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1. Input Motion Proper specification of an input motion is an important part of any ground response analysis ProShake allows you to view a variety of potential input motions and select the ones that are most appropriate for the analysis The selection and review of input motions takes place on the Input Motion form The upper part of the Input Motion form requests global information that applies to all of the input motions you select the lower part requests information for each individual input motion Number of Motions ProShake places no limit on the number of input motions that can be specified for a given run the memory capacity of your computer will place a practical limit on the number of motions but it will generally be larger than the number that most users will wish to use Enter the number of input motions you want to use and ProShake will provide that number of tab forms on which you can select and or enter input motion data A ProShake Input Manager C PROSHAKE SHAKE DAT oj x File Input Manager Solution Manager Output Manager Help Maximum Number of Iterations Profle J mputmoton ina approximates nonlinear soil Number of Motions 2 Maximum Number of Iterations 8 behavior by iter ating toward strain i eoi oso Enor Tolerance 5 0 __ compatible soil properties You can Meal Object Motion Object Motion Plots specify the maximum number of
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3. The Other Parameters form offers the opportunity to compute a variety of useful ground motion parameters at the tops of any of the layers selected in Step 17 Highlight the layer you are interested in and then click on the Calculate button to see the numerical values of the parameters This information can be copied in tabular format to the Report Finally the Animation form allows you to view the variation of horizontal displacements with both depth and time for each input motion that an animation was requested for you 11 40 41 42 ProShake User s Manual did this for the single input motion of this example in Step 23 Click on the Prepare Animation button it will take a few moments for ProShake to load and integrate the computed motions at the tops of all layers in the profile When the animation form appears select the slow speed for best resolution Immediately below the animation axes is a plot of the input motion you can use it along with the Current Record Time display to track the progress of the animation Select the desired Start Record Time for this record enter a value of 8 sec to eliminate the first 8 sec of the motion where nothing much is happening Click on the Start button to begin the animation You will view a yellow line that represents the position of an originally vertical plane passing through your soil profile Note the response at the impedance contrast between the soft silty clay and the stiff cl
4. EERC 88 15 Earthquake Engineering Research Center University of California Berkeley Vucetic M and Dobry R 1991 Effect of soil plasticity on cyclic response Journal of Geotechnical Engineering ASCE Vol 117 No 1 pp 89 107 54
5. eksheisisiziehsimoi minns 6a number of material layers including a half te Curve Seed and Idriss 1970 space layer at the bottom of the profile the Dasiping Core Sand Idriss 1990 E memory capacity of your computer may Plot Modulus and Damping Curves introduce a practical upper limit to the hace eee 50 nits gt number of layers but it is likely to be larger Unit Weight 125 0 ect fia ae than the number of layers that you would EE m choose to use Enter the number of layers dl ll EE you want to use and ProShake will provide Essenu _Yiow Profile that number of tab forms on which you can enter soil profile data An individual soil 16 ProShake User s Manual layer may be represented by more than one material layer As an alternative users may find it more efficient to enter material data directly on the Summary Data form Depth to Water Table Enter the depth to the water table if any Use U S or metric units the other will be calculated automatically when you move to the next data field ProShake uses this depth along with the layer thickness and unit weight data to compute effective vertical stresses If left blank ProShake will assume that no groundwater exists in the entire profile ProShake will compute initial porewater pressures as zero above and hydrostatic below the water table Layer Information The main portion of the Soil Profile w
6. the input motion data file will not be changed By changing the time step you will change both the frequency content and the duration but not the amplitude of the input motion This is a rather crude way of modifying the frequency content time step changes of more than about 20 should be considered very carefully Cutoff Frequency The equivalent linear mode of ProShake computes ground response in the frequency domain Briefly it represents an input motion as the sum of a series of sine waves of different amplitudes frequencies and phase angles Because most of the energy in an earthquake motion is concentrated in a range of relatively low frequencies and because high frequency motions have little effect on most civil structures ProShake doesn t require you to spend time on the higher frequencies that contribute little to the total response The cutoff frequency specifies the upper limit of frequencies that ProShake will consider cutoff frequencies of 15 to 20 Hz are usually adequate for most soil profiles The speed of the analysis will increase as the cutoff frequency is decreased but the execution time is generally not long enough to justify low cutoff frequencies Number of Terms in Fourier Series ProShake uses a Fast Fourier Transform FFT to convert the input motion time domain into a Fourier series frequency domain After computing the response in the frequency domain it uses an inverse FFT to transform the solution back to
7. 45 ProShake User s Manual problem described in the Tutorial section of this User s Manual The tutorial problem involved a 50 ft thick layer of soft silty clay overlaying a 50 ft thick layer of stiff clay The thick soft nature of the silty clay layer also produces ground surface motions with relatively low accelerations and long periods Acceleration g The following plot illustrates this response 0 15 0 10 EES SHAKE91 0 05 ProShake 0 00 1e sali hayya N AA Af lial Nas Na fo Cee wal a aa AA Ee b L Wal p Te wy Tr wy Vy Ww 0 05 9 5 20 25 30 0 10 1 Time sec 0 15 Again the differences between the ground surface accelerations produced by ProShake and SHAKE91 are very small even when the time scale is expanded as shown below Acceleration g Acceleration g 0 15 7 O04 eee SHAKE91 ProShake 0 05 A Fa 0 00 I i Any Peel V e N u r y 0 05 7 Time sec 0 10 0 15 0 15 7 00 EE SHAKE91 ProShake 0 05 0 00 SS eee 0 ha 11 2 11 4 11 6 11 8 ee Time sec 0 10 0 15 1 46 ProShake User s Manual Response spectra are also very similar S ar SHAKES TEH as illustrated for structural damping A a O E SHAKE91 20 ratios of 5 and 20 to the right The D an distinguishing feature of the tutorial 3 problem from the ground response standpoint is the presence of the strong o impedance contrast at the boundary 8 between
8. Enter the shear wave velocity if available in ft sec or in m sec the other will be calculated automatically If you enter unit weight and shear wave velocity the corresponding maximum shear modulus will be computed from Gmax P vg Modulus Reduction Curve The modulus reduction curve describes the manner in which the shear modulus varies with shear strain amplitude The curve itself expresses the modulus ratio defined as the secant shear modulus divided by the maximum shear modulus as a function of shear strain amplitude The secant shear modulus used in the ground response calculations is computed as the product of the modulus reduction factor and the maximum shear modulus Because soils exhibit nonlinear stress strain behavior their secant shear moduli decrease with increasing strain level The shape of the modulus reduction curve indicates how nonlinear the material is a linear material would have a horizontal modulus reduction curve the modulus reduction factor would be 1 0 at all strains In general soil nonlinearity increases with decreasing plasticity index A number of investigators have studied the modulus reduction behavior of different soils and proposed standard modulus reduction curves for those soils ProShake provides a list of modulus reduction curves to choose from and also allows you the option of defining your own modulus reduction curve To view the list simply click on the drop down arrow to the right of the data
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10. and specify the characteristics of each individual input motion File Name Open Remove Enter the complete name of the input motion file here or use the Open command button to browse through all Windows 95 directories Description Enter the alphanumeric description of your choice here This description will be attached to all pertinent data and graphics copied to the Report or written to your Data File The length of the description is limited to 128 characters Number of Acceleration Values ProShake uses digitized earthquake records This term indicates the number of acceleration values in the current input file The number of acceleration values in a ProShake earthquake record cannot exceed 16 384 Peak Acceleration The maximum absolute acceleration of the current input file is displayed here You can change this value if you want to scale the accelerations to a different maximum acceleration for your analysis the input motion data file will not be changed By changing the maximum acceleration you will change all acceleration values in the input motion by the same factor The frequency content and duration of the input motion will not be affected by amplitude scaling Time Step 22 ProShake User s Manual The time step that separates the acceleration values in the input motion data file is displayed here You can change this value if you want to change the frequency content or duration of the input motion for your analysis
11. computed using strain compatible modulus and damping values obtained in the Solution Manager for the particular motion being used To plot the Transfer Functions follow these steps 1 Specify the Number of Frequencies default 201 and the Frequency Step default 0 1 Hz for computing the transfer functions Transfer function values will be computed and plotted from 0 Hz to 20 Hz 201 1 0 1 Hz the default values should provide satisfactory resolution in most cases 2 Click a check box in the Include column to specify a transfer function plot 3 Click in the adjacent cell in the Motion column Use the drop down list box to select the motion you want to use The strain compatible modulus and damping values for this motion will be used to compute the transfer function 4 Click in the next cell to the right in the Layer A column Select the Layer number you want to use in the numerator of the transfer function equation 5 In the column labeled Outcrop A select whether to treat Layer A as an outcrop or within profile motion 6 Repeat Steps 4 and 5 for Layer B which will be in the denominator of the transfer function equation Repeat Steps 2 through 6 to define additional transfer functions to be plotted Any of the layers can be defined as an outcrop or within profile for computing transfer functions Then simply click on the Plot button to create the transfer function plots Transfer functions like all complex va
12. file and enter it here 8 Enter the field width The ground motion file will allot a certain number of characters for each acceleration value Note that the field width includes negative signs the decimal point and any blank spaces Determine the field width and enter it here 9 Enter the time interval Each of the acceleration values in the ground motion file will be separated by a certain time interval usually 0 005 0 01 or 0 02 sec The time step is often shown in one of the header lines 13 ProShake User s Manual 10 Select the units of acceleration in the file you are converting Choose from fraction of gravity g cm sec m sec in sec or ft sec Most ground motion files will express accelerations in g s but some use other units Note that 1 gal 1 cm sec 11 After providing all of the required information click on OK ProShake will read your file and write a new file with the same acceleration data expressed in g s arranged in ProShake format Your original file will be unchanged Modulus Damping Curve Editor Utility ProShake approximates the nonlinear inelastic behavior of soils using an iterative equivalent linear approach This approach requires that the variation of secant shear modulus and damping ratio with shear strain be specified This behavior is described by modulus reduction and damping curves A modulus reduction curve illustrates the variation of normalized secant shear modulus secan
13. frequencies and phase angles A relatively simple solution for the response of the soil profile to sine waves of different frequencies in the form of a transfer function is used to obtain the response of the soil deposit to each of the input sine waves The overall response is obtained by summing the individual responses to each of the input sine waves This section describes the basic mathematics of the process for a problem involving a single soil layer illustrates how that problem can be solved using a widely available mathematical programming language and extends the approach to layered systems Single Soil Layer The following paragraphs describe the basis of the analysis used in ProShake and follow the general approach of Kramer 1996 Zs That reference provides substantial background material and a more detailed description of ground response analyses than is presented in this User s Manual To illustrate the basic approach used in ProShake consider a z aft fe uniform soil layer lying on an elastic layer of rock that extends to r j infinite depth as illustrated to the right If the subscripts s and r refer to soil and rock respectively the horizontal displacements due to vertically propagating harmonic s waves in each material can be written as us Zs t AselOltks2s B ell t kszs a uy Zp t A ell ttkren 4 Bei t k zr 2 where is the circular frequency of the harmonic wave and k is the complex wave
14. is released Effective Shear Strain The amplitude of a harmonic sinusoidal shear strain time history that would be equivalent to the time history of shear strain from an actual earthquake record The effective shear strain is equal to the product of the maximum shear strain and the strain ratio Frequency Content the distribution of acceleration amplitudes in the frequency domain The frequency content can be obtained from the shape of the Fourier spectrum of the motion Impedance Ratio the ratio of specific impedances of two adjacent soil layers where the specific impedance is defined as the product of the density and shear wave velocity of a material Input Motion Format ProShake input motion files are formatted in a certain way The two input motion files included in the distribution of ProShake yerba eq and treas eq are in the proper format Input motion files in any other format can be converted to ProShake Input Motion Format by using the Convert Ground Motion File utility Modulus Error the difference between shear modulus values in successive iterations divided by the shear modulus value used in the most recent iteration expressed as a percentage Peak Acceleration the maximum absolute value of acceleration in an acceleration time history Peak Displacement the maximum absolute value of displacement in a displacement time history Peak Shear Strain the maximum absolute value of shear strain in a shear str
15. iterations File Name C XEDUSHAKE TREAS EQ___ Acceleration vs Time _ m i 5 Open Remove J Velocity vs Time here ProShake will continue until it secinun EAE URE SAND SANTA CRUZ WING lt lt lt a escription reaches this limit or until the tolerance i i Husid Piot criterion is satisfied ProShake uses a No of Acceleration Values 2000 __ a f Peak Acceleration g ois Phase Spectrum procedure to adjust the soil properties that Time Step sect Cutoff Frequency Hz I converges more quickly and reliably than a Oa T me __Response Spectrum that used in previous versions Of SHAKE obiect motion Location imaton a For most soil profiles strain compatible Lager P Outerop NoYes Other Parameters properties will be reached in a few iterations During execution the number of iterations is displayed by ProShake s Solution Graphics Error Tolerance As ProShake iterates toward strain compatible modulus and damping values the difference between the modulus and damping values from one iteration to the next becomes smaller and smaller You can specify any error tolerance defined as the maximum percentage change in shear modulus or damping ratio between successive iterations ProShake will iterate toward strain compatible soil properties until the tolerance criterion is satisfied for all layers or until the maximum number of iterations is reached The results of many ground respons
16. the File menu in the Output Manager and open the file tutorial lyr There are many options for viewing the results of your analysis in the Output Manager The primary plot types are organized on a series of six tabs Ground Motion Plots Stress and Strain Plots Response Spectrum Plots Depth Plots Other Parameters and Animation The Ground Motion Plots form allows you to plot time histories and Fourier spectra at the tops of the layers you selected in Step 17 of the tutorial You may plot one or more motions on the same graph by checking the desired boxes Go ahead and create a couple plots of your output Note that these plots can be copied to the Report from the Output Manager just as they could from the Input Manager The Stress and Strain Plots form allows plotting of time histories and spectra of shear stress and shear strain for our example plots should be available at the tops of Layers 2 and 11 The Response Spectrum Plots form allows you to plot any or all of the response spectra that you requested in Step 17 For this example ground surface response spectra with 5 10 and 20 damping were requested select them all and plot them on the same graph then copy the graph to the Report The Depth Plots form can be used to plot the variation of several quantities with depth for one or more input motions Since our analysis used only one input motion check the box for Motion 1 and try plotting some of these quantities with depth
17. Enter the number of curves defining your new model If modulus reduction behavior depends only on strain level in your model you will only need one curve If modulus reduction behavior depends on a second parameter e g plasticity index in the Vucetic Dobry model enter the number of values of that parameter for which modulus reduction data will be entered 6 in the case of the Vucetic Dobry model 14 ProShake User s Manual 6 Enter an alphanumeric description of the second parameter 7 Enter the number of points defining each curve this is equal to the number of strain values at which modulus reduction ratio is to be specified 8 If you specified more than one curve for a model in which modulus reduction behavior depends on another parameter in addition to strain level enter the values of that parameter for which modulus reduction curves are to be entered in each column of the first row of the data grid 9 Enter the desired strain values in the left most column and the corresponding modulus reduction ratio values in the appropriate Modulus columns 10 When the data is entered and you have checked it click OK 11 To add additional curves repeat steps 3 to 10 for each curve 12 Click Save The data you have entered will be saved and be available for subsequent use via the pulldown menu in the Input Manager The pulldown menu will display the model name you entered in Step 4 and if applicable the parameter name you specif
18. Help CAPRO E SHAKE LYR Output C o oC eee Parameter Parameter Unit G LindLin C Lin Log Acceleration Period C g s C Log Lin C Log Log Velocity C Frequency C ft sec 2 Displacement C em sec 2 X 1 03 Y 1 72 Copy to Report Wite Data o Fie Return Upon clicking the Plot button acceleration spectra are plotted as a function of period on arithmetic scales by default However velocity and displacement spectra can be plotted from the plot form Also the abcissa can be changed to frequency and the scales to logarithmic from the plot form All response spectrum plots can be copied to the Report or have their data written to the Data File Depth Plots It is often useful to examine the variation of ground motion amplitudes with depth the Depth Plot form allows ProShake users to do this Parameters that can be plotted as functions of depth include peak acceleration peak velocity peak displacement peak shear stress peak shear strain effective shear strain shear modulus damping ratio and cyclic stress ratio Parameters from multiple input motions can be combined on the same plot using the check boxes in the Include column 28 ProShake User s Manual ta Peak Shear Stress BEE C PROSHAKE SHAKE LYR Output Ground Motion Plots Stress and Strain Plote Response Spectrum Plots Depth Plots Other Parameters p Plot I
19. ProShake User s Manual ProShake Ground Response Analysis Program Version 1 1 User s Manual EduPro Civil Systems Inc Redmond Washington Copyright EduPro Civil Systems Inc All rights reserved ProShake User s Manual Customer License Agreement EDUPRO CIVIL SYSTEMS INC LICENSOR IS WILLING TO LICENSE THE SOFTWARE WITH WHICH THIS LICENSE IS INCLUDED TO YOU ONLY IF YOU ACCEPT ALL OF THE TERMSIN THIS LICENSE AGREEMENT PLEASE READ THE TERMS CAREFULLY BEFORE YOU OPEN THE PACKAGE BECAUSE BY OPENING THE SEALED DISK PACKAGE YOU ARE AGREEING TO BE BOUND BY THE TERMS OF THIS AGREEMENT IF YOU DO NOT AGREE TO THESE TERMS LICENSOR WILL NOT LICENSE THIS SOFTWARE TO YOU AND IN THAT CASE YOU SHOULD RETURN THIS PRODUCT PROMPTLY INCLUDING THE PACKAGING THE UNOPENED DISK PACKAGE AND ALL WRITTEN MATERIALS FOR A FULL REFUND Ownership of the Software 1 The enclosed Licensor software program Software and the accompanying written materials are owned by Licensor and are protected by United States copyright laws by laws of other nations and by intemational treaties Therefore you must treat the software like any other copyrighted material except that you may make one copy of the software solely for backup or archival purposes and transfer the software to a single hard disk provided that you keep the original solely for backup or archival purposes Y ou may not copy the printed materials accompanying the software Grant Of Lic
20. The strain compatible shear modulus and damping ratio remain constant throughout the duration of an earthquake when the strains induced in the soil are small and when they are large Permanent strains cannot be computed and porewater pressures cannot be computed However the equivalent linear approach has been shown to provide reasonable estimates of soil response under many conditions of practical importance 42 ProShake User s Manual Verification As stated earlier in the User s Manual ProShake was written from scratch using the same computational procedure used in the original version of SHAKE Schnabel et al 1972 Though the basic procedures are the same some aspects of their numerical implementation were different As a result verification of the accuracy of ProShake and comparison of its results with the results from previous versions of SHAKE are required Verification Using Analytical Solutions ProShake has been verified against exact analytical solutions for the simple loading cases for which such solutions are available and found to produce accelerations that match the exact solutions perfectly to at least the first six decimal points with acceleration measured in g s Comparison with SHAKE Additional verification of the numerical implementation of ProShake can be obtained by comparing its results with those of previous versions of SHAKE when both are applied to the same problem Because SHAKE91 is the most comm
21. ain time history Peak Shear Stress the maximum absolute value of shear stress in a shear stress time history Peak Velocity the maximum absolute value of velocity in a velocity time history 52 ProShake User s Manual Quiet Zone a portion of an input motion with zero or very small accelerations Because the frequency domain solution of ProShake implies periodicity i e that the input motion repeats itself indefinitely a quiet zone may be required for the computed response to an individual application of the input motion to be distinct Tab Label the label found on the protruding portion of a tab form The tab label shows which of the tab forms is active Only one tab form can be active at a time Trailing Zeroes acceleration values of 0 0 that are appended to the end of an input motion file to bring the total number of acceleration values to an integer power of 2 53 ProShake User s Manual References Dobry R and Vucetic M 1987 Dynamic properties and seismic response of soft clay deposits Proceedings International Symposium on Geotechnical Engineering of Soft Soils Mexico City Vol 2 pp 51 87 Housner G W 1959 Behavior of structures during earthquakes Journal of the Engineering Mechanics Division ASCE Vol 85 No EM14 pp 109 129 Idriss I M and Sun J I 1992 SHAKE91 A computer program for conducting equivalent linear seismic response analyses of horizontally layered s
22. ay The small displacements at the end of the time history result from a slight drift in the input motion Finally take a look at the Report You should see the input data for the analysis summarized in tabular form and any plots you copied to the Report You may print the Report from ProShake and or save it for later reference You have now completed a ProShake analysis To see how easy it is to work with ProShake go back to the Input Manager open tutorial dat and make some changes to your input file As you will see making the changes running the analysis again and viewing the results can all be accomplished very quickly and easily 12 ProShake User s Manual ProShake Utilities ProShake has two utilities that allow users to reformat digitized ground motions to be used with ProShake and to input their own soil models by adding new modulus reduction and damping curves Both utilities save new data in a form recognizable to ProShake for future analyses Convert Ground Motion File Digitized earthquake ground motions are available from many different sources and the formats in which they are provided by those sources are often different ProShake like any other ground response analysis program expects to see the ground motion values in a particular format To allow the user to specify any ground motion as a ProShake input motion ProShake includes a utility for converting and saving ground motions in the format required by ProShak
23. ce the cursor anywhere on the plot and click the right mouse button This will produce a Graph Control dialog with tabs labeled Style Data Titles Axis Fonts Markers Background and System These tabs allow virtually any characteristic of the plot to be modified as the user desires The forms on which all ProShake plots are displayed also contain two buttons one titled Copy to Report and the other titled Write Data to File The first copies the plot and pastes it into the ProShake Report The copy that goes to the report is formatted with black lines and axes on a white background even though the plot displayed on the screen is formatted differently Users may also want to save some data e g ground motions or response spectra for subsequent use or additional processing ProShake allows you to write data to an output file The data is written sequentially and labeled in the same manner as in the report Many of the ProShake plots have a Crosshair feature This feature simply allows the user to see the numerical values of the parameters that are being plotted When the cursor is moved to the plot area it changes from an arrow to crosshairs and the values of the parameters at the locations of the crosshairs are displayed 34 ProShake User s Manual ProShake uses a frequency domain approach to solve the ground response problem In simple terms the input motion is represented as the sum of a series of sine waves of different amplitudes
24. d the equivalent damping ratio is equal to the damping ratio that would be computed based on the area within the hysteresis loop the secant shear modulus and the maximum shear strain The relationship between this equivalent damping ratio and shear strain is characterized by means of a damping curve The nature of this curve which has an ordinate of damping ratio and an abscissa of log shear strain has been well established for many soils ProShake has a library of damping 41 ProShake User s Manual curves that can be selected in the Input Manager In an equivalent linear analysis the first iteration is performed using shear modulus and damping ratios that correspond to some initially estimated level of shear strain In ProShake the first iteration is based on an assumed shear strain of 0 001 Following the first iteration the effective shear strain defined as Y eff Ry Y max where Ry is a strain reduction factor often taken as TE Gl Y 10 is computed The shear modulus and damping ratio corresponding to Yey is then used for the next iteration This process is repeated until the computed effective strain does not change much from one iteration to the next At this point the equivalent linear process is said to have converged While the equivalent linear approach allows the most important effects of nonlinear inelastic soil behavior to be approximated it must be emphasized that it remains a linear method of analysis
25. d For this example enter the shear wave velocity of Layer 1 150 m sec Note that striking the Enter key after entering the shear wave velocity causes ProShake to compute the maximum shear modulus corresponding to the shear wave velocity and unit weight of the material Now Layer 1 has been defined and it is time to move on to the other layers Though the properties of the other layers can be defined in the same way it will be faster for our example to enter subsequent data using the Summary Data tab Click on that tab just to the left of the tab for Layer 1 You will then see the Layer 1 input data displayed in a compact tabular form For our example the silty clay is actually 50 ft 14 15 16 17 18 ProShake User s Manual thick and we will represent it in our ProShake analysis by ten 5 ft thick layers Rather than type all of this data in 10 times we will use the drag and drop feature of the Summary Data form To do this put the cursor anywhere within the area that defines Layer 1 on the Summary Data form Press and hold the left mouse button then move the cursor down to the area that defines Layer 2 Release the mouse button and you will see that all of the data from Layer 1 has been assigned to Layer 2 Now repeat this process to define the properties of Layers 3 10 For our example the silty clay layer is underlain by 50 ft of very stiff clay which we will represent using five 10 ft thick layers To enter the data
26. d as an outcrop motion Animation 23 ProShake User s Manual ProShake s animation feature needs to be selected individually for individual input motions When you select the animation feature ProShake will automatically compute acceleration time histories at the tops of all layers These accelerograms are then double integrated in the Output Manager to obtain the animated displacements Object Motion Plots It is often helpful to examine the characteristics of potential input motions graphically before using them ProShake allows you to look at your input motions in a variety of ways Many of these graphs include a crosshair function which allows you to see the numerical value of a particular point on the graph Acceleration vs Time Select for a graph of acceleration vs time The graph can be copied to the Report and or the data written to the Data File After viewing click on Return to go back to the Input Motion form Velocity vs Time Select for a graph of velocity vs time The graph can be copied to the Report and or the data written to the Data File After viewing click on Return to get back to the Input Motion form Displacement vs Time Select for a graph of displacement vs time The graph can be copied to the Report and or the data written to the Data File After viewing click on Return to get back to the Input Motion form Husid Plot A Husid plot shows how the energy of the ground motion is distributed in time Mathematical
27. e To use the Convert Ground Motion File utility follow these steps 1 Select Convert Ground Motion File from the Utilities menu 2 An Open File Dialog Box with the title Earthquake File Name will appear on the screen Select or enter the name of the ground motion file you wish to convert to ProShake format 3 A Convert Ground Motion File form will then appear on the screen The upper part of the box will display the first five lines of the ground motion file you plan to convert Below that display is a series of text boxes that allow you to specify the format of the file 4 Specify the name of the output file for the ProShake formatted file you are creating You can use any filename you wish but ProShake will look first for files with the eq extension 5 Enter the number of header lines This is the total number of lines at the top of the file before the actual ground motion data The header lines often contain alphanumeric descriptions and or numerical information about the motion number of data points time step maximum value etc 6 Enter the number of values the number of data points in the ground motion file This information is often shown in the header lines 7 Enter the number of values per line Ground motion data files are written in many different formats but usually consist of 6 8 acceleration values written on each line Determine how many individual acceleration values are on each line of your ground motion
28. e the Vucetic Dobry curve requires that you specity the plasticity index the required data boxes will appear to the right To select a damping curve from the list just click on it See Modulus Damping Curve Editor Utility section to define your own damping curve ProShake offers the following damping curve options Vucetic Dobry Constant Sun Golesorkhi and Seed Rock Ishibashi Zhang Custom Seed Idriss A more detailed description of the models may be found in the subsequent section titled Built In Soil Models Plot Modulus Reduction and Damping Curves ProShake allows you to view the modulus reduction and damping curves graphically These graphs also feature Copy to Report and Write Data to File capabilities Summary Data The Summary Data form allows the SSUES SSitsiSSeay oy x i File Input Manager Solution Manager Output Manager Help soil profile data to be entered and or di d b 1 f Profile ___InputMotion L Repot edite in a tabular format le Title Example 150 ft layer Experienced ProShake users may O CO wa o of Layers 17 epth to Water Table find this format more efficient for Beotio aaa a n Summary Data 1 2 3 4 516 7 8 39110 11 12 13 14 15 16 17 data entry The Summary Data form has a drag and drop feature that allows all of the 2 Pas y aa eee characteristics of one layer to be Ps H Sy Se assigned to another layer The drag C A and dro
29. e ProShake animation can be played at three speeds fast real time and slow and can be started at any time during the record Due to the speed limit of the Visual Basic graphics routine that displays the animation the fast and real time speeds are accomplished by skipping different numbers of time steps hence animations of some records may appear to jump a bit at those speeds Viewing the animation at the slow speed setting will provide a smoother view of the displacement profile For the example shown above selecting a starting time of about 8 sec would allow the most interesting part of the animation to be viewed in a reasonable amount of time when the slow speed is selected Transfer Function Plots A transfer function describes the relationship between two motions in the frequency domain Consider two motions A and B with Fourier Series A f and B f respectively The motions can be related by A HP BO where H f is a transfer function Therefore the transfer function can be written as the ratio H f APBA When damping is present transfer functions are complex valued 30 ProShake User s Manual ProShake allows plotting of transfer functions between any two layers for any of the motions used in the analysis from the Transfer Function form in Output Manager A maximum of six different transfer functions can be computed and plotted at one time using the check boxes in the Include column Transfer functions are
30. e analyses do not change much at tolerance levels below about 5 and ProShake will use this as a default value During execution the variation of modulus and damping error with depth is illustrated by ProShake s Solution Graphics 21 ProShake User s Manual Strain Ratio The strain ratio is the ratio of effective shear strain to maximum shear strain in each layer ProShake takes transient input motions and computes transient output motions The computed shear strain is an important output parameter because of the strain dependence of the shear modulus and damping ratio The process of iteration toward strain compatible modulus and damping values requires comparison of the strains computed in each iteration of ProShake with the strains on which the modulus and damping values are based Because equivalent linear modulus and damping characteristics are based on laboratory tests with uniform harmonic loading the transient shear strain computed by ProShake must be converted to an effective shear strain for this comparison Historically the strain ratio has often been taken as 0 65 but can better be selected as M 1 10 where M is the magnitude of the earthquake that produced the input motion Object Motion An object motion is an input motion read from a data file and assigned to a particular layer boundary in the soil profile ProShake computes the response at other points in the soil profile to the object motion In this section you will select
31. e displayed in the Object Motion box the peak acceleration time step and cutoff frequency can be changed if desired Various plots and common ground motion parameters for the object motion can be obtained by clicking on the buttons at the right side of this form you should spend a little time playing with these Assign the object motion to the top of bedrock by entering 16 in the Layer field within the Object Motion Location box Specify this motion as an outcrop motion by checking the appropriate box Select Yes in the Animation box This will instruct ProShake to compute the response at the locations necessary to produce an animated view of ground response that can be viewed in the Output Manager The soil profile and input motion have now been completely characterized Save the input data file with the name tutorial dat Documentation of Input 25 26 Click on the large Report button on the main Input Manager form This will open a dedicated word processor with a template that shows all of the input data in tabular form The report can be printed directly from ProShake or saved in Rich Text Format for subsequent editing using a more powerful word processor Graphics can also be copied to the report Go back to the Input Motion form and plot the time history of acceleration of the input motion Click the button labeled Copy to Report and then go back to the Report You should see that the input motion has been copied to
32. e plasticity index you enter Note that ProShake initially sets the damping model as identical to the modulus reduction model by default If you want to change the damping model you may do so by selecting a different model in the same manner used to select the modulus reduction model Check your modulus reduction and damping curves by clicking on the button labeled Plot Modulus and Damping Curves This will show the curves you specified in yellow and the curves of the Vucetic Dobry model in green Note that the two left most green curves represent plasticity indices of 0 and 15 respectively You should see that the yellow PI 10 curve is in the appropriate position relative to the PI 0 and PI 15 curves Place the cursor anywhere on the plot and click the right mouse button The forms that pop up allow you to change the characteristics of the plot This feature is available for all of the plots that ProShake generates Now return to the Soil Profile form and move the cursor to either of the Thickness fields again you can enter the thickness in ft or in m whichever is more convenient For this example enter a thickness of 5 ft for Layer 1 Enter the unit weight 100 pcf for Layer 1 Now you need to specify the low strain stiffness of Layer 1 This can be done either by entering the maximum shear modulus Gmax or by entering the shear wave velocity Using whatever units are most convenient enter one or the other in the appropriate fiel
33. e the program is executing the Solution Manager presents a graphical display ProShake User s Manual that allows the user to track the progress of the analysis Upon completion of the analysis the Solution Manager saves the results in a file with a lyr extension Output Manager The Output Manager allows the user to generate a wide range of plots of the results of the analysis It requires that the user specify a valid output data file with the lyr extension and then provides a number of forms for plotting time histories spectra variations of parameters with depth and for computation of scalar parameters The Output Manager also allows the user to view an animation of the horizontal displacements throughout the soil profile many users find this feature very helpful for developing an intuitive understanding of the response of the soil profile All plots generated in the Output Manager can be copied to the Report Report The Report produced by a word processor that is built into ProShake The Report allows the user to keep a record of each analysis All input data is automatically written to the Report and updated when the Report is accessed All plots generated in the Input Manager and Output Manager can be copied to the Report and saved in a format that can be read by other more powerful word processors Many users find the Report useful for internal documentation of their analyses and for preparation of project reports for their client
34. each of the frequencies in the Fourier series The abscissas of the second third and fourth plots are frequency in Hz The third plot shows the modulus the square root of the sum of the squares of the real and imaginary parts of the transfer function The transfer function is clearly seen to have a series of local peaks that illustrate the nature of amplification that will take place at the natural frequencies of the soil layer note that the greatest amplification will take place at the lowest natural frequency where the transfer function reaches its global maximum The fourth plot shows the Fourier amplitude spectrum of the output ground surface motion which is numerically equal to the product of the input motion second plot and the transfer function third plot The origin of this spectrum is clearly seen by comparing the second third and fourth plots the peaks in the fourth plot the output motion are related to the peaks in the second plot the input motion and the third plot the transfer function Finally the last plot shows the output ground surface motion in the time domain as obtained by taking the inverse Fourier transform of the output motion in the frequency domain Multiple Soil Layers The basic approach described in the preceding sections is also used to analyze layered soil deposits in ProShake the only difference is that the transfer function is different for a layered soil deposit The transfer function for a layer
35. ed soil deposit must account for the transmission and reflection of waves at boundaries between adjacent layers much as those factors were accounted for at the soil rock boundary in the previous section 39 ProShake User s Manual Consider the soil deposit shown to the right Within a given layer say layer j the horizontal t2 h2 G 2 displacements will be given by ie Da R ho Go a rj uj zj t 4 je i Bje i2 elt 11 Ze f hei Gel j 1 j 1 At the boundary between layer j and layer j 1 compatibility of displacements requires that p y P q ZN hN Gy Xn TN 7N 1 GN 1 yay N 1 AEB a Ae NEB e N 12 Continuity of shear stresses requires that y q G k uss fae ikh ikh Aj By p Aje 7 Bie its 13 G j k j 1 Note that Equations 12 and 13 are analogous to Equations 7 and 8 respectively Defining aj amplitudes for layer j 1 can be obtained from the amplitudes of layer j by solving Equations 12 and 13 as the complex impedance ratio at the boundary between layers j and j 1 the wave 1 y 1 oi Ajaa zAjlitat ei t B 1 03 e i 14a 1 oe 1 i Bjsi zAjll ajelkihi B 1405 e tins 14b At the ground surface zj 0 the requirement that the shear stress must be zero means that A B Applying Equations 14 recursively for j 1 2 3 N the coefficients Aj and B j 41 can be related to A and B by A j 1 4 j 1 Ay 15a B j41 bj 1 By 15b where the functions aj and b represent
36. ee managers an Input Manager a Solution Manager and an Output Manager and a Report In the normal sequence of operations the user will move from the Input Manager to the Solution Manager and then on to the Output Manager as indicated graphically below The Report can be accessed from both the Input Manager and the Output Manager Input Solution Output Manager Manager Manager The program structure is designed to allow complete flexibility For example users may bypass the normal sequence to go directly to the Output Manager to examine the results of previous analyses The basic functions of the three managers and the Report are described below Input Manager The Input Manager allows all input data to be entered checked and saved prior to program execution The required input data consists of soil profile data and input motion data The Input Manager provides a series of forms on which the required data can be entered and on which the desired output can be specified The Input Manager allows input data to be viewed graphically a valuable aid in checking for data entry errors All input data and plots generated in the Input Manager can be copied to the Report The input data is saved in a file with a dat extension Solution Manager The Solution Manager performs the actual ground response analysis It requires that the user specify a valid input data file with the dat extension and then performs the required computations Whil
37. ense 2 Licensor grants to you the right to use one copy of the Software on a single computer Y ou may load one copy into permanent memory of one computer and may use that copy or the enclosed diskettes only on that same computer Use by several users at more than one terminal accessing a single copy of this software is not authorized You may not transfer this program between computers across a network For a single user computer or stand alone workstation this software is considered in use when a portion or all of the software is resident in memory resident in virtual memory or stored whether on hard disk or other device You may not install the software on a network 3 This license is valid only for use within the United States of America and its territories Restrictions on Use and Transfer 4 You may not copy the Software except that 1 you may make one copy of the Software solely for backup or archival purposes and 2 you may transfer the Software to a single hard disk provided you keep the original solely for backup or archival purposes Y ou may not copy the written materials 5 You may permanently transfer the Software and accompanying written materials including the most recent update and all prior versions if you retain no copies and the transferee agrees to be bound by the terms of this Agreement Such a transfer terminates your license Y ou may not rent or lease the Software or otherwise transfer or assign the right to use the
38. epth our example shows significant impedance product of shear wave velocity and density contrasts at the boundaries between the silty clay and the stiff clay at the bottom of Layer 10 and between the stiff clay and bedrock bottom of Layer 15 As we will see these impedance contrasts will have a strong influence on the seismic response of our soil profile The locations at which output is to be computed are indicated by green ovals you should see these at the tops of Layers 1 2 and 11 Specification of Input Motion 19 Now the input motion must be specified Click on the large Input Motion button on the main Input Manager form This will bring up a form that allows you to select an input motion define its characteristics view it graphically and compute various ground motion parameters associated with the motion 20 21 22 23 24 ProShake User s Manual Enter 1 for the number of motions ProShake allows you to analyze a soil profile using many different input motions in an individual run For this example leave the strain ratio maximum number of iterations and error tolerance at their default values Click the Open button on the tab form for Motion 1 From the Open File menu that appears select the file named yerba eq This file contains a strong motion record obtained at a rock outcrop on Yerba Buena Island in San Francisco Bay during the 1989 Loma Prieta earthquake The characteristics of the record will b
39. er open the Rich Text Format file using the Windows based word processor of your choice The report feature allows you to easily paste data and graphics into the document of your choice One of the main features of the A ProShake Input Manager C PROSHAKE SHAKE DAT ioj x A i Eile Input Menager Solution Manager Output Manager Help a ae a Mang ee Report summary As you enter input data from the Soil Profile and Input Fle Edt Fomst Update Motion forms in the Input a aie Manager the data is stored in arrays that are linked to the report oo scare par EduShake Report Input motion and output location hoi proie data are also stored in linked pote vane examie 150 ayer arrays By selecting Update menu pumte taves 17 from the ProShake report the soil cme 555r May en ey usec MME CNS Dampnacuws py profile input motion and output location data will be displayed in a compact table in the report This feature will allow you to keep a Page iA line 1 Col 1 written record of each analysis you perform of course you can use the word processor to add comments of your own to the report ProShake Report SHAKE HED H EA mE Sand 5 00 125 00 3 881 99 1 000 00 Sand Seed and Idriss Sand Idriss 1990 1 2 Sand 5 00 125 00 3 144 41 900 00 Sand Seed and Idriss Sand Idriss 1990 3 Sand 10 00 125 00 3 194 41 900 00 Sand Seed and Idriss Sand Idriss 1990 4 Sand 10 00 125 00 3 503 49 950 00 Sand Seed a
40. er s Manual The easiest way to learn the basics of ProShake s organization and operation is to complete the tutorial exercise detailed in this section The tutorial will take you through nearly all of ProShake s functions it should take you about 20 minutes to complete The first step in the tutorial exercise is to start the ProShake program Click on the Windows 95 Start button move to Programs to ProShake and then click on the ProShake icon to start the program After it has started you can work your way through the tutorial The first screen ProShake displays shows the ProShake symbol and six menus from left to right Input Manager Solution Manager Output Manager Utilities Help and Exit Let s look at the last three first ProShake includes two utilities One allows you to add new modulus reduction and damping curves or to modify existing curves These can be useful when the library of built in modulus reduction and damping curves are not appropriate for one or more of the soil types you need to analyze The other allows you to convert digitized earthquake records to ProShake format Use of these utilities is described later in the User s Manual ProShake has an extensive help system that operates like most conventional Windows help systems and can be accessed in two ways First clicking on the Help menu will allow you to choose between working your way through the contents of the ProShake help system and searching for the s
41. f the potential effects of the ground motion on different structures For object motion response spectra ProShake assumes 5 structural damping Crosshairs ProShake screen graphs include a crosshair feature that allows you to identify the coordinates of any point on the graph By moving the cursor onto the graph the arrow turns into a set of crosshairs The coordinates of the center of the crosshairs is given in the Crosshair Position box The x and y coordinates are those on the horizontal and vertical axes of the graph respectively and the units are the same as those of the graph Other Parameters ProShake will allow you to compute other characteristics of an input motion Clicking on this button allows you to compute any of the following ground motion parameters Peak Acceleration Response Spectrum Intensity Peak Velocity Predominant Period Peak Displacement Bracketed Duration RMS Acceleration Trifunac Duration Arias Intensity 25 ProShake User s Manual Solution Manager The solution manager is used to execute the equivalent linear analysis of ProShake The user must select a valid ProShake data file for execution The solution manager will save the selected output in a file with a lyr filename extension e g PSRUN lyr upon execution of the data file PSRUN dat a ose Ge The solution manager will display solution A Ext View State Window Help graphics during execution of the equivalent linear analysis The solution g
42. field If the modulus curve you select requires additional data for example the Vucetic Dobry curve requires that you specify the plasticity index the required data fields will appear to the right To select a modulus reduction curve from the menu just click on it See Modulus Damping Curve Editor Utility section to define your own modulus reduction curve ProShake offers the following modulus reduction curve options Vucetic Dobry Gravel Sun Golesorkhi and Seed Linear Ishibashi Zhang Rock Seed Idriss Custom A more detailed description of the models may be found in the subsequent section titled Built In Soil Models Damping Curve The damping curve describes the manner in which the damping ratio varies with shear strain amplitude Because soils exhibit nonlinear inelastic stress strain behavior their equivalent damping ratios increase with increasing strain level Different types of soil exhibit different damping characteristics In general soil damping increases with decreasing plasticity index 18 ProShake User s Manual A number of investigators have studied the damping behavior of different soils and proposed standard damping curves for those soils ProShake provides a list of damping curves to choose from and also allows you the option of defining your own damping curve To view the menu simply click on the drop down arrow to the right of the data field If the damping curve you select requires additional data for exampl
43. for Layer 11 first copy the properties of Layer 10 to Layer 11 by dragging and dropping Now change the thickness of Layer 11 from 5 ft to 10 ft click on the thickness cell for Layer 11 and type 10 followed by the Tab key Using the same procedure change the material name to Stiff Clay the unit weight to 120 pcf Gma to 1 800 ksf and the modulus and damping parameters to 20 indicating PI 20 Now use the drag and drop feature to copy the properties of Layer 11 to Layers 12 through 15 Finally the properties of the half space bedrock must be specified Working either on the Summary Data form or on the tab for Layer 16 enter the input properties for bedrock with a unit weight of 150 pcf and shear wave velocity of 2500 ft sec Assign the Rock modulus reduction and damping curves to Layer 16 Now we must specify what information is to be computed during the ground response analysis Go to the tab for Layer 1 and click on the Select Output button On the form that appears check the boxes for acceleration and velocity Also check the box for acceleration response spectrum and enter damping ratios of 5 10 and 20 Repeat this process for Layers 2 and 11 but now requesting plots of shear strain and shear stress for those layers Now that all of the layers are defined check for obvious errors such as a misplaced decimal point by clicking the View Profile button The profile shows the variation of unit weight and shear wave velocity with d
44. ied in Step 6 ProShake Help ProShake has extensive help capabilities The ProShake help system follows standard Windows help file protocol Each screen that ProShake displays provides access to the Help system through a pull down menu Also context sensitive help is available by clicking on the item for which more information is desired then pressing the F1 key There are two options for navigating through the Help system The first is initiated by selecting Contents from the Help menu This selection will allow you to explore the structure of ProShake by working your way through the Input Manager Solution Manager or Output Manager Each selection takes you through the various managers and has explanations for each item on each form that ProShake displays The second option for using the Help system is through the use of the index activated by selecting Search for Help on from the Help menu The index is particularly helpful if you know what you re looking for either scroll down through the alphabetical list of help topics or begin typing the name of the item you are looking for When you have found the item you want either double click on it or highlight it and click on Display 15 ProShake User s Manual The ProShake Interface The ProShake interface is designed to be intuitive efficient and easy to use As previously described ProShake is organized into three main components the Input Manager the Solution Manager and
45. igh level functions that allow many complicated calculations and graphics commands to be processed in a single line of text The MATLAB program is well commented and should be relatively easy to follow 37 ProShake User s Manual A MATLAB script for computing the seismic response of a uniform damped soil layer on elastic bedrock Input data corresponds to Example 7 3 in Kramer S L 1996 Geotechnical Earthquake Engineering load gle dat n length gle for j 2 n 1 a j gle j 1 981 end a 1 0 0 dt 0 02 df 1 n dt t 0 0 dt n dt f 0 0 df n df Prentice Hall 653 pp soil layer thickness soil shear wave velocity rock shear wave velocity soil unit weight rock unit weight soil damping ratio rock damping ratio load input motion shift and convert input motion to g s time step frequency increment set up time vector set up frequency vector afft fft a n absfft abs afft for j 1 n 2 1 b j 2 absfft j f j 5 end alpha_z rho_s vss 1 i xs rho_r vsr 1 i xr complex impedance ratio h 1 1 0 for j 2 n 24 1 ksH j 2 pi f j height vsst xs i vss h j 1 cos ksH j i alpha_z sin ksH j h n 3 4 conj h 4 end for j 1 n 2 1 habs j abs h j end subplot 5 1 1 plot t a subplot 5 1 2 plot ff b subplot 5 1 3 plot ff habs for j 1 n 1 acc j afft j h 4 set up single sided FAS wave number x thickness left half of tran
46. imum absolute value of displacement The peak displacement provides a useful measure of the strength of the lower frequency components of a ground motion Predominant Period The predominant period is the period corresponding to the maximum value of the Fourier spectrum Because Fourier spectra are typically quite jagged the period corresponding to the highest peak in a raw spectrum may not correspond well to the strongest part of the motion For that reason some users may want to obtain predominant periods from smoothed spectra The cross hair feature can be used to estimate predominant period from ProShake Fourier spectrum plots Response Spectrum Intensity The response spectrum intensity Housner 1959 is defined as 25 SI E PSV E T aT 0 1 48 ProShake User s Manual i e the area under the pseudo velocity response spectrum between periods of 0 1 second and 2 5 seconds In ProShake the response spectrum intensity is computed for a structural damping ratio of 5 It captures important aspects of the amplitude and frequency content in the range of primary importance for structures in a single parameter RMS Acceleration The RMS acceleration is a single parameter that includes the effects of the amplitude and frequency content of a strong motion record 1 Ta agus a t dt Td 0 where 7 is the duration of the motion Because the integral is not strongly influenced by large high frequency accelerations which occur o
47. indow contains a series of tabbed forms that allow you to enter material property data for each material layer The active material layer form is indicated by the tab label Material Name Enter the alphanumeric description of your choice or leave it blank The material name will be stored in the Analysis Summary in the Report The length of the description is limited to 20 characters Thickness Enter the layer thickness in feet or in meters the other will be calculated automatically Because ProShake computes ground motions at layer boundaries you ll want to select layer thicknesses to provide a layer boundary at each depth at which ground motions are to be computed This may require specification of adjacent layers with identical properties Unit Weight Enter the unit weight in pef or in KN m the other will be calculated automatically Moist unit weights should be used for layers above the water table Because porewater moves with the soil during earthquake shaking saturated unit weights should be used below the water table Maximum Shear Modulus Enter the maximum shear modulus if available either in ksf or in MPa the other will be calculated automatically If you enter unit weight and maximum shear modulus the corresponding shear wave velocity will be computed from where Gmax is maximum shear modulus p is density y is unit weight and g is the acceleration of gravity 17 ProShake User s Manual Shear Wave Velocity
48. indows graphical user interface that both simplifies and speeds the analysis and interpretation of seismic ground response If you have used EduShake you will find that ProShake is virtually identical except that the restrictions that prevent EduShake from being used for general problems are removed If you are an experienced user of SHAKE or SHAKE85 or SHAKE91 you will find that ProShake allows you to input and check data faster and more easily perform analyses more quickly and interpret your results much more easily and efficiently than previous versions of SHAKE If you are new to ground response analysis you will find the intuitive interface of ProShake easy to learn and use Background ProShake evolved from an attempt to provide a user friendly interface to SHAKE for geotechnical earthquake engineering students Many current students have only been exposed to C or other programming languages and are not familiar with FORTRAN and its formatting conventions When first using SHAKE therefore they often encounter difficulties in preparing their input getting the right number in the right column and reformatting their output to put it in a form that spreadsheets or graphics programs can recognize As a result many students spend more time worrying about input and output than they do learning about ground response Initially a relatively simple system consisting of a front end preprocessor and back end postprocessor for SHAKE91 wa
49. ion ProShake applies the cutoff frequency before any required scaling in this way the accelerations that are actually used as input in the analysis are equal to the desired accelerations The 43 ProShake User s Manual difference between these approaches is small for reasonably high cutoff frequencies but the approach taken in ProShake is considered to be more appropriate The relative performance of ProShake and SHAKE91 can be illustrated using the example problem from the original SHAKE User s Manual Schnabel et al 1972 This problem for which the input file is contained in the file shake dat involves the response of a 150 ft thick soil deposit Analyzing the deposit using both ProShake and SHAKE91 produces the time histories of ground surface acceleration shown below 0 25 0 20 0 15 0 10 0 05 0 00 tafea ae 0 05 Acceleration g 0 10 0 15 0 20 0 25 1 RAEE SHAKE91 ProShake Time sec The differences between the ground surface accelerations produced by ProShake and SHAKE91 are very small To make these differences more apparent portions of the time histories are expanded in the two plots shown below 0 25 0 20 0 15 0 10 0 05 0 00 Brua SHAKE91 ProShake APS A Makaa 0 05 iy Acceleration g 0 10 0 15 0 20 0 25 l Ji eae 44 0 25 0 20 0 15 0 10 0 05 0 00 ProShake User s Ma
50. ion and damping curves for different ranges of plasticity index Separate curves for 5 lt PI lt 10 10 lt PI lt 20 20 lt PI lt 40 40 lt PI lt 80 and PI gt 80 were developed ProShake will ask for the plasticity index of the soil and use it to assign the proper curve i e it does not interpolate Ishibashi Zhang Modulus reduction and damping characteristics particularly for low plasticity soils are also influenced by effective confining pressure Ishibashi and Zhang 1993 proposed expressions for shear modulus and damping ratio that accounted for plasticity index and effective confining pressure ProShake will compute the effective confining pressure but you must provide the plasticity index In calculating the effective confining pressure an at rest earth pressure coefficient Ko of 0 5 is assumed It should be noted that the actual Ishibashi and Zhang equations predict G Gmax Values slightly greater than 1 over a range of low strains ProShake sets G Gmax 1 0 for these values ProShake does not modify the damping curves however for the effects of this limiting value See also Ishibashi 1992 Seed Idriss Sand Seed and Idriss 1970 developed the first widely used modulus reduction and damping curves for sand Their curves showed a range of modulus reduction behavior ProShake allows you to select the average of that range or the upper or lower bounds Gravel Seed at al 1984 developed modulus reduction and dam
51. iven by 2 ranio F Obviously the transfer function is a complex function It can be rewritten using Euler s Law as 1 cosk H ia sink H Flo 10 Solution of Single Layer Problem Because the transfer function is defined as the ratio of the soil surface amplitude to the rock outcrop amplitude the soil surface amplitude can be obtained as the product of the rock outcrop amplitude and the transfer function Therefore the response of the soil layer to a periodic input motion can be obtained by the following steps 1 Express the input rock outcrop motion in the frequency domain as a Fourier series as the sum of a series of sine waves of different amplitudes frequencies and phase angles For an earthquake motion this Fourier series will have both real and imaginary parts 2 Define the transfer function Equation 10 The transfer function will have both real and imaginary parts 3 Compute the Fourier series of the output ground surface motion as the product of the Fourier series of the input bedrock motion and the transfer function This Fourier series will also have both real and imaginary parts 4 Express the output motion in the time domain by means of an inverse Fourier transform These steps are coded into a program using the mathematical processing program MATLAB in the box located below The syntax of a MATLAB program is similar to common languages such as FORTRAN and BASIC but MATLAB contains h
52. lued functions have real and imaginary part The transfer function can be expressed in terms of its real and imaginary parts as H f Re H f i Im H f where Re H f and Im H f are the real and imaginary parts of H f respectively and i 1 ProShake allows the transfer function to be plotted in four different ways Amplitude shows the ratios of the amplitudes of the motions at different frequencies Numerically given by the square root of the sum of the squares of the real and imaginary parts of the transfer function 31 ProShake User s Manual Phase angle shows the phase angles between the two motions at different frequencies Numerically given by the arctangent of the ratio of imaginary part to the real part of the transfer function Can be expressed in radians or degrees Real part shows the real part of the transfer function at different frequencies Imag part shows the imaginary part of the transfer function at different frequencies Report ProShake allows you to save numerical and graphical data in the form of a report because ProShake comes with its own Windows based word processor While the ProShake word processor will serve the needs of many it is not as powerful as Microsoft Word or WordPerfect If you prefer to use more powerful word processors use the ProShake word processor for temporary storage save the report file in Rich Text Format using the Save As menu item of the report form and lat
53. ly it is a plot of normalized cumulative squared acceleration i e t fla at H t _ flat Pat 0 vs time The Husid plot can be used for some measures of ground motion duration see Trifunac duration Fourier Spectrum A transient input motion can be represented using a Fourier series as the sum of a series of sine waves with different amplitudes frequencies and phase angles A Fourier amplitude spectrum is a plot of amplitude vs frequency for each of these sine waves The Fourier amplitude spectrum illustrates the frequency content of the motion Phase Spectrum 24 ProShake User s Manual A phase spectrum is a plot of phase angle vs frequency for all of the sine waves that make up a Fourier series The phase spectrum controls the manner in which ground motion energy is distributed in time the overall shape of a time history is related to the phase spectrum Unlike Fourier spectra phase spectra have no discernible structure Power Spectrum A power spectrum shows how the power of a ground motion signal is distributed with respect to frequency The power spectrum really provides the same information as the Fourier spectrum its values are the squares of the values of the Fourier spectrum Response Spectrum A response spectrum presents the maximum absolute response acceleration velocity or displacement of single degree of freedom oscillators of different natural periods As such it gives a good indication o
54. me plot plots of multiple Fourier or power spectra on the same graph can illustrate differences in frequency content effectively Time history of accelerations can also be saved to a file in PsoShake Input Motion Format for use as input motion for future analysis by cliking on the Save As button You will be prompted for file name s Stress and Strain Plots Time histories of shear stress and shear strain can be constructed from the Stress and Strain Plots tab Any of these _ can be copied to the ecg or have their data written to the Data File ta Time History of Shear Strain C PROSHAKESSHAKE LYR gA Pros jutpul janag MI File ea Hees EEA TETEE Output Ground Motion Plots Stress and Strain Plots Response Spectrum Plots Depth Plots Other Parameters Pe Outcrop aye 2 No Time History 2 No Fourier Spectrum C Phase Spectrum Power Spectrum p Plot Parameter Shear Strain C Shear Stress Plot 27 ProShake User s Manual Response Spectrum Plots Response spectra can be plotted using the Response Spectrum Plots tab which is selected by clicking on the labeled tab Multiple response spectra from different depths and or for different damping ratios or input motions can be selected for a single plot using the check boxes in the Include column KA ProShake Output Manager C PR File InputManager Solution Manager Output Manager
55. n originally vertical line throughout an input motion An animation can be viewed for each input motion for which animation was selected on the Input Motion form in the Input Manager To view an animation highlight the desired input motion and click on the Prepare Animation button 29 ProShake User s Manual EEE EA ProShake will take a few moments to load the data for the animation The animation is based on the computed displacements at the top of each layer with linear interpolation of displacements between layer boundaries As a result more realistic animations can be achieved by increasing the number of soil layers in a profile however the increased computational requirements will slow program execution somewhat 0 15 0 10 0 05 0 00 0 05 0 10 Current Record Time sec ki Total Duration sec Zot ProShake animations scale the me computed displacements so that the maximum computed displacement is slightly less than the full scale value of the horizontal axis This was done in order to clearly illustrate the pattern of the displacements in most cases the amplitudes of the displacements will be greatly exaggerated When used with input motions that have not been baseline corrected some apparent residual displacements may occur these displacements are relics of drift in the input motion and should not be taken to imply the existence of residual strains or stresses in the equivalent linear analysis Th
56. nd Idriss Sand Idriss 1990 4 By default the report contains an Analysis Summary of the Soil Profile Input Motion and output selections Whenever you select Copy to Report the item of interest will be copied into the report Although items are copied sequentially it is often advisable to type labels into the report so that the items can be identified at a later time Text items usually numbers are written in column format Graphics items are displayed black on white in the report even if they are displayed differently within ProShake 32 ProShake User s Manual 33 ProShake User s Manual ProShake Graphics ProShake allows rapid generation of many different types of plots In the Input Manager users can plot modulus reduction and damping curves various time histories and spectra for input motions and a graphical view of the soil profile In the Output Manager plots of time histories spectra and depth variations are all available Some of the common elements of these plots are described in the following paragraphs For clarity on the computer monitor the plots are displayed as light generally yellow or white curves and axes on a darker background The axes are selected to cover the entire range of data and clearly illustrate the variation of the parameter being plotted Nevertheless some users may want to change the characteristics of the plots this is easily accomplished in ProShake To modify a plot pla
57. ning the analysis and documenting the results of the analysis Each of these steps are Bedrock y 150 pcf Vg 2 500 ft sec described in detail in the following sections Completion of the tutorial will provide a very good introduction to the structure and operation of ProShake Definition of Layer Properties 1 Select the Input Manager from the initial ProShake screen This will bring up a form that allows you to define a soil profile select an input motion and keep a record of your input data in a report If you wanted to open an existing input file you could do so under the File menu on this screen there is an input file named shake dat that you may want to look at when you ve completed this tutorial it contains the example soil profile used in the original SHAKE user s manual Type in a title for the soil profile This title should identify the soil profile to you and other potential users it will be echoed on subsequent screens and in output files Hit the Tab key after entering the title to automatically move the cursor to the next field or move to the next field using the mouse Enter the number of layers for the analysis For this example enter 16 then hit Tab this will provide 15 soil layers plus the underlying halfspace Note how ProShake provides 16 tabs when the number of layers is entered each tab will allow you to input the appropriate data for the corresponding layer Enter the depth of the groundwater
58. nly over a very short period of time and because it is influenced by the duration of the motion the rms acceleration can be very useful for engineering purposes ProShake uses the Trifunac duration for computation of the RMS acceleration Trifunac Duration The Trifunac duration Trifunac and Brady 1975 is defined as the time interval between the points at which 5 and 95 of the energy in a ground motion have been delivered Numerically it corresponds to the time between the 5 and 95 points on a Husid plot 49 ProShake User s Manual Built In Soil Models Vucetic Dobry Vucetic and Dobry 1991 building on the work of Kokoshu 1980 in an investigation motivated by the performance of Mexico City clay in the 1985 Michoacan earthquake showed clearly how modulus and damping behavior are influenced by soil plasticity Wucetic and Dobry developed families of modulus reduction and damping curves as functions of plasticity index ProShake allows you to specify any plasticity index the program will determine the corresponding curves by interpolation The curves originally proposed by Vucetic and Dobry are shown on the plots in green from left to right they represent PI 0 PI 15 PI 30 PI 50 PI 100 and PI 200 The curve for the selected PI is obtained by linear interpolation and shown in yellow See also Dobry and Vucetic 1987 Sun Golesorkhi and Seed Sun Golesorkhi and Seed 1988 developed a series of modulus reduct
59. nual RETE SHAKE91 ProShake 0 051 1 0 11 2 11 0 10 0 15 0 20 0 25 1 Acceleration g 11 6 11 8 12 0 Time sec Even when the time scale is expanded tremendously the strongest part of the computed response shows very close agreement between the two programs The programs can also be compared from the standpoint of response spectra the computed ground surface response spectra for structural damping ratios of 5 and 10 are illustrated to the right Again the response spectra are very similar in fact part of the differences in these plots is explained by the fact that ProShake and SHAKE91 compute spectral accelerations at different periods Another comparison can be made with respect to the equivalent linear properties that both programs converge to SHAKE91 5 SHAKE91 10 ProShake 5 ProShake 10 Tos oO 0 0 0 5 1 0 1 5 2 0 2 5 Period sec The equivalent linear shear moduli from the final iteration of ProShake and SHAKE91 are shown below Again the very close agreement between the moduli from the two programs verifies their consistency _ 15000 D S 5 10000 xe z ROLE e ee O a SHAKE91 ProShake D 0 0 50 100 150 Depth ft The same set of comparisons can be made for other ground response problems The following plots compare the responses predicted by ProShake and SHAKE91 when both are applied to the
60. number No shear stress can exist at the ground surface z 0 so OUs 0 t _ t 0 t Gsy 0 t G 0 3 Zs where G G 1 2i amp is the complex shear modulus of the soil Substituting Equation 1 into Equation 3 and differentiating gives Griks Asei sO Bye ks pit G ik As Bse 0 4 which is satisfied when A Bs Compatibility of displacements and continuity of stresses at the soil rock boundary require 35 ProShake User s Manual Us Zs A uy zp 9 T s Zs H T z 0 Substituting Equations 1 and 2 into Equation 5 Aslan ewiksH A B From Equation 6 and the definition of shear stress t G du dz Asi Gk elk eR i Grr Ay By or cap Aalto ewiksH A B ENE The ratio Gyky oss x eu rer where a is known as the complex impedance ratio Solving Equations 7 and 8 simultaneously gives Apa zd raze 1 2 n B T tit 1 a e iks 5 6 7 8 9a 9b If a vertically propagating shear wave of amplitude A traveled upward through the rock and the soil was not present the free surface effect at the rock outcrop would produce a bedrock outcropping motion of amplitude 2A If the soil was present the free surface motion amplitude would be EEE 4A 1 ae eiks4 1 0 e iksH 36 ProShake User s Manual The transfer function F defined as the ratio of the soil surface amplitude to the rock outcrop amplitude is g
61. oil deposits User s Guide University of California Davis California 13 pp Ishibashi I 1992 Discussion to Effect of soil plasticity on cyclic response by M Vucetic and R Dobry Journal of Geotechnical Engineering ASCE Vol 118 No 5 pp 830 832 Ishibashi I and Zhang X 1993 Unified dynamic shear moduli and damping ratios of sand and clay Soils and Foundations Vol 33 No 1 pp 182 191 Kokoshu T 1980 Cyclic triaxial test of dynamic soil properties for wide strain range Soils and Foundations Vol 20 No 2 pp 45 60 Kramer S L 1996 Geotechnical Earthquake Engineering Prentice Hall Upper Saddle River New Jersey 653 pp Schnabel P B Lysmer J and Seed H B 1972 SHAKE A computer program for earthquake response analysis of horizontally layered sites Report No EERC 72 12 Earthquake Engineering Research Center University of California Berkeley California Seed H B and Idriss LM 1970 Soil moduli and damping factors for dynamic response analyses Report No EERC 70 10 Earthquake Engineering Research Center University of California Berkeley Seed H B Wong R T Idriss I M and Tokimatsu K 1986 Moduli and damping factors for dynamic analyses of cohesionless soils Journal of Geotechnical Engineering ASCE Vol 112 No 11 pp 1016 1032 Sun J I Golesorkhi R and Seed H B 1988 Dynamic moduli and damping ratios for cohesive soils Report No
62. only used version of SHAKE in current geotechnical earthquake engineering practice a number of such comparisons between ProShake and SHAKE91 have been performed the results of a typical comparison are described in this section The numerical implementation of ProShake differs from that of SHAKE91 in the following ways 1 ProShake uses 32 bit arithmetic rather than the 16 bit arithmetic used in SHAKE91 This is primarily a result of recent advances in development platforms 32 bit Fortran became available for personal computers after the development of SHAKE91 and before the development of ProShake 2 ProShake uses a different Fast Fourier Transform FFT routine The routine used in ProShake taken from the International Mathematical Software Library IMSL represents a more recent and efficient implementation of the FFT 3 ProShake uses a more efficient and robust procedure to iterate toward strain compatible soil properties For most analyses the last iteration required to drop the modulus and damping error below the specified error tolerance in ProShake will produce smaller final errors than the last iteration for the same error tolerance in SHAKE91 4 ProShake handles cutoff frequencies slightly differently than SHAKE91 SHAKE91 applies its cutoff frequency after scaling the input motion to the specified peak acceleration as a result the actual peak acceleration used in the analysis can be different than the desired peak accelerat
63. p feature can be very useful Is SR e ac for entering data when multiple a a a A a material layers have similar properties the properties of one layer can be input and then assigned to the other layers by dragging and dropping Individual properties of the other layers can then be changed by editing as necessary To drag and drop place the cursor anywhere on the line data for each layer is displayed on an individual line that you want to copy then press the left mouse button and hold it as you move the cursor down to the layer you want to paste the information to Then release the mouse button The data for one layer will be copied to the other layer Select Output E u s OS View Profile 19 Select Ouput ProShake User s Manual Output can be requested for the top of any soil layer in the profile prior to program execution Output is divided into three main categories that are displayed on the Select Output form Time History Time histories of acceleration velocity displacement shear strain and shear stress can be selected for any layer The exception is that shear stress and shear strain cannot be selected for Layer 1 because their values are always zero at the ground surface Response Spectrum Acceleration velocity and or displacement response spectra can be computed at up to three structural damping ratios Response spectra are computed at 95 structural periods ranging from 0 to 10 seconds Spectra Fo
64. pecific item you are interested in The second way of accessing the help system is through its context sensitive capability simply move the cursor to the field you want information for then press F1 The Exit command is self explanatory clicking on it will end the program Setting Up an Analysis Setting up a ProShake analysis involves defining the properties of all soil layers within the profile to be analyzed specifying the characteristics of the input motion that will be applied to the soil profile defining the quantities to be computed and documenting the input data Follow the steps in the following sections to set up run and view the results of a typical ground response analysis ProShake User s Manual vA The tutorial will set up and solve for Soft silty clay the response of the soil profile shown Y 100 pef to the left when subjected to a bedrock E 150 m seg motion equal to that recorded at Yerba 50 ft P 10 Buena Island in the 1989 Loma Prieta earthquake The soil profile consists of a 50 ft thick layer of soft silty clay over a 50 ft thick layer of stiff clay underlain by bedrock The groundwater level is Stiff clay at the ground surface The input Ysat 120 pef motion is to be applied at the top of 50 ft Gmax 1 800 ksf bedrock PI 20 The tutorial will take you through the main steps in a typical ProShake analysis definition of layer properties specification of input motion documentation of input run
65. ping curves for gravel These curves are based on the average behavior of 12 inch diameter cyclic triaxial tests on four different gravels Rock Modulus reduction and damping curves for rock were included in sample data files for the original SHAKE program Schnabel et al 1970 50 ProShake User s Manual Linear ProShake allows you to specify a linear elastic or linear viscoelastic material When you select this material ProShake will use the maximum shear modulus and prompt you to enter a damping ratio You should note that the transfer function for an undamped linear elastic layer will have singularities at the natural frequencies of the layers these can lead to numerical problems that prevent program execution 51 ProShake User s Manual Analysis Summary a summary of the soil profile input motion and output selections for the analysis The analysis summary is written to the Report from there it can be printed and placed in a project or assignment file Cyclic Stress Ratio the ratio of the peak shear stress to the vertical effective stress Damping Error the difference between damping ratio values in successive iterations divided by the damping ratio value used in the most recent iteration expressed as a percentage Drag and Drop By holding the left mouse button down any line corresponding to a particular material layer can be copied and placed at the location of the cursor at the time the left mouse button
66. raphics will display three plots for each input motion The leftmost plot will illustrate the variation of effective shear strain with depth for each iteration the effective shear strain values should converge to a constant profile with increasing numbers of iterations The center and rightmost plots illustrate the variation of modulus error and damping error with depth for each iteration As the Fannari program iterates toward strain compatible soil properties the errors should decrease When the errors decrease below the error tolerance specified on the Input Motion form of the Input Manager at all depths or when the maximum number of iterations has been reached the program will cease iterating The solution graphics are intended to help the user better understand the behavior of the soil deposit being analyzed and to help identify and correct potential problems with the analysis ProShake uses iteration logic that is more advanced than that used in previous versions of SHAKE as a result it converges more quickly and more reliably than previous versions Soil profiles with extraordinarily soft layers or extraordinarily high impedance ratios however may converge slowly or not at all such behavior often indicates an error in the input Output Manager The output manager processes all output and allows all results to be plotted graphically Several types of plots including ground motion plots stress and strain plots response spec
67. s ProShake User s Manual Installing ProShake The first step in using ProShake is to install the program ProShake comes on two 3 5 disks labelled Disk 1 and Disk 2 and with a hardware key that fits into the parallel port of your computer The hardware key will protect your investment in ProShake by preventing unauthorized use or copying of the program In order to run ProShake the hardware key must be installed on your computer The hardware key is otherwise transparent to the computer if you are already using the parallel port for a particular device you may insert the hardware key in the parallel port and plug your device into the other end of the hardware key ProShake runs under the Windows 95 or NT 4 0 operating system it will not run under earlier versions of Windows e g Windows 3 1 To install ProShake Start your computer Start the Windows 95 operating system Place ProShake Disk 1 in the a drive Click on the Windows 95 Start button and select Run Type the following in the command line Pn er a setup exe and click on OK 6 Follow the instructions on the screen ProShake will be installed in a directory called ProShake unless you specify otherwise An Uninstall program will also be installed in that directory in the event that you need to remove ProShake from your computer After installation ProShake can be accessed using the Windows 95 Start button then to Programs and on to ProShake ProShake Us
68. s envisioned As the programming effort proceeded however it became clear that much greater capabilities could be achieved by developing a single integrated program At that point the computational portion of the program was written from scratch in FORTRAN and the interface developed in Visual Basic As the program began to take shape it s potential benefits to practicing engineers became apparent At that point two versions of the program were developed EduShake and ProShake EduShake fulfills the original goal of the developers it is a full featured program that is available at no cost to students faculty and other interested parties EduShake is limited however to the use of only two input motions this is sufficient for well constructed assignments to provide students with a good understanding of seismic ground response but not sufficient to allow the program to be used for commercial purposes The development of EduShake evolved through several stages and was eventually beta tested by graduate students researchers and practicing engineers After a few modifications in response to the comments of the beta testers EduShake was made available in the public domain Shortly ProShake User s Manual thereafter the restrictions of EduShake were removed and a few additional features added to produce ProShake ProShake Features ProShake offers many features that make it easy and efficient to use features not found in other gro
69. sfer function right half of transfer function modulus of transfer function for plotting plot input motion time domain plot FAS of input motion frequency domain plot modulus of transfer function freq domain compute output motion in frequency domain end for j 1 n 2 1 accl j 2 abs acc j compute FAS of output motion end subplot 5 1 4 plot ff accl atime n real ifft acc subplot 5 1 5 plot t atime plot FAS of output motion frequency domain plot output motion time domain The variables defined in the first part of the MATLAB program correspond to Example 7 3 in Kramer 1996 This example considers the response of a 540 ft thick soil layer of soil vss 1500 ft sec Y 125 pcf and 5 overlying bedrock v 5000 ft sec y 160 pcf and E 2 The MATLAB program generates the plots shown below 38 ProShake User s Manual 0 5 saad ae 0 5 non 540 15 20 25 30 35 40 0 48 5 10 15 20 25 rn 0 0 027 gt 10 1p 20 25 oont h ee i 0 Lasn i 40 5 10 15 20 25 o ngjiten anm 0 5 10 15 20 25 30 35 40 The first of these plots shows a time history of acceleration of the 40 sec input motion in the time domain Immediately below this is the Fourier amplitude spectrum of the input motion the Fourier amplitude spectrum shows the variation of amplitude with frequency for
70. spectra Fourier spectra power spectra and phase spectra and plots of the maximum amplitudes of various parameters with depth Scalar parameters such as peak acceleration peak velocity peak displacement RMS acceleration Arias Intensity predominant period and bracketed duration can be computed for any depth within the soil profile ProShake can display an animation of the horizontal displacements of a soil profile excited by earthquake shaking The animation provides greatly improved intuitive understanding of the response of the soil profile and can help the user identify potential hazards that might otherwise go undetected ProShake User s Manual ProShake has a built in word processor that is linked to the program in a way that allows analyses to be documented thoroughly and easily in a ProShake Report The ProShake Report can include text tables and graphics all of which can be cut and pasted into more powerful word processors for final report preparation These are only some of the features that ProShake offers to simplify and speed the process of performing and interpreting the results of ground response analyses As you become more familiar with the program other helpful features will become apparent Program Structure ProShake is designed to provide an intuitive interface that simplifies and speeds the process of performing and interpreting the results of ground response analyses The program is organized into thr
71. t shear modulus divided by maximum shear modulus or G Gmax with strain A damping curve illustrates the variation of equivalent viscous damping ratio with strain The modulus reduction and damping behavior of many soils is well understood and several models have been proposed to characterize them ProShake has a number of built in modulus reduction and damping models but users may wish to add new models using the modulus damping curve editor To add a new modulus reduction or damping curve follow these steps 1 Select Modulus Damping Curve Editor from the Utilities Menu A Modulus Damping Curve Library Editor box will appear on the screen displaying modulus and strain values for Model No 1 the Vucetic Dobry model Note that there are 6 curves in the Vucetic Dobry model each corresponding to a different plasticity index and that each curve is defined at 16 different strain levels Individual modulus reduction values can be changed but any changes should be documented or preferably saved with a different model name 2 If you want to create a new damping curve select Damping in the upper box If not leave Modulus selected 3 Click the Add button You will now have a blank form on which to enter the modulus reduction data for your new model 4 Give the model a name You may use any alphanumeric name but make sure that it is different than the names of the existing models The length of the name is limited to 50 characters 5
72. t motion by a Fourier series and use of transfer functions for solution of the wave equation rely on the principle of superposition which is only valid for linear systems To approximate the actual nonlinear inelastic response of soil T an equivalent linear approach can be utilized In the equivalent linear approach linear analyses are performed with soil properties that are iteratively adjusted to be consistent with an effective level of shear strain induced in the soil In the equivalent linear approach the shear modulus is taken as the y secant shear modulus which as shown to the right approximates an average shear modulus over an entire cycle of loading As the level of shear strain increases the secant shear modulus decreases The relationship between secant shear modulus and shear strain amplitude can be characterized by means of a modulus reduction curve The nature of this curve which has an ordinate of modulus ratio G Gmax and an abscissa of log shear strain has been well established for many soils ProShake has a library of modulus reduction relationships that can be selected in the Input Manager The solution algorithm used in SHAKE and ProShake assumes viscous soil damping which it represents using a complex shear modulus Viscous damping implies behavior that would be characterized by elliptical stress strain loops Because actual stress strain loops are seldom elliptical an equivalent damping ratio is use
73. table Because ProShake performs total stress analyses the groundwater table depth is not needed for the ground response analysis rather it is used when vertical effective stresses need to be computed For this example enter 0 0 in either the ft or m box the other will automatically be calculated ProShake allows you to enter input data in either US or SI units and to mix and match units 10 11 12 13 ProShake User s Manual Now you are ready to enter input data for the first layer Making sure that the tab for Layer 1 is active it should be at the front of the stack of tabs with the layer number displayed in blue enter a material name for Layer 1 This can be any alphanumeric string for this example call the first layer Soft Silty Clay The next step is to select a modulus reduction curve ProShake has a series of built in modulus reduction curves extracted from the geotechnical earthquake engineering literature To see the list of built in curves click on the button at the right side of the modulus reduction curve field For this example select Vucetic Dobry The Vucetic Dobry model describes modulus reduction and damping behavior as a function of plasticity index When you select this model ProShake will prompt you for a plasticity index enter 10 for the plasticity index ProShake will interpolate between the modulus reduction and damping curves presented by Vucetic and Dobry to obtain curves that correspond to th
74. tem Include Motion 1 C Peak Acceleration 2 C Peak Velocity C Peak Displacement 150 Peak Shear Stress 0 1000 0 3000 4000 C Peak Shear Strain EQ No 1 C Effective Shear Strain C Shear Modulus C Damping Ratio pa Cross Hair Position X 2132 55 Y 89 05 Copy to Report sne vstat rae Return i a Parameters can also be copied to the report in tabular form by clicking Copy to Report button Other Parameters ProShake will allow you to compute other characteristics of the computed motion at the top of any layer at which acceleration data has been computed Clicking on the Calculate button on the Other Parameters tab allows computation of the ground motion parameters shown on the Other Parameters form to the right Calculated parameter values can also be copied to the report in tabular form by clicking Copy to Report EA ProShake Output Manager C PROSHAKE SHAKE LYR ori File Input Manager Solution Manager Cupu Manager Help Peak Acceleration g 0 369 Peak Velocity ft sec 1 6264 Peak Displacement ft 0 4709 RMS Acceleration g 0 1197 Arias Intensity ft sec 4 25 Response Spectrum Intensity g 2 0 0143 Predominant Period sec 0 64 5 60 Bracketed Duration sec Animation The Animation feature allows ProShake users to view the horizontal displacements of a
75. the Output Manager Within each of these managers ProShake displays a series of forms on which data can be entered and or results displayed The following sections illustrate the most significant forms displayed by ProShake and describes the items that appear on those forms Input Manager The input manager is used to prepare input files that can be executed by ProShake specifically definition of the Soil Profile and specification of all Input Motions Soil Profile The Soil Profile form is accessed by clicking on the Profile button in the Input Manager The screen that appears is shown below and the information entered on the Soil Profile form described in the following paragraphs Profile Information The upper part of the Soil Profile window requests global information that applies to the entire profile rather than to individual material layers Profile Title Enter the alphanumeric title of your choice here or leave it blank The title will be displayed whenever the Soil Profile window is activated It will be stored when you save your soil profile data and it will also be written into the Report The length of the title is limited to CESZMMIIMENTS File Input Manager Solution Manager Output Manager Help 80 characters Profile Profile Title Example 150 ft layer Number of Layers No of Layers 17 Depth to Water Table 10 0 a 0 m ProShake allows you to define an unlimited Ses I1
76. the effects of the wave interactions that take place at all of the layer interfaces above layer j 1 Then a transfer function relating the motions at the tops of any two layers say layers i and j can be expressed as 40 ProShake User s Manual _ 4 b aj b Fj 16 This transfer function can become quite complicated but it is used in exactly the same way as the much simpler transfer function developed for the single layer case In fact the MATLAB program that illustrated the single layer case could be used to compute the response for a multi layered problem by changing only one line the line where the transfer function is defined with the comment left half of transfer function Equivalent Linear Analysis The nonlinear and inelastic behavior of soil is well established in geotechnical engineering The nonlinearity of soil stress strain behavior means that the shear modulus of the soil is constantly changing The inelasticity means that the soil unloads along a different path than its loading path thereby dissipating energy at the points of contact between particles Rigorous analysis of the mechanical response of soils to any type of loading dynamic or otherwise would require that the stress strain behavior of each element of soil be tracked directly in the time domain The method of analysis used in SHAKE and ProShake cannot allow for nonlinear stress strain behavior because its representation of the inpu
77. the report at whatever location the report cursor was in Any ProShake plot can be copied to the report to provide documentation of a ground response analysis 27 Now save the report with the name tutorial hed Running the Analysis 28 Torun the ProShake analysis select the Solution Manager 29 The Solution Manager will analyze any input data file you desire The default extension for ProShake input files is dat though other filename extensions can also be used To run the analysis you have just set up select the data file tutorial dat 10 30 ProShake User s Manual ProShake will then perform the analysis You will see how the program iterates toward strain compatible soil properties during the analysis this feature will help you develop a better understanding of the response of your soil deposit The word Running will appear in the lower left corner of the screen and will be replaced by the word Finished at completion of the analysis and a dialog box will appear When the analysis is completed click OK on the dialog box that appears to exit Solution Manager The results of the analysis performed by the Solution Manager will automatically be written to a file with the same name as your data file but with the extension lyr in this case tutorial lyr Examining the Results of the Analysis 31 32 33 34 35 36 37 38 39 To view the results of your analysis select the Output Manager Go to
78. the soft silty clay and the stiff Bo clay This impedance contrast causes large strains near the bottom of the soft 0 0 2 e 0 5 1 0 1 5 2 0 2 5 Period sec silty clay layer that lead to low shear moduli in the equivalent linear model 1500 wn 1000 E 50t T SHAKE91 3 ProShake ep 0 0 10 20 30 40 50 60 70 80 90 100 Depth ft 47 ProShake User s Manual Strong Motion Parameters Arias Intensity The Arias Intensity Arias 1970 also influenced by amplitude frequency content and duration is defined as i 2 a t Iq 3 1 t dt The Arias Intensity has units of velocity and is usually expressed in meters per second Since it is obtained by integration over the entire duration rather than over the duration of strong motion its value is independent of the method used to define the duration of strong motion Bracketed Duration The bracketed duration is the time interval between the first and last exceedances of a threshold acceleration Bolt 1969 The threshold acceleration is set at 0 05g in ProShake Peak Acceleration The maximum absolute value of acceleration The peak acceleration provides a useful measure of the strength of the higher frequency components of a ground motion Peak Velocity The maximum absolute value of velocity The peak velocity provides a useful measure of the strength of the intermediate frequency components of a ground motion Peak Displacement The max
79. the time domain The FFT is a very efficient numerical procedure but it requires the total number of acceleration values to be an integer power of 2 e g 1024 2048 4096 etc ProShake allows up to 16 384 2 terms in the object motion If the number of acceleration values in your input motion file is less than some power of 2 ProShake will add the required number of trailing zero acceleration values to bring the total length to the number of terms you specify for the Fourier series Because the Fourier series implies periodicity it assumes that the total time history including the trailing zeros repeats itself indefinitely you need to make sure you have enough trailing zeros to form a quiet zone sufficiently long to allow the response to die out before the next motion begins The best results are usually obtained when the last third or more of the total time history is quiet Object Motion Location The input motion can be applied at the top of any layer in your soil profile from the ground surface to the bottom half space layer Enter the layer number at which your input motion is to be applied here The input motion may be applied as an outcrop motion or as a motion within the soil profile Your selection here depends on your input motion If the input motion was recorded by an instrument located on the ground surface or if it was obtained by computation at a point on the ground surface of some numerical model it should be specifie
80. ton 14 If you have any questions conceming this Agreement or wish to contact Licensor for any reason please write EduPro Civil Systems Inc 5141 189 Avenue NE Redmond Washington 98195 15 U S Govemment Restricted Rights The Software and documentation are provided with Restricted Rights Use duplication or disclosure by the G ovemment is subject to restrictions set forth in subparagraph c 1 of The Rights in Technical D ata and Computer Software clause at D FARS 252 227 7013 or subparagraphs c 1 i and 2 of Commercial Computer Software Restricted Rights at 48 CFR 52 227 19 as applicable Supplier is EduPro Civil Systems Inc 5141 189 Avenue NE Redmond Washington 98195 ii ProShake User s Manual Table of Contents Introduction 1 Background 1 ProShake Features 2 Program Structure 3 Installing ProShake 5 Tutorial 6 Utilities 13 ProShake Help 15 The ProShake Interface 16 Input Manager 16 Solution Manager 26 Output Manager 26 Report 30 ProShake Graphics 32 Theory 33 Verification 41 Strong Motion Parameters 46 Built In Soil Models 48 Definitions 50 References 32 iii ProShake User s Manual Introduction Welcome to ProShake a new computer program for seismic ground response analysis of horizontally layered soil deposits ProShake was developed from EduShake a public domain program developed to help engineering students understand the mechanics of seismic ground response ProShake features a W
81. trum plots and depth plots are available The output manager also allows computation of other parameters Finally the output manager can be used to view an animation of the ground response Each of these can be selected by clicking on the appropriate tab 26 ProShake User s Manual Ground Motion Plots A variety of plots can be constructed from the Ground Motion Plots tab which is selected by clicking on the labeled tab Three ground motion parameters acceleration velocity and displacement can be plotted as functions of time or frequency Four different plot types are available Time History Fourier Spectrum Phase Spectrum and Power Spectrum plots Any of these plots can be copied to the Report or have their data written to the Data File A Prosi put PROSHAK KE LY File Ses aR TEA Heb Ground Motion Plots Stress and Strain Plots Response Spectrum Plots Depth Plots Other Parameters Plot Type Time History Fourier Spectrum Phase Spectrum C Power Spectrum p Plot Parameter Acceleration C Velocity C Displacement o re Copy to Report Wte Data warae Betum Ground motion parameters from multiple depths or from multiple input motions can be selected for a single plot using the check boxes in the Include column While it is unlikely that users will want to plot multiple time histories or phase spectra on the sa
82. und response analysis software packages Some of the most significant of these features are listed below English or metric units can be used and the units can be entered in whatever format is most convenient during input A number of built in soil models can be selected from pulldown menus ProShake will interpolate as necessary to the conditions of your analysis and will allow you to add your own soil models and store them for later use Soil profile data can be entered quickly using drag and drop techniques and can be checked graphically for errors prior to analysis Input motions can be viewed graphically in many different ways as time histories as spectra and in terms of a variety of ground motion parameters The number of input motions that can be analyzed at a time is limited only by available RAM and the results from all input motions can be plotted together Each input motion can have up to 16 384 acceleration values The progress of the program is displayed graphically during execution Plots showing the variation of shear strain and modulus damping errors during iteration toward convergence can help illustrate site response as well as identify possible errors in input data A wide variety of output parameters from any depth within the soil profile can be plotted with the click of a button The plots include time histories of acceleration velocity displacement shear stress and shear strain response
83. urier spectra phase spectra and power spectra can be computed for acceleration velocity and or displacement View Profile ProShake s Input Graphics allow you to view the soil profile and input parameters assigned to various material layers This feature is very useful for detecting errors or other problems with the input data mis typed parameters or misplaced decimal points will show up very clearly in the profile fe Profile Graphics xi Example 150 ft layer Number DescriptiorMotion Output Shear Wave Velocity Unit Weight Sand NNS Sand Sand Sand D Clay Cl Om on aj wN visualizing impedance contrasts at layer boundaries coat The profile shows the name thickness unit weight and shear wave velocity for each material layer The profile indicates the depths at which the input motions are applied with solid red ovals for motions within the profile and open ovals for outcrop motions and the depths at which output is calculated with solid green ovals for motions within the profile and open ovals for outcrop motions The profile plot can be copied to the Report The profile is also useful for Because impedance ratios control the partitioning of wave energy reflected and transmitted at layer boundaries it is useful to know where the highest impedance ratios are located 20 ProShake User s Manual

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