The modular structure of MTR/SASSI is specifically designed for practical applications with the following characteristics:
- Site response analysis, impedance analysis, and formation of the basic stiffness and mass matrices for the structure can be performed separately. The results are stored on disc files.
- In general if the seismic wave field, external loads, soil properties, or the arrangement of the superstructure are changed, then only part of the computation needs to be repeated.
- The final solution is stored (in the form of transfer functions) on a disk file from which specific response quantities can be extracted without re-computing the entire solution.
- Both deterministic and probabilistic results can be obtained from the above file.
The program module SITE solves the eigenvalue problem of Rayleigh and Love wave cases for a horizontally layered site. The results of the eigenvalue solution are saved on Tape 2, which will later be used to (1) solve the site response problem in program module CNTRL and (2) compute the transmitting boundaries used in solving the impedance problem in program modules POINT2 and POINT3. Thus, the program module SITE must be executed before the program modules CNTRL, POINT2 and POINT3. (back to top)
The site response problem is solved by the program module CNTRL. This program reads the site properties and eigenvalue solution via Tape 2, the nature of the control motion from the input data, and, using this information, calculates the mode shapes and wave numbers. The results are then stored on Tape 1, which will later be used for seismic analysis. Thus, Tape 1 will not be generated for forced vibration problems. Up to 6 different seismic load cases can be analyzed simultaneously in a single CNTRL run. The program module CNTRL also has the capability to calculate incoherent ground motion input using coherence functions. (back to top)
POINT2 and POINT3
The flexibility matrix for the interaction nodes is calculated for each frequency of interest by the program modules POINT2 and POINT3 for 2-D and 3-D problems, respectively. The program requires Tape 2 as input, and stores the results on Tape 3. Thus, the program module SITE must be executed before the program modules POINT2 and POINT3. Recent enhancements to the POINT3 program provides capability for ring load solutions for pile/soil interaction analyses incorporating pile group effects. This new pile group analysis procedure replaces the old Spile and hybrid pile element procedures. . (back to top)
The program module HOUSE is a standard finite element program. The element library includes 3D solid, general 3D beam, 3D flat plate/shell, 2D plane-strain, general 3D spring, 2D plane Love wave, 3D pile, 3D pipe, 2D nonlinear soil, 3D nonlinear Soil, general 3D stiffness / mass, and general 3D super elements. HOUSE forms the frequency-independent total mass and complex-valued stiffness matrices of the structure and excavated soil, and stores the results on Tape 4. The program module HOUSE can also output the modal properties (natural frequencies, mode shapes and mass participation factors) of the fixed-base structure primarily for comparison with those of the imported and/or translated models from elsewhere. (back to top)
The program module MOTOR forms the elements of the load vector, which correspond to impact forces acting externally on the structure, or to forces acting within the structure from rotating machinery. The generated information is stored on Tape 9. Up to 6 load cases can be analyzed simultaneously in a single MOTOR run. (back to top)
The program module ANALYS is the heart of MTR/SASSI. It uses the results of program modules SITE, POINT, HOUSE, and MOTOR to assemble the coefficient matrix and solve for the final transfer functions for each specified load case. ANALYS also controls the restart modes of the program.
The results of ANALYS runs in terms of frequency-dependent, complex-valued transfer functions are stored on Tape 8. For typical problems, the transfer functions only need to be solved for 60 to 80 frequencies. The remaining transfer function values are obtained by interpolation in the complex frequency domain. The actual interpolations are performed in the post-processors such as MOTION, STRESS, IFORCE, FSUM, SNODE, etc. The three components of seismic input motion may be applied simultaneously. The program can analyze multiple load cases (up to 6) simultaneously in a single run and the results are saved on separate Tape 8’s. (back to top)
COMBN5 and COMBN8
The program module COMBN5 reads the subgrade impedance matrices stored for different frequency solutions on two input Tape 5s, and combines them into a new Tape 5 which will then contain the combined impedance matrices from both tapes. If duplicate frequency solutions are encountered, the latter will be discarded. The new solution algorithm for high performance computing implemented in MTR/SASSI Linux Enterprise (LE), Super Computing and Cloud Computing do not generate and store Tape 5, and as such do not use COMBN5 program module.
