by the generator, with a frequency of 10 Hz and amplitude of 10 kn/m 2. Only 5 cycles are considered, corresponding to a total time of 0.5 sec. Applying the dynamic load: 1. Select Dynamic analysis - Automatic time stepping in the General tab sheet. 2-5

13 DYNAMICS MANUAL 5. Set all parameters to zero in the window Dynamic loading-load System A. Before running the calculation, select points on the surface at about 0 m, 1.4 m, 1.9 m, and 3.6 m from the left boundary of the model. They will be used by the Curves program to visualise the deformation as a function of time. You can now start the calculation. Additional calculation with damping: In a second calculation material damping is introduced by means of Rayleigh damping. First a copy of the project is made in the Input program. Then in the dynamic phases of the generator project material damping is introduced. 1. Start the Input program and select the generator project. 2. Save the project under another name. 3. Start the Calculations program and open the copy of the generator project. 4. Select phase Select Manual setting in the Iterative procedure box. 6. Change the damping parameters Rayleigh α and β to and 0.01 respectively (See Figure 2.5). 7. Select phase Repeat steps 5 and 6. Figure 2.5 Iterative procedure. Manual settings window 2-7

14 PLAXIS OUTPUT The Curves program is particularly useful for dynamic analysis. You can easily display the actual loading as a function of time (input) as well as displacements, velocities and accelerations of preselected points as a function of time. Figure 2.6 shows the evolution of the applied load with time, as defined by the calculation phases 3 and Sum-MloadA Legend Load time curve Time [s] Figure 2.6 Load time curve Figure 2.7 shows the fact that waves are spreading radially ('geometric damping'). This phenomenon can be noticed when comparing the amplitudes at different distances from the generator. Displacement [m] 4.00E E-05 Legend Point at (1.4,10) Point at (1.9,10) Point at (3.6,10) E E Time [s] Figure 2.7 Displ.- time on the surface at different distances to the vibrating source, without damping (Standard settings: Rayleigh α = 0; β = 0) 2-8

15 DYNAMICS MANUAL The presence of damping is clear by comparing the amplitude of the waves after the removal of the alternating force (after t = 0.5 s). Compare Figure 2.7 (without damping) with Figure 2.8 (with damping). Displacement [m] 3.00E E-05 Legend Point at (1.4,10) Point at (1.9,10) Point at (3.6,10) 1.00E E E E Time [s] Figure 2.8 Displ.- time. With damping (Manual settings: Rayleigh α = ; β = 0.01) It is possible in the Output program to display displacements, velocities and accelerations at a particular time, by choosing the appropriate option in the Deformations menu. Figure 2.9 shows the total accelerations in the soil at the end of phase 3 (t = 0.5 s). Figure 2.9 Total accelerations in the soil at the end of phase 3 2-9

16 PLAXIS 2.2 PILE DRIVING This example involves the driving of a pile through an 11 m thick clay layer into a sand layer. The concrete pile has a diameter of 0.4 m. The situation is depicted in Figure Pile driving is a dynamic process that causes vibrations in the surrounding soil. Moreover, excess pore pressures are generated due to the quick stress increase around the pile. In this example attention is focused on the irreversible deformations below the pile. In order to simulate this process most realistically, the behaviour of the sand layer is modelled by means of the Hardening Soil model. clay pile Ø 0.4 m 11 m sand 7 m Figure 2.10 Pile driving situation GEOMETRY MODEL The situation is modelled by means of an axisymmetric finite element model in which the pile is located around the axis of symmetry (see Figure 2.11). In the general settings, the standard gravity acceleration is used (9.8 m/s 2 ). The unit of time should be set to seconds [s]. Both the soil and the pile are modelled with 15-node volume elements. The subsoil is divided into an 11 m thick clay layer and a 7 m thick sand layer underneath. Interface elements are placed around the pile to model the interaction between the pile and the soil. The interface should be extended for about half a meter into the sand layer (see Figure 2.12). A proper modelling of the pile-soil interaction is important to include the material damping caused by the sliding of the soil along the pile during penetration and to allow for sufficient flexibility around the pile tip. Use the zoom option to create the pile and the interface. 2-10

17 DYNAMICS MANUAL 18 A x = 0.2 interface standard fixities y y=6.6 absorbent boundaries y=7 0 x 30 Figure 2.11 Geometry model of pile driving problem The boundaries of the model are taken sufficiently far away to avoid a direct influence of the boundary conditions. Standard absorbent boundaries are used at the bottom and at the right hand boundary to avoid spurious reflections. In order to model the driving force, a distributed unit load (system A) is created on top of the pile. This load is shortly activated to a certain level in a calculation. Pile Interface (0.0, 7.0) Clay (0.2, 7.0) Extended interface (0.2, 6.6) Sand Figure 2.12 Extended Interface MATERIAL PROPERTIES The clay layer is modelled with the simple Mohr-Coulomb model. The behaviour is considered to be undrained. An interface strength reduction factor is used to simulate the reduced friction along the pile shaft. In order to model the non-linear deformations below the tip of the pile in a right way, the sand layer is modelled by means of the Hardening Soil model. Because of the fast loading process, the sand layer is also considered to behave undrained. The short 2-11

18 PLAXIS interface in the sand layer does not represent soil-structure interaction. As a result, the interface strength reduction factor should be taken equal to unity (rigid). The pile is made of concrete, which is modelled by means of the linear elastic model considering non-porous behaviour. In the beginning, the pile is not present, so initially the clay properties are also assigned to the pile cluster. The parameters of the two layers and the concrete pile are listed in Table 2.3. Table 2.3 Material properties of the subsoil and pile Parameter Symbol Clay Sand Pile Unit Material model Model Mohr-C. Hardening-S Linear elast. - Type of behaviour Type Undrained Undrained Non-porous - Dry weight γ dry kn/m 3 Wet weight γ wet kn/m 3 Young's modulus E ref kn/m 2 Oedometer modulus E oed kn/m 2 Power m Unloading modulus E ur kn/m 2 Poisson's ratio ν Reference stress P ref kn/m 2 Cohesion c kn/m 2 Friction angle ϕ Dilatancy angle ψ Interface strength reduction R inter (rigid) 1.0 (rigid) - It should be noted that there is a remarkable difference in wave velocities between the clay layer and the concrete pile due to the large stiffness difference. This may lead to small time increments (many sub steps) in the automatic time stepping procedure. This causes the calculation process to be very time consuming. Many sub steps may also be caused by a very small (local) element size. In such situations it is not always vital to follow the automatic time stepping criterion. You can reduce the number of sub steps in the Manual setting of the Iterative procedure (page 3-7). When the Hardening Soil model is used wave velocities are not shown because they vary due to the stress-dependent stiffness MESH GENERATION The mesh is generated with a global coarseness set to coarse (default). A local refinement is made in the pile cluster. The result of the mesh generation is plotted in Figure

19 DYNAMICS MANUAL A 18 y 0 x 30 Figure 2.13 Finite element mesh for pile driving problem INITIAL CONDITIONS Water pressures: The phreatic level is considered to be high; a general phreatic line is drawn along the ground surface. Hydrostatic pore pressures are generated in the whole geometry according to this phreatic line. Initial stresses: Initial effective stresses are generated by the K 0 procedure, using the default values. Note that in the initial situation the pile is not present yet and that the clay properties should be assigned to the corresponding clusters CALCULATIONS The analysis consists of three calculation phases. In the first phase the pile is created. In the second phase the pile is subjected to a single stroke, which is simulated by activating half a harmonic cycle of load system A. In the third phase the load is kept zero and the dynamic response of the pile and soil is analysed in time. The last two phases involve dynamic calculations. Phase 1: 1. Select Plastic calculation - Load Advancement Ultimate level in the general tab sheet. 2. Select Staged construction in the parameter tab sheet. 3. Assign the pile properties to the pile cluster. 2-13

20 PLAXIS Phase 2: 1. Select Dynamic analysis - Automatic time stepping in the general tab sheet. 2. Enter 10 for the Additional steps. 3. Reset displacements to zero. 4. Enter 0.01 s for the Time interval. 5. Select Manual setting for the iterative procedure and click Define. The initial number of Dynamic sub steps is relatively large, due to the large difference in wave speeds and the small element sizes (see remark at Material properties page 2-12). Set the number of Dynamic sub steps to 1. All other settings remain at their default. Hence, Rayleigh damping is not considered. 6. Click next to Load system A in the multiplier tab sheet to apply the dynamic loading. Enter the values as indicated in Figure Figure 2.14 Dynamic loading parameters The result of this phase is half a harmonic cycle of the external load in system A. At the end of this phase, the load is back to zero. Phase 3: 1. Select Dynamic analysis in the general tab sheet. 2. Enter 190 for the Additional steps 3. Enter a Time interval of 0.19 s. 4. Select the Manual setting for the Iterative procedure and click Define. Set the number of Dynamic sub steps to

21 DYNAMICS MANUAL 5. In the Multiplier tab sheet, all multipliers remain at their default values. 6. Click next to Load system A and set all parameters in the Dynamic Loading window to zero. 7. Select a node at the top of the pile for load displacement curves OUTPUT Figure 2.15 shows the settlement of the pile top as a function of time. From this figure the following observations can be made: The maximum vertical settlement of the pile top due to this single stroke is about 16 mm. However, more than 3 mm of this settlement is recovered. The final settlement is almost 12 mm. Most of the settlement occurs in phase 3 after the stroke has ended. This is due to the fact that the compression wave is then still propagating downwards in the pile, causing additional settlements. Unless the absence of Rayleigh damping, the vibration of the pile is damped due to soil plasticity and the fact that wave energy is absorbed at the model boundaries. Uy [m] ,00E-03-8,00E-03-0,012-0,016 End of stroke Time [sec] Figure 2.15 Pile top settlement as a function of time 2-15

22 PLAXIS When looking at the output of the second calculation phase (t = 0.01 s, i.e. just after the stroke), it can be seen that large excess pore pressures occur very locally around the pile tip. This reduces the shear strength of the soil and contributes to the penetration of the pile into the sand layer. The excess pore pressures remain also in the third phase since consolidation is not considered. Figure 2.16 shows the shear stresses in the interface elements at t = 0.01 s. This plot is obtained by using a manual scaling factor of 100 and zooming into the small area of stresses along the pile. The plot shows that the maximum shear stress is reached all along the pile, which indicates that the soil is sliding along the pile. shear stress down along the pile (interface) maximum shear stress as defined by Mohr-Coulomb criterium Figure 2.16 Shear stresses in the interface at t = 0.01 s When looking at the deformed mesh of the last calculation phase (t = 0.2 s), it can also be seen that the final settlement of the pile is about 12 mm. In order to see the whole dynamic process it is suggested to use the option Create Animation to view a 'movie' of the deformed mesh in time. 2.3 BUILDING SUBJECTED TO AN EARTHQUAKE This example involves a four-storey building subjected to an earthquake. A real accelerogram of an earthquake recorded by USGS in 1989 is used for the analysis. It is contained in the standard SMC format (Strong Motion CD-ROM), which can be read and interpreted by PLAXIS (See also page 3-12). 2-16

23 DYNAMICS MANUAL INPUT The building has four storeys plus a basement. It is 6 m wide and 25 m long. The total height from the ground level is 4 x 3 m = 12 m and the basement is 2 m deep. The dead load and a percentage of the live load acting on each floor are added up, amounting up to 5 kn/m 2. This value is taken for the weight of the floors as well as for the weight of the walls GEOMETRY MODEL The length of the building is much larger than its width. The earthquake is also supposed to have a dominant effect across the width of the building. Hence, a plane strain analysis can be performed. 15-node elements are used to simulate the situation. The unit of time is set to seconds [s]. The other dimensions are left to their defaults (length: [m], force: [kn]). The subsoil consists of a relatively soft soil layer of 20 m thickness, which is overlaying a rock formation. The latter is not included in the model. The building itself is composed of 5-node beam elements. The clusters of the building are filled with soil material when generating the mesh, but these clusters are deactivated for the initial situation. The vertical boundaries are taken relatively far away from the building. Physical damping in the building and the subsoil is simulated by means of Rayleigh damping (see calculations page 3-8). The earthquake is modelled by imposing a prescribed displacement at the bottom boundary. In contrast to the standard unit of length used in PLAXIS [m], the displacement unit in the SMC format is [cm]. Therefore the input value of the horizontal prescribed displacements is set to 0.01 m. (When using [ft] as unit of length, this value should be ft). The vertical component of the prescribed displacement is kept zero (u x =0.01m and u y =0.00m). At the far vertical boundaries, absorbent boundary conditions are applied to absorb outgoing waves. PLAXIS has a convenient default setting to generate standard boundary conditions for earthquake loading using SMC-files. This option can be selected from the Loads menu. In this way the boundary conditions as described above are automatically generated (see Figure 2.17). y=32 beam elements 20 absorbent boundary standard fixities y=18 absorbent boundary 0 prescribed displacement 100 Figure 2.17 Geometry model with standard earthquake boundary conditions 2-17

24 PLAXIS MATERIAL PROPERTIES The properties of the subsoil are given in Table 2.4. The soil consists of loam, which is assumed to be linear elastic. The stiffness is higher than one would use in a static analysis, since dynamic loadings are usually fast and cause very little deformations. The presence of the groundwater is neglected. The building is also considered to be linear elastic. The walls and the plates have similar beam properties, which are listed in Table 2.5. Table 2.4 Material properties of the subsoil Parameter Name Value Unit Material model Model Elastic - Type of material behaviour Type Drained - Soil weight γ 17.0 kn/m 3 Young's modulus (constant) E ref kn/m 2 Poisson's ratio ν Considering a gravity acceleration of 9.8 m/s 2, the above properties are equivalent with a shear wave velocity of about 85 m/s and a compression wave velocity of about 140 m/s. Table 2.5 Material properties of the building (beam properties) Parameter Name Floors / Walls Unit Material model Model Elastic - Normal stiffness EA kn/m Flexural rigidity EI 9000 knm 2 /m Weight w 5.0 kn/m/m Poisson's ratio ν MESH GENERATION 20 y 0 x 100 Figure 2.18 Finite element mesh 2-18

25 DYNAMICS MANUAL For the mesh generation, the global coarseness is set to 'coarse' and the clusters inside the building are refined twice. This is because of the high concentration of stresses that can be expected just in and under the building elements (See Figure 2.18) INITIAL CONDITIONS Water pressures: The generation of water pressures can be skipped, since pore pressures are not considered in this example. Initial stresses: In the initial situation the building is not present yet; therefore the beams and the clusters above the ground surface must be deactivated. The initial state of stresses is generated by the K 0 -procedure, with a K 0 -value of 0.5 for all active clusters CALCULATIONS The calculation involves two phases. The first one is a normal plastic calculation in which the building is constructed. The second is a dynamic analysis in which the earthquake is simulated. In order to analyse the effects of the earthquake in detail the displacements are reset to zero at the beginning of this phase. Phase 1: 1. Select Plastic calculation - Load-advancement ultimate level in the general tab sheet. 2. Select Staged construction as the loading input in the parameter tab-sheet and click Define. 3. Activate the beams of the building and de-activate the soil cluster in the basement. All clusters inside the building should now be inactive. 20 y x Figure 2.19 Construction of the building 2-19

26 PLAXIS Phase 2: 1. Select Dynamic analysis - Automatic time stepping for the calculation type in the General tab sheet. 2. Set the number of Additional steps to 250 in the Parameters tab-sheet. 3. Select Reset the displacements to zero. 4. Set the Time interval to 10 sec in the loading input box. 5. Select Manual setting for the Iterative procedure. 6. Click Define. 7. Enter the Rayleigh damping factors α = β = Select the Multiplier tab sheet. 9. Click next to the Σ -Mdisp multiplier. 10. Select the option Load multiplier from data file. Figure 2.20 Selection of SMC file 11. Select the appropriate SMC file (225A.smc). This file can be found in the PLAXIS program directory. The data provided in this file is an accelerogram, thus the option Acceleration has to be selected from the File contents box (See Figure 2.20). 2-20

27 DYNAMICS MANUAL 12. Click OK. 13. Select points for load displacement curves at the top and basement of the building and at the bottom of the mesh. You may now start the calculation. Hint: Plaxis assumes the data file is located in the current project directory when no directory is specified in the Dynamic loading window. > In the SMC files, data is given for each s (200 values per second). The calculation step size does not correspond with the data given in the file, but the calculation program will interpolate a proper value for the actual time of each step OUTPUT The maximum horizontal displacement at the top op the building is 75 mm and occurs at t=4.8 s. Figure 2.21 shows the deformed mesh at that time. The output program also provides data on velocities and accelerations. The maximum horizontal acceleration at the top of the building is 3.44 m/s 2 (0.34 G) and occurs at t=2.88 s (see Figure 2.22). Figure 2.21 Deformed mesh at at t = 4.80 s (step 121). Maximum horizontal deformation at the top: u x = 75 mm Figure 2.22 Horizontal accelerations at t = 2.88 s (step 73). Maximum value at the top: a x = 3.44 m/s

28 PLAXIS Figure 2.23 and Figure 2.24 show, respectively, time-displacement curves and timeacceleration curves of the bottom, the basement and the top of the building. From Figure 2.24 it can be seen that the maximum accelerations at the top of the building are much larger than the accelerations from the earthquake itself. Displacement [m] Legend Bottom of Mesh Bottom of Basement Top of Builing Time [s] Figure 2.23 Time-displacement curve for bottom, basement and top of building 2-22

29 DYNAMICS MANUAL Acceleration [m/s2] Legend Bottom of Mesh Bottom of Basement Top of Builing Time [s] Figure 2.24 Time-acceleration curve for bottom, basement and top of building 2-23

30 PLAXIS 2-24

31 DYNAMICS MANUAL 3 REFERENCE The procedure to perform a dynamic analysis with PLAXIS is very similar to the procedure for a static analysis, i.e. creation of a geometry model, mesh generation, initial stress generation, defining and executing calculation, evaluation of results. For the general explanation of the basic functionality of PLAXIS you are advised to read the tutorial and reference sections in the complete manual (PLAXIS manual Version 7). In this part of the manual the functionality of the Dynamics module is explained. The working order for a dynamic analysis in PLAXIS is followed in the explanation. Input: General settings Loads and Boundary conditions Prescribed displacements Absorbent boundaries Elastic parameters Calculations: Selecting dynamic analysis Parameters Multipliers Output: Animations Velocities Accelerations Curves: Velocities Accelerations 3-1

32 PLAXIS 3.1 INPUT The following topics will be discussed in this chapter: General settings Loads and Boundary conditions Prescribed displacements Absorbent boundaries Elastic parameters GENERAL SETTINGS In the general settings of a new project you can define the basic conditions for the dynamic analyses you want to perform. Dynamic analyses in PLAXIS can be roughly divided into two types of problems: Single-source vibrations Earthquake problems Single-source vibrations Single-source vibration problems are often modelled in an axisymmetric model, even if one would normally use a plane strain model for static deformations. This is because waves always spread out radially and this leads to a reduction of the amplitude with increasing radius, since the wave energy is divided over an increasing width. This effect is called 'geometric damping' and it is automatically included in an axisymmetric model. In single-source problems, geometric damping is generally the most important contribution to damping in general. Hence, for problems of single source vibrations it is essential to use an axisymmetric model. Earthquake problems In earthquake problems the dynamic loading source is usually applied all along the bottom of the model and shear waves will propagate upwards. This type of problems is generally modelled using a plane strain model. Note that a plane strain model does not include the geometric damping. Hence it may be necessary to include material damping to obtain realistic results. (See also page 3-8) Gravity acceleration By default, the gravity acceleration, g, is set to 9.8 m/s 2. This value is used to calculate the material density, ρ [kg/m 3 ], from the unit of weight, γ ( ρ = γ / g ). The material density is used to calculate the wave velocities V s and V p (See theory on page 5-4). 3-2

35 DYNAMICS MANUAL Figure 3.1 Elastic parameters in Mohr-Coulomb and linear elastic models 3.2 CALCULATIONS In the Calculations program you can define the dynamic loads by activating displacements and loads as a function of time with their corresponding multipliers. For general information on parameters and multipliers you are referred to the complete PLAXIS manual Version 7, Reference section 4.5 and section 4.6. In this part of the manual you can find information on the following: Selecting dynamic analysis Dynamic parameters: Time stepping Rayleigh parameters Newmark parameters Dynamic loading: Harmonic loading Load multipliers from file Block loads 3-5

37 DYNAMICS MANUAL ITERATIVE PROCEDURE MANUAL SETTING The iterative procedure for a dynamic analysis can be defined manually. The following parameters will be explained: Dynamic sub steps Rayleigh alpha and beta Newmark alpha and beta Boundaries C 1 and C 2 Figure 3.2 Default parameters of iterative procedure for dynamic analysis Dynamic sub steps For each additional step PLAXIS calculates the number of sub steps necessary to reach the estimated end time with a sufficient accuracy on the basis of the generated mesh and the calculated δt critical (see theory on critical time step page 5-4). If the wave velocities (material stiffness) in a model show remarkable differences or if locally the model contains very small elements the standard number of sub steps PLAXIS calculates can be very large. In such situations it may not always be vital to follow the automatic time stepping criterion. You can change the calculated number of Dynamic sub steps in the manual settings of the iterative procedure in the parameter tab sheet. Be aware that in doing so the calculation results may be less accurate. 3-7

38 PLAXIS Rayleigh alpha and beta Material damping in the soil is generally caused by its viscous properties, friction and the development of plasticity. However, the PLAXIS soil models do not include viscosity. Instead, a global damping term is assumed, which is proportional to the mass and stiffness of the system (Rayleigh damping): C = α M + β K Where C represents the damping, M the mass, K the stiffness and α (alpha) and β (beta) are the Rayleigh coefficients. Rayleigh alpha is the parameter that determines the influence of the mass in the damping of the system. The higher the alpha value, the more the lower frequencies are damped. Rayleigh beta is the parameter that determines the influence of the stiffness in the damping of the system. The higher the beta value, the more the higher frequencies are damped. According to the standard settings there is no Rayleigh damping (Rayleigh alpha and Rayleigh beta equal to 0.0) (See Figure 3.2). Damping can be introduced in the Manual settings by using small values of Rayleigh alpha and/or Rayleigh beta. In single-source type of problems using an axisymmetric model, it may not be necessary to include Rayleigh damping, since most of the damping is caused by the radial spreading of the waves (geometric damping). However, in plane strain models, such as for earthquake problems, Rayleigh damping may be required to obtain realistic results. Newmark alpha and beta The Newmark Alpha and Beta parameters in the manual settings for the iterative procedure determine the numeric time-integration according to the implicit Newmark scheme. In order to obtain a stable solution these parameters have to satisfy the following conditions: Newmark β 0.5 and Newmark α 0.25 (0.5 + β) 2 For an average acceleration scheme you can use the standard settings: α = 0.25 and β = 0.5 (See Figure 3.2). For a damped Newmark scheme you can use the settings: α = and β = 0.6 Boundary C 1 and C 2 C 1 and C 2 are relaxation coefficients used to improve the wave absorption on the absorbent boundaries. C 1 corrects the dissipation in the direction normal to the boundary and C 2 in the tangential direction. If the boundaries are only subjected to pressure waves perpendicular to them, relaxation is not necessary (C 1 = C 2 =1). When there are also shear waves (which is generally the case), C 2 has to be adjusted to improve the absorption. The default values are C 1 =1 and C 2 =0.25 (See Figure 3.2). 3-8

42 PLAXIS ASCII file This file is an ASCII file that can be created by the user with any text editor. In every line a pair of values (actual time and corresponding multiplier) is defined, leaving at least one space between them. The time should increase in each new line. It is not necessary to use constant time intervals. If the time steps in the dynamic analysis are such that they do not correspond with the time series given in the file, the multipliers at a given time will be linearly interpolated from the data in the file. If the time in the calculation is beyond the last time value in the file a constant value, equal to the last multiplier in the file will be used in the calculations. SMC file The SMC (Strong Motion CD-ROM) format is currently used by the U.S. Geological Survey National Strong-motion Program to record data of earthquakes and other strong vibrations. This format uses ASCII character codes and provides text headers, integer headers, real headers, and comments followed by either digitised time-series coordinates or response values. The header information is designed to provide the user with information about the earthquake and the recording instrument. Most of the SMC files contain accelerations, but they may also contain velocity or displacement series and repines spectra. The strong motion data are collected by the U.S. Geological Survey and are available from the National Geophysical Data Center (NGDC) of the National Oceanic and Atmospheric Administration. Information on NGDC products is available on the World-wide Web at or by writing to : National Geophysical Data Center NOAA/EGC/1 325 Broadway Boulder, Colorado USA Hint: The length unit used in the SMC files is [cm], so accelerations are given in [cm/s2]. This has consequences for the input value of the prescribed displacements. SMC files should be used in combination with prescribed boundary displacements at the bottom of a geometry model. When using the standard length unit [m] it is necessary to use input values of 0.01 [m] for prescribed displacements. Alternatively, when using a standard length unit of [ft] it is necessary to use input values of [ft] (1/[feet in cm]) for prescribed displacements. In this way the SMC file can directly be used as input for the dynamic component of the Σ-Mdisp multiplier in a dynamic analysis to study the effects of earthquakes. 3-12

44 PLAXIS you want to have all steps available for the output, the option Delete intermediate steps in the parameter tab sheet of the Calculations program should be disabled. For dynamic steps several velocity and acceleration options are available in the Deformations menu. You can select the total velocities, the total accelerations, the horizontal components and the vertical components. Selection of phases from Create Animation window After selecting the menu option Create Animation, a window appears in which the phase(s) must be selected that are to be included in the animation (see Figure 3.7). In order to select a range of phases, select the first phase of the range and then the last phase of the range while holding down the <Shift> key. After selecting the phase(s), click OK to start the process. The progress of this process is indicated in a separate window. If a large number of steps is to be included in the animation, the process may take some minutes after which the animation is presented. The result is stored in an animation file in the project.dta directory and can be reused without regenerating. Figure 3.7 Selection of phases from Create Animation window 3.4 CURVES For the general use of the Curves program you are referred to section 6 of the complete PLAXIS manual Version 7. In addition to the standard version of PLAXIS with the Dynamic analysis module you can display the velocity or acceleration as well as displacements as a function of time. 3-14

45 DYNAMICS MANUAL Hint: If you want to display motion for a particular point in the geometry you have to select this point with the option Select points for curves in the Calculations program. Plots of time versus displacements, velocities, accelerations or multiplier or any other combination can be displayed. Select the corresponding radio buttons (See Figure 3.8). Figure 3.8 Dynamic fields in Curve generation window 3-15

### 1 Introduction. Abstract

Abstract This paper presents a three-dimensional numerical model for analysing via finite element method (FEM) the mechanized tunneling in urban areas. The numerical model is meant to represent the typical

### DYNAMIC ANALYSIS OF PILES IN SAND BASED ON SOIL-PILE INTERACTION

October 1-17,, Beijing, China DYNAMIC ANALYSIS OF PILES IN SAND BASED ON SOIL-PILE INTERACTION Mohammad M. Ahmadi 1 and Mahdi Ehsani 1 Assistant Professor, Dept. of Civil Engineering, Geotechnical Group,

### Recent Research on EPS Geofoam Seismic Buffers. Richard J. Bathurst and Saman Zarnani GeoEngineering Centre at Queen s-rmc Canada

Recent Research on EPS Geofoam Seismic Buffers Richard J. Bathurst and Saman Zarnani GeoEngineering Centre at Queen s-rmc Canada What is a wall (SEISMIC) buffer? A compressible inclusion placed between

### EA (kn/m) EI (knm 2 /m) W (knm 3 /m) v Elastic Plate Sheet Pile

1. Introduction Nowadays, the seismic verification of structures has dramatically evolved. Italy is surrounded many great earthquakes; hence it would be unwise to totally ignore the effects of earthquakes

### 2D Embankment and Slope Analysis (Numerical)

2D Embankment and Slope Analysis (Numerical) Page 1 2D Embankment and Slope Analysis (Numerical) Sunday, August 14, 2011 Reading Assignment Lecture Notes Other Materials FLAC Manual 1. 2. Homework Assignment

### Finite Element Solutions for Geotechnical Engineering

Release Notes Release Date: July, 2015 Product Ver.: GTSNX 2015 (v2.1) Integrated Solver Optimized for the next generation 64-bit platform Finite Element Solutions for Geotechnical Engineering Enhancements

### Lateral Earth Pressure

1 of 11 6/2/2012 4:28 AM Lateral Earth Pressure The magnitude of lateral earth pressure depends on: 1. Shear strength characteristics of soil 2. Lateral strain condition 3. Pore water pressure 4. State

### Instabilities and Dynamic Rupture in a Frictional Interface

Instabilities and Dynamic Rupture in a Frictional Interface Laurent BAILLET LGIT (Laboratoire de Géophysique Interne et Tectonophysique) Grenoble France laurent.baillet@ujf-grenoble.fr http://www-lgit.obs.ujf-grenoble.fr/users/lbaillet/

### THEME A. Analysis of the elastic behaviour of La Aceña arch-gravity dam

THEME A Analysis of the elastic behaviour of La Aceña arch-gravity dam Gjorgi KOKALANOV, Professor, Faculty of Civil Eng., Skopje, Republic of Macedonia Ljubomir TANČEV, Professor, Faculty of Civil Eng.,

### Measurement and estimation of vibration of old buildings

Measurement and estimation of vibration of old buildings Gerhard Niederwanger Institute for Strength of Materials, University of Innsbruck, Austria Email: Gerhard. Nieder\vanger@uibk. ac. at Abstract Vibrations

VOL., NO., DECEMBER 8 ISSN 89-8 -8 Asian Research Publishing Network (ARPN). All rights reserved. CONSOLIDATION BEAVIOR OF PILES UNDER PURE LATERAL LOADINGS Qassun S. Mohammed Shafiqu Department of Civil

### SOIL-BASEMENT STRUCTURE INTERACTION ANALYSIS ON DYNAMIC LATERAL EARTH PRESSURE ON BASEMENT WALL

International Conference on Earthquake Engineering and Disaster Mitigation, Jakarta, April 1-15, SOIL-BASEMENT STRUCTURE INTERACTION ANALYSIS ON DYNAMIC LATERAL EARTH PRESSURE ON BASEMENT WALL Nurrachmad

### Response Spectrum Analysis Shock and Seismic. FEMAP & NX Nastran

Response Spectrum Analysis Shock and Seismic FEMAP & NX Nastran Table of Contents 1. INTRODUCTION... 3 2. THE ACCELEROGRAM... 4 3. CREATING A RESPONSE SPECTRUM... 5 4. NX NASTRAN METHOD... 8 5. RESPONSE

### Dynamic Earth Pressure Problems and Retaining Walls. Behavior of Retaining Walls During Earthquakes. Soil Dynamics week # 12

Dynamic Earth Pressure Problems and Retaining Walls 1/15 Behavior of Retaining Walls During Earthquakes - Permanent displacement = cc ' 2 2 due to one cycle of ground motion 2/15 Hence, questions are :

### Model tests and FE-modelling of dynamic soil-structure interaction

Shock and Vibration 19 (2012) 1061 1069 1061 DOI 10.3233/SAV-2012-0712 IOS Press Model tests and FE-modelling of dynamic soil-structure interaction N. Kodama a, * and K. Komiya b a Waseda Institute for

### Validation of empirical formulas to derive model parameters for sands

Validation of empirical formulas to derive model parameters for sands R.B.J. Brinkgreve Geo-Engineering Section, Delft University of Technology, Delft, Netherlands/Plaxis B.V., Delft, Netherlands E. Engin

### EXTENDED ABSTRACT. Combined Pile Raft Foundation

EXTENDED ABSTRACT Combined Pile Raft Foundation Rui Diogo Gomes da Silva Supervisor: Prof. Jaime Alberto dos Santos December 2009 1. Introduction The piled raft foundation is an innovative design concept

### Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay

56 Module 4: Lecture 7 on Stress-strain relationship and Shear strength of soils Contents Stress state, Mohr s circle analysis and Pole, Principal stressspace, Stress pathsin p-q space; Mohr-Coulomb failure

### SOIL-STRUCTURE INTERACTION, WAVE PASSAGE EFFECTS AND ASSYMETRY IN NONLINEAR SOIL RESPONSE

SOIL-STRUCTURE INTERACTION, WAVE PASSAGE EFFECTS AND ASSYMETRY IN NONLINEAR SOIL RESPONSE Mihailo D. Trifunac Civil Eng. Department University of Southern California, Los Angeles, CA E-mail: trifunac@usc.edu

### Modified Cam-clay triaxial test simulations

1 Introduction Modified Cam-clay triaxial test simulations This example simulates a series of triaxial tests which can be used to verify that Modified Cam-Clay constitutive model is functioning properly.

### Modelling Progressive Failure with MPM

Modelling Progressive Failure with MPM A. Yerro, E. Alonso & N. Pinyol Department of Geotechnical Engineering and Geosciences, UPC, Barcelona, Spain ABSTRACT: In this work, the progressive failure phenomenon

### Chapter 3 LAMINATED MODEL DERIVATION

17 Chapter 3 LAMINATED MODEL DERIVATION 3.1 Fundamental Poisson Equation The simplest version of the frictionless laminated model was originally introduced in 1961 by Salamon, and more recently explored

### 1.5 STRESS-PATH METHOD OF SETTLEMENT CALCULATION 1.5 STRESS-PATH METHOD OF SETTLEMENT CALCULATION

Module 6 Lecture 40 Evaluation of Soil Settlement - 6 Topics 1.5 STRESS-PATH METHOD OF SETTLEMENT CALCULATION 1.5.1 Definition of Stress Path 1.5. Stress and Strain Path for Consolidated Undrained Undrained

Instructor : Dr. Jehad Hamad Chapter (7) 2017-2016 Soil Properties Physical Properties Mechanical Properties Gradation and Structure Compressibility Soil-Water Relationships Shear Strength Bearing Capacity

### Example-3. Title. Description. Cylindrical Hole in an Infinite Mohr-Coulomb Medium

Example-3 Title Cylindrical Hole in an Infinite Mohr-Coulomb Medium Description The problem concerns the determination of stresses and displacements for the case of a cylindrical hole in an infinite elasto-plastic

### AN IMPORTANT PITFALL OF PSEUDO-STATIC FINITE ELEMENT ANALYSIS

AN IMPORTANT PITFALL OF PSEUDO-STATIC FINITE ELEMENT ANALYSIS S. Kontoe, L. Pelecanos & D.M. Potts ABSTRACT: Finite Element (FE) pseudo-static analysis can provide a good compromise between simplified

### NEW DOWN-HOLE PENETROMETER (DHP-CIGMAT) FOR CONSTRUCTION APPLICATIONS

NEW DOWN-HOLE PENETROMETER (DHP-CIGMAT) FOR CONSTRUCTION APPLICATIONS 1 2 C. Vipulanandan 1, Ph.D., M. ASCE and Omer F. Usluogullari 2 Chairman, Professor, Director of Center for Innovative Grouting Materials

### Static & Dynamic. Analysis of Structures. Edward L.Wilson. University of California, Berkeley. Fourth Edition. Professor Emeritus of Civil Engineering

Static & Dynamic Analysis of Structures A Physical Approach With Emphasis on Earthquake Engineering Edward LWilson Professor Emeritus of Civil Engineering University of California, Berkeley Fourth Edition

### Soil strength. the strength depends on the applied stress. water pressures are required

Soil Strength Soil strength u Soils are essentially frictional materials the strength depends on the applied stress u Strength is controlled by effective stresses water pressures are required u Soil strength

### Numerical and Theoretical Study of Plate Load Test to Define Coefficient of Subgrade Reaction

Journal of Geotechnical and Transportation Engineering Volume 1 Issue 2 Numerical and Theoretical Study of Plate Load Test to Define Coefficient of Subgrade Reaction Naeini and Taherabadi Received 9/28/2015

### MATERIAL MECHANICS, SE2126 COMPUTER LAB 3 VISCOELASTICITY. k a. N t

MATERIAL MECHANICS, SE2126 COMPUTER LAB 3 VISCOELASTICITY N t i Gt () G0 1 i ( 1 e τ = α ) i= 1 k a k b τ PART A RELAXING PLASTIC PAPERCLIP Consider an ordinary paperclip made of plastic, as they more

### Dynamic Analysis of a Reinforced Concrete Structure Using Plasticity and Interface Damage Models

Dynamic Analysis of a Reinforced Concrete Structure Using Plasticity and Interface Damage Models I. Rhee, K.J. Willam, B.P. Shing, University of Colorado at Boulder ABSTRACT: This paper examines the global

### 1D Ground Response Analysis

Lecture 8 - Ground Response Analyses Page 1 1D Ground Response Analysis 1. 2. 3. Dynamic behavior of soils is quite complex and requires models which characterize the important aspects of cyclic behavior,

### Practical methodology for inclusion of uplift and pore pressures in analysis of concrete dams

Practical methodology for inclusion of uplift and pore pressures in analysis of concrete dams Michael McKay 1 and Francisco Lopez 2 1 Dams Engineer, GHD Pty 2 Principal Dams/Structural Engineer, GHD Pty

### PILE-SUPPORTED RAFT FOUNDATION SYSTEM

PILE-SUPPORTED RAFT FOUNDATION SYSTEM Emre Biringen, Bechtel Power Corporation, Frederick, Maryland, USA Mohab Sabry, Bechtel Power Corporation, Frederick, Maryland, USA Over the past decades, there has

### Centrifuge Shaking Table Tests and FEM Analyses of RC Pile Foundation and Underground Structure

Centrifuge Shaking Table s and FEM Analyses of RC Pile Foundation and Underground Structure Kenji Yonezawa Obayashi Corporation, Tokyo, Japan. Takuya Anabuki Obayashi Corporation, Tokyo, Japan. Shunichi

### A Pile Pull Out Test

1 Introduction A Pile Pull Out Test This example simulates pulling a pile out of the ground. It is not a realistic field case, but numerically the simulation makes it possible to verify the behavior of

### Numerical modeling of free field vibrations due to pile driving using a dynamic soil-structure interaction formulation

Numerical modeling of free field vibrations due to pile driving using a dynamic soil-structure interaction formulation H.R. Masoumi, G. Degrande Department of Civil Engineering, K.U.Leuven, Kasteelpark

### MODELING SLAB-COLUMN CONNECTIONS REINFORCED WITH GFRP UNDER LOCALIZED IMPACT

MODELING SLAB-COLUMN CONNECTIONS REINFORCED WITH GFRP UNDER LOCALIZED IMPACT QI ZHANG and AMGAD HUSSEIN Faculty of Engineering, Memorial University of Newfoundland St. John s, Newfoundland, Canada, A1B

### CHAPTER 6: ASSESSMENT OF A COMPREHENSIVE METHOD FOR PREDICTING PERFORMANCE

CHAPTER 6: ASSESSMENT OF A COMPREHENSIVE METHOD FOR PREDICTING PERFORMANCE 6.1 Overview The analytical results presented in Chapter 5 demonstrate the difficulty of predicting the performance of an improved

### Final Exam Solution Dynamics :45 12:15. Problem 1 Bateau

Final Exam Solution Dynamics 2 191157140 31-01-2013 8:45 12:15 Problem 1 Bateau Bateau is a trapeze act by Cirque du Soleil in which artists perform aerial maneuvers on a boat shaped structure. The boat

### Game Physics. Game and Media Technology Master Program - Utrecht University. Dr. Nicolas Pronost

Game and Media Technology Master Program - Utrecht University Dr. Nicolas Pronost Soft body physics Soft bodies In reality, objects are not purely rigid for some it is a good approximation but if you hit

### Harmonized European standards for construction in Egypt

Harmonized European standards for construction in Egypt EN 1998 - Design of structures for earthquake resistance Jean-Armand Calgaro Chairman of CEN/TC250 Organised with the support of the Egyptian Organization

### Chapter (5) Allowable Bearing Capacity and Settlement

Chapter (5) Allowable Bearing Capacity and Settlement Introduction As we discussed previously in Chapter 3, foundations should be designed for both shear failure and allowable settlement. So the allowable

### ALASKA ENERGY AUTHORITY AEA ENGINEERING FEASIBILITY REPORT. Appendix B8. Finite Element Analysis

ALASKA ENERGY AUTHORITY AEA11-022 ENGINEERING FEASIBILITY REPORT Appendix B8 Finite Element Analysis Susitna-Watana Hydroelectric Project Alaska Energy Authority FERC Project No. 14241 December 2014 Seismic

Chapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING ) 5.1 DEFINITION A construction member is subjected to centric (axial) tension or compression if in any cross section the single distinct stress

### Geotechnical Modeling Issues

Nonlinear Analysis of Viaducts and Overpasses Geotechnical Modeling Issues Steve Kramer Pedro Arduino Hyung-Suk Shin University of Washington The Problem Approach Soil Soil Soil Soil Soil Soil Soil Soil

### EVALUATING RADIATION DAMPING OF SHALLOW FOUNDATIONS ON NONLINEAR SOIL MEDIUM FOR SOIL-STRUCTURE INTERACTION ANALYSIS OF BRIDGES

EVALUATING RADIATION DAMPING OF SHALLOW FOUNDATIONS ON NONLINEAR SOIL MEDIUM FOR SOIL-STRUCTURE INTERACTION ANALYSIS OF BRIDGES Abstract Jian Zhang 1 and Yuchuan Tang 2 The paper evaluates the radiation

### Frequency response analysis of soil-structure interaction for concrete gravity dams

Frequency response analysis of soil-structure interaction for concrete gravity dams Anna De Falco 1, Matteo Mori 2 and Giacomo Sevieri 3 1 Dept. of Energy, Systems, Territory and Construction Engineering,

### INVESTIGATION OF SATURATED, SOFT CLAYS UNDER EMBANKMENTS. Zsolt Rémai Budapest University of Technology and Economics Department of Geotechnics

INVESTIGATION OF SATURATED, SOFT CLAYS UNDER EMBANKMENTS PhD thesis Zsolt Rémai Budapest University of Technology and Economics Department of Geotechnics Budapest December, 2012 1. IMPORTANCE OF THE RESEARCH

### Finite Element Modelling with Plastic Hinges

01/02/2016 Marco Donà Finite Element Modelling with Plastic Hinges 1 Plastic hinge approach A plastic hinge represents a concentrated post-yield behaviour in one or more degrees of freedom. Hinges only

### COMPARISON BETWEEN 2D AND 3D ANALYSES OF SEISMIC STABILITY OF DETACHED BLOCKS IN AN ARCH DAM

COMPARISON BETWEEN 2D AND 3D ANALYSES OF SEISMIC STABILITY OF DETACHED BLOCKS IN AN ARCH DAM Sujan MALLA 1 ABSTRACT The seismic safety of the 147 m high Gigerwald arch dam in Switzerland was assessed for

### Destructuration of soft clay during Shield TBM tunnelling and its consequences

Destructuration of soft clay during Shield TBM tunnelling and its consequences Hirokazu Akagi Abstract It is very important to prevent ground settlement associated with shield TBM tunnelling in soft ground

www.novotechsoftware.com The standard penetration test (SPT) is an in-situ dynamic penetration test designed to provide information on the geotechnical engineering properties of soil. The test procedure

### Plane and axisymmetric models in Mentat & MARC. Tutorial with some Background

Plane and axisymmetric models in Mentat & MARC Tutorial with some Background Eindhoven University of Technology Department of Mechanical Engineering Piet J.G. Schreurs Lambèrt C.A. van Breemen March 6,

### SEISMIC ANALYSIS OF AN EMBEDDED RETAINING STRUCTURE IN COARSE-GRAINED SOILS

4 th International Conference on Earthquake Geotechnical Engineering June 25-28, 27 Paper No. 97 SEISMIC ANALYSIS OF AN EMBEDDED RETAINING STRUCTURE IN COARSE-GRAINED SOILS Luigi CALLISTO, Fabio M. SOCCODATO

### NUMERICAL ANALYSIS OF PASSIVE EARTH PRESSURES WITH INTERFACES

III European Conference on Computational Mechanics Solids, Structures and Coupled Problems in Engineering C.A. Mota Soares et.al. (eds.) Lisbon, Portugal, 5-8 June 2006 NUMERICAL ANALYSIS OF PASSIVE EARTH

### DETERMINING THE STRESS PATTERN IN THE HH RAILROAD TIES DUE TO DYNAMIC LOADS 1

PERIODICA POLYTECHNICA SER. CIV. ENG. VOL. 46, NO. 1, PP. 125 148 (2002) DETERMINING THE STRESS PATTERN IN THE HH RAILROAD TIES DUE TO DYNAMIC LOADS 1 Nándor LIEGNER Department of Highway and Railway Engineering

### FLAC3D analysis on soil moving through piles

University of Wollongong Research Online Faculty of Engineering - Papers (Archive) Faculty of Engineering and Information Sciences 211 FLAC3D analysis on soil moving through piles E H. Ghee Griffith University

### Geotechnical Earthquake Engineering

Geotechnical Earthquake Engineering by Dr. Deepankar Choudhury Professor Department of Civil Engineering IIT Bombay, Powai, Mumbai 400 076, India. Email: dc@civil.iitb.ac.in URL: http://www.civil.iitb.ac.in/~dc/

### Numerical Modeling of Direct Shear Tests on Sandy Clay

Numerical Modeling of Direct Shear Tests on Sandy Clay R. Ziaie Moayed, S. Tamassoki, and E. Izadi Abstract Investigation of sandy clay behavior is important since urban development demands mean that sandy

### Structural Dynamics Lecture 4. Outline of Lecture 4. Multi-Degree-of-Freedom Systems. Formulation of Equations of Motions. Undamped Eigenvibrations.

Outline of Multi-Degree-of-Freedom Systems Formulation of Equations of Motions. Newton s 2 nd Law Applied to Free Masses. D Alembert s Principle. Basic Equations of Motion for Forced Vibrations of Linear

### EN Eurocode 7. Section 3 Geotechnical Data Section 6 Spread Foundations. Trevor L.L. Orr Trinity College Dublin Ireland.

EN 1997 1: Sections 3 and 6 Your logo Brussels, 18-20 February 2008 Dissemination of information workshop 1 EN 1997-1 Eurocode 7 Section 3 Geotechnical Data Section 6 Spread Foundations Trevor L.L. Orr

### Foundations of High Rise Buildings

Foundations of High Rise Buildings Prof. Dr.-Ing. Yasser El-Mossallamy Professor of Geotechnical Engineering Ain Shams Univ. Cairo, Egypt c/o Arcadis Consult, Germany y.el-mossallamy@arcadis.de Slide:

### About 75 persons attended the celebration

PLAXIS Nº 9 - JULY 2000 Bulletin of the PLAXIS Users Association (NL) Plaxis bulletin Plaxis B.V. P.O. Box 572 2600 AN Delft The Netherlands E-mail: bulletin@plaxis.nl IN THIS ISSUE: Editorial Column Vermeer

### 6. NON-LINEAR PSEUDO-STATIC ANALYSIS OF ADOBE WALLS

6. NON-LINEAR PSEUDO-STATIC ANALYSIS OF ADOBE WALLS Blondet et al. [25] carried out a cyclic test on an adobe wall to reproduce its seismic response and damage pattern under in-plane loads. The displacement

### Nonlinear Finite Element Modeling of Nano- Indentation Group Members: Shuaifang Zhang, Kangning Su. ME 563: Nonlinear Finite Element Analysis.

ME 563: Nonlinear Finite Element Analysis Spring 2016 Nonlinear Finite Element Modeling of Nano- Indentation Group Members: Shuaifang Zhang, Kangning Su Department of Mechanical and Nuclear Engineering,

### STUDY OF THE BEHAVIOR OF PILE GROUPS IN LIQUEFIED SOILS

STUDY OF THE BEHAVIOR OF PILE GROUPS IN LIQUEFIED SOILS Shin-Tower Wang 1, Luis Vasquez 2, and Lymon C. Reese 3, Honorary Member,, ASCE ABSTRACT : 1&2 President & Project Manager, Ensoft, Inc. Email: ensoft@ensoftinc.com

### GROUND VIBRATION PREDICTION AND ASSESSMENT

GROUND VIBRATION PREDICTION AND ASSESSMENT R.M. Thornely-Taylor Rupert Taylor Ltd 1. INTRODUCTION Vibration is often grouped with noise and regarded as a kindred topic. Noise, after all, begins as vibration,

1 7 SEISMIC LOADS 7.1 Estimation of Seismic Loads 7.1.1 Seismic load and design earthquake motion (1) For ordinary buildings, seismic load is evaluated using the acceleration response spectrum (see Sec.7.2)

### Propagation of Seismic Waves through Liquefied Soils

Propagation of Seismic Waves through Liquefied Soils Mahdi Taiebat a,b,, Boris Jeremić b, Yannis F. Dafalias b,c, Amir M. Kaynia a, Zhao Cheng d a Norwegian Geotechnical Institute, P.O. Box 393 Ullevaal

### Foundation Analysis LATERAL EARTH PRESSURE

Foundation Analysis LATERAL EARTH PRESSURE INTRODUCTION Vertical or near-vertical slopes of soil are supported by retaining walls, cantilever sheet-pile walls, sheet-pile bulkheads, braced cuts, and other

### QUAKE/W ProShake Comparison

1 Introduction QUAKE/W Comparison is a commercially available software product for doing one-dimensional ground response analyses. It was developed and is being maintained under the guidance of Professor

### PROPOSED CHANGE TO THE 2012 BUILDING CODE O. REG. 332/12 AS AMENDED

Ministry of Municipal Affairs PROPOSED CHANGE TO THE 2012 BUILDING CODE O. REG. 332/12 AS AMENDED CHANGE NUMBER: SOURCE: B-04-01-15 Ontario-NBC CODE REFERENCE: Division B / 4.1.8.2. Division B / 4.1.8.4.

### 7. STRESS ANALYSIS AND STRESS PATHS

7-1 7. STRESS ANALYSIS AND STRESS PATHS 7.1 THE MOHR CIRCLE The discussions in Chapters and 5 were largely concerned with vertical stresses. A more detailed examination of soil behaviour requires a knowledge

### FIS Specifications for Flex Poles (Edition May 2008) Original Text: German

FIS Specifications for Flex Poles (Edition May 2008) Original Text: German 1 Field of Application and Basic Information The following FIS specifications for flex poles are intended to ensure that flex

### Lecture 9: Harmonic Loads (Con t)

Lecture 9: Harmonic Loads (Con t) Reading materials: Sections 3.4, 3.5, 3.6 and 3.7 1. Resonance The dynamic load magnification factor (DLF) The peak dynamic magnification occurs near r=1 for small damping

### ANALYSIS OF LATERALLY LOADED FIXED HEADED SINGLE FLOATING PILE IN MULTILAYERED SOIL USING BEF APPROACH

INDIAN GEOTECHNICAL SOCIETY, KOLKATA CHAPTER GEOTECHNICS FOR INFRASTRUCTURE DEVELOPMENT KOLKATA 11 th 12 th March 2016, Kolkata, West Bengal, India ANALYSIS OF LATERALLY LOADED FIXED HEADED SINGLE FLOATING

### Numerical simulation of inclined piles in liquefiable soils

Proc. 20 th NZGS Geotechnical Symposium. Eds. GJ Alexander & CY Chin, Napier Y Wang & R P Orense Department of Civil and Environmental Engineering, University of Auckland, NZ. ywan833@aucklanduni.ac.nz

### Seismic design of bridges

NATIONAL TECHNICAL UNIVERSITY OF ATHENS LABORATORY FOR EARTHQUAKE ENGINEERING Seismic design of bridges Lecture 3 Ioannis N. Psycharis Capacity design Purpose To design structures of ductile behaviour

### NON-LINEAR VISCOELASTIC MODEL OF STRUCTURAL POUNDING

3 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August -6, 004 Paper No. 308 NON-LINEAR VISCOELASTIC MODEL OF STRUCTURAL POUNDING Robert JANKOWSKI SUMMARY Pounding between structures

### Lab Practical - Discontinuum Analysis & Distinct Element Method

Lab Practical - Discontinuum Analysis & Distinct Element Method Part A The Basics The Universal Distinct Element Code (UDEC) is a two-dimensional numerical program based on the distinct element method

### Study on elevated light rail induced vibration attenuation along the surrounding ground

Study on elevated light rail induced vibration attenuation along the surrounding ground Changqing Liu ; Yude Zhou ; Ying Tu 3 ; Weimin Xu 4 Shanghai Academy of Environmental Sciences 508 Qinzhou Rd, 0033

### ANALYSIS OF A VERTICAL SEGMENTAL SHAFT USING 2D & 3D FINITE ELEMENT CODES

International Journal of GEOMATE, Aug, 2017, Vol.13, Issue 36, pp.138-146 Geotec., Const. Mat. & Env., ISSN:2186-2990, Japan, DOI: http://dx.doi.org/10.21660/2017.36.88132 ANALYSIS OF A VERTICAL SEGMENTAL

### Structural System, Machines and Load Cases

Machine-Induced Vibrations Machine-Induced Vibrations In the following example the dynamic excitation of two rotating machines is analyzed. A time history analysis in the add-on module RF-DYNAM Pro - Forced

### Chapter 5. Vibration Analysis. Workbench - Mechanical Introduction ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.

Workbench - Mechanical Introduction 12.0 Chapter 5 Vibration Analysis 5-1 Chapter Overview In this chapter, performing free vibration analyses in Simulation will be covered. In Simulation, performing a

### VORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NON-LINEAR MATERIALS

The 4 th World Conference on Earthquake Engineering October -7, 008, Beijing, China VORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NON-LINEAR MATERIALS K.

### PLEASURE VESSEL VIBRATION AND NOISE FINITE ELEMENT ANALYSIS

PLEASURE VESSEL VIBRATION AND NOISE FINITE ELEMENT ANALYSIS 1 Macchiavello, Sergio *, 2 Tonelli, Angelo 1 D Appolonia S.p.A., Italy, 2 Rina Services S.p.A., Italy KEYWORDS pleasure vessel, vibration analysis,

### EARTHQUAKE-INDUCED SETTLEMENT AS A RESULT OF DENSIFICATION, MEASURED IN LABORATORY TESTS

13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 3291 EARTHQUAKE-INDUCED SETTLEMENT AS A RESULT OF DENSIFICATION, MEASURED IN LABORATORY TESTS Constantine

### Introduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams.

Outline of Continuous Systems. Introduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams. Vibrations of Flexible Strings. Torsional Vibration of Rods. Bernoulli-Euler Beams.

### The Dynamic Response Analysis of Concrete Gravity Dam under the Earthquake

Copyright 2013 Tech Science Press SL, vol.9, no.1, pp.23-36, 2013 The Dynamic Response Analysis of Concrete Gravity Dam under the Earthquake Yang Lu 1, Li Shi-Min 1, Cao Peng 2 and Shen Xin-Pu 1 Abstract:

### Influence of Soil Models on Numerical Simulation of Geotechnical works in Bangkok subsoil

Influence of Soil Models on Numerical Simulation of Geotechnical works in Bangkok subsoil Tanapong Rukdeechuai, Pornkasem Jongpradist, Anucha Wonglert, Theerapong Kaewsri Department of Civil Engineering,

### INELASTIC RESPONSES OF LONG BRIDGES TO ASYNCHRONOUS SEISMIC INPUTS

13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 24 Paper No. 638 INELASTIC RESPONSES OF LONG BRIDGES TO ASYNCHRONOUS SEISMIC INPUTS Jiachen WANG 1, Athol CARR 1, Nigel

### APPENDIX F CORRELATION EQUATIONS. F 1 In-Situ Tests

APPENDIX F 1 APPENDIX F CORRELATION EQUATIONS F 1 In-Situ Tests 1. SPT (1) Sand (Hatanaka and Uchida, 1996), = effective vertical stress = effective friction angle = atmosphere pressure (Shmertmann, 1975)