The program module COMBN8 makes it possible to consider new frequencies of analysis and to combine the results with the old transfer functions. This program reads the transfer functions stored on multiple input Tape 8’s, and combines them into a new Tape 8 which will then contain the combined transfer functions from all tapes. (back to top)
The purpose of the (deterministic) post-processor MOTION is to produce maximum values and time histories of output response (accelerations, velocities, and displacements). It may also output transfer functions and acceleration response spectra.
The program reads the time history of the reference input motion (or force) from input file REF, and transforms it into the frequency domain using the Fast Fourier Transform (FFT) algorithm. It then reads the un-interpolated transfer functions from Tape 8 (or 8’s) for the selected output responses, performs the interpolation and convolution with the input motion(s) [or force(s)], and returns to the time domain using the inverse Fast Fourier Transform algorithm. The resulting time histories of response may be outputted directly and saved on Tape TH, or converted to output response spectra and saved on Tape SP. The maximum response values and transfer functions can also be outputted directly and saved on Tape RV and TF, respectively.
The transfer functions for multiple load cases (up to 6) are outputted and saved on separate Tapes TF’s. In addition the program combines the transfer function results for multiple load cases using SRSS method with the results saved on Tape TF-SRSS. The SRSS results of the transfer functions from multiple load cases are often used in force vibration analysis of machine foundations.
The transfer functions corresponding to the three components of input motion may also be processed simultaneously. The time histories of co-directional responses from input in three directions are then summed algebraically or using 100-80-80 procedure, and used to calculate the final requested response quantities.
Maximum values and acceleration response spectra for multiple load cases can be outputted in terms of time history summation, 100-80-80 rule or SRSS method. (back to top)
The program module STRESS is used to calculate the maximum values and time histories of stresses and strains in the structural elements. The transfer functions corresponding to the three components of input motion may be processed simultaneously. The time histories of co-directional stresses from input in three directions are then summed algebraically and used to calculate the final requested response quantities. The maximum value and time history of stresses may be outputted directly and saved on Tape SRV and STH, respectively.
Secondary soil non-linearity due to SSI effects can be modeled by incorporating a portion of the foundation soil in the vicinity of the structure as part of the structure model. The nonlinear soil blocks are modeled using nonlinear soil elements. The initial properties of the nonlinear soil elements can be set to reflect the soil consolidation effects under self-weight of the structure. The properties of each soil element within the nonlinear soil block are then monitored and adjusted by the program based on the computed values of effective shear strain in that element. This provides a numerically powerful and efficient method for incorporating soil non-linearity due to SSI effects in a 3D SSI analysis.
Tapes 4 and 8 as well as time history of input motion (or force) are part of the input for this program. (back to top)
The program module IFORCE calculates the soil reaction forces due to dynamic soil pressures acting on the embedded exterior walls and basemat of the structure. The program reads the structural mass and complex-valued stiffness matrices from Tape 4, the un-interpolated response transfer functions from Tapes 8, and the input motion(s) from the input file REF. The results of nodal forces may be outputted in terms of maximum values, time histories, and transfer functions. The time history of dynamic soil reaction forces may be saved on Tape DF.
The transfer functions corresponding to the three components of input motion may be processed simultaneously. The time histories of co-directional soil reaction forces from input in three directions are then summed algebraically and used to calculate the final results. (back to top)
The program module FBASE computes the response of a structural system on a fixed or flexible base. The analysis may be performed for external dynamic or static forces acting on the structure, or for a given seismic input motion at the base of the structure.
FBASE provides four different methods for inputting flexible base foundation impedance matrix. They include spring-mass-dashpot (KMC) model, frequency dependent impedance (FDI) model, lumped parameter foundation (LPF) model and component mode synthesis (CMS) model.
FBASE reads the structural mass and complex-valued stiffness matrices from Tape 4, either the input dynamic loads from Tape 9 or the seismic input motion from the input data file, and flexible-base impedance parameters from the input data file, and then calculates the response of the structure for each frequency of analysis. For seismic problems, the results are outputted in terms of absolute acceleration transfer functions (response acceleration / input acceleration) while for forced vibration problems, the results are outputted in terms of displacement transfer functions (response displacement/input force). The resulting transfer functions are stored on Tape 8, which can be inputted into the post-processors MOTION, STRESS and RANDOM to calculate the required responses at selected nodes.
The transfer functions corresponding to the three components of input motion may be processed simultaneously. The time histories of co-directional responses are then summed algebraically and the results are used to calculate the final response quantities. (back to top)
The program module GFORCE computes the mass-proportional forces applied in the global x- y- and z-directions to all nodes of the structure. The program reads the structural information from Tape 4 and generates a list of forces at structure nodes based on the mass of the structural elements and nodes.
Dead Load Analysis: The program GFORCE can be used to generate gravity loads by applying a uniform acceleration of -1g in the z-direction. The results outputted on Tape GF can then be used to construct an input to run MOTOR to calculate gravity load information on Tape 9. This tape may then be inputted to the program modules ANALYS or FBASE for dead load SSI analysis. The results of dead load analysis can then be combined with those of seismic loads.
Pseudo-Acceleration Analysis: The program GFORCE can be used to generate equivalent static forces at selected structural nodes for pseudo-acceleration analysis. The maximum acceleration values calculated from MOTION from full SSI analysis and saved on Tape RV can be inputted to GFORCE to calculate pseudo-acceleration forces at structural nodes. The nodal forces, Fn are calculated from following equation:
Fn = Mn . |Una | . g
Where Mn is mass of node n and |Una| is the absolute acceleration value in g’s obtained from Tape RV and g is the acceleration of gravity.The results outputted on Tape SGF can then be used to construct an input file to run MOTOR to calculate pseudo-acceleration information on Tape 9. This tape may then be inputted to the program modules ANALYS or FBASE for pseudo-acceleration analysis. The user can output the g-forces at few selected structural nodes or at all nodes of the structure. (back to top)
The program module SNODE computes the far-field soil responses. Although these responses may also be obtained by including additional far-field soil nodes in the SSI model, the SNODE procedure greatly reduces the numerical effort and memory requirements necessary to calculate the above responses. In addition, if a far-field soil node was not originally included in the SSI model but it is later desired, SNODE will enable calculating such responses without having to re-run the original SSI model.
The program reads the structural information from Tape 4, point load solutions from Tape 3 and un-interpolated transfer functions from Tape 8 for the SSI model that has been analyzed. It then calculates the response of the far-field soil nodes in terms of transfer functions at the same frequencies that the SSI model was analyzed for. The results are then output in a new Tape 8, which can be input to the post-processor MOTION to calculate maximum values and time histories of computed acceleration, velocity and/or displacement response as well as acceleration response spectra. It is noted that the new Tape 8 is not an augmented version of the original Tape 8 generated from the original SSI analysis; therefore, it cannot be used for input to other post-processors such as STRESS, IFORCE, etc. (back to top)
The (probabilistic) post-processor RANDOM is in many respects similar to the program module MOTION. However, instead of inputting the time history of the control motion, it takes a power spectral density (PSD) function of this motion as input. It then calculates the root mean square (RMS) and power spectral density (PSD) responses of the structure. (back to top)
The program module RIMP computes foundation impedance and compliance functions for single and multiple rigid surface foundations of arbitrary shape supported on soil media. Although these impedance functions may also be obtained through general flexible foundation SSI analysis in MTR/SASSI, the new procedure RIMP greatly reduces the numerical effort and memory requirements necessary to calculate the above foundation impedance and compliance functions. It does this by taking advantage of the rigidity of the foundation and thus bypasses the inversion of the full subgrade flexibility matrix in ANALYS.
The program module RIMP reads the flexibility matrices from Tape 7 (obtained through Mode 3 in ANALYS) and the geometry of the rigid foundation system from the input data file. Then, for each specified frequency, it calculates the corresponding foundation impedance and compliance matrices. The selected impedance and compliance components may be further interpolated to obtain smooth functions. The results of RIMP analysis are printed out as well as saved on output Tape IMP (for impedance) and CMP (for compliance) for plotting purposes or for later processing in the program module FBASE. (back to top)
The program module DISIMP computes the uncoupled frequency-dependent distributed foundation impedance at all foundation interaction degrees-of-freedom from separate loading in the x-, y- and z-directions. This program is executed in preparation for running the program module FRMFDI. The distributed foundation impedance is similar to the modulus of subgrade reaction. It consists of a complex diagonal matrix which is calculated by dividing the subgrade reaction forces by the corresponding subgrade displacements at each foundation interaction degree-of-freedom for each frequency of analysis.
The program reads the structural information from Tape 4 and the un-interpolated transfer functions on Tape 8 from SSI analysis and, in the case of seismic analysis additional un-interpolated transfer functions on Tape 8s from scattering analysis. This information is then used to calculate the complex-valued impedance functions at each interaction degree-of-freedom for each frequency of analysis on Tape 6. (back to top)
The program module FRMFDI reads the uncoupled foundation impedance generated by the program module DISIMP and calculates the distributed frequency-dependent foundation impedance (FDFI) model on Tape FDI. The information on Tape FD” may then be input into the program module FBASE (through input data file) to calculate the SSI response in the frequency domain using the distributed foundation impedance. However, Tape “xxx_t.FDI” is specifically developed for input to the program module FRMKMC to calculate distributed parameter foundation impedance model (KMC) for time domain SSI analyses.
The input to program module FRMFDI consists of the distributed impedance functions provided in the global directions from input Tape 6’s. The FDFI results are saved on Tape FDI. (back to top)
The program module FRMKMC reads the distributed frequency-dependent foundation impedance (FDFI) functions generated by the program module FRMFDI on Tape “FDI” and calculates the equivalent distributed parameter foundation impedance (DPFI) model in terms of constant foundation spring, mass and dashpot on Tape KMC. The information on Tape “KMC” may be input back into the program module FBASE (through input data file) to calculate the SSI response in the frequency domain using the KMC. However, Tape KMC is specifically developed for input to time domain analysis programs for SSI response analyses. (back to top)
The program module FSUM computes the total inter-story forces and moments in the structure. The forces include two horizontal shear forces in the global x- and y-directions and the vertical force in the z-direction. The moments include two overturning moments about the x- and y-axis and the torsional moment about the z-axis. The moments are calculated about a single reference point specified by the user.
The program reads the structural information from Tape 4 and un-interpolated transfer functions from Tape 8 for the structure that has been analyzed. It then calculates the total inter-story forces and moments. For embedded structures, the calculated inter-story forces and moments include the effects of soil reaction forces on the basement walls. For fixed-base structural models, the mass of the fixed nodes are not included in the calculation of the inter-story forces and moments. These additional forces and moments shall be calculated separately and added to the total forces and moments at fixed node elevations. The results may be output in terms of maximum values, values at selected time and time histories of the calculated forces and moments. The input time histories are obtained from Tape “REF” and the time history results are saved on output Tape “IF”.
The transfer functions corresponding to the three components of input motion may be processed simultaneously. The time histories of co-directional responses from input in three directions are then summed algebraically and used to calculate the final response quantities. (back to top)
The program module IMPED computes foundation impedance and compliance functions for a rigid foundation of arbitrary shape supported on soil media or on pile foundations using the transfer functions calculated and saved on Tape 8’s. The program reads un-interpolated transfer functions from Tape 8’s and for each specified frequency calculates the 6×6 foundation compliance matrix associated with 6 rigid body motions (3 translations along the x-, y- and z-axis and 3 rotations about the same axis) at the center of rigid foundation. The foundation compliance matrix is then inverted to calculate the corresponding 6×6 rigid foundation impedance matrix. The calculated compliance and impedance matrices are then printed out.
The user has an option to save and output the selected components of impedance matrix in terms of the calculated frequency-dependent foundation impedance on Tape IMP and constant-valued foundation impedance parameters (KMC) on Tape “KMC”. The information on the above tapes can then be imported to the excel spreadsheet to plot foundation impedance versus frequency or used as input to the program module FBASE (via input data file) to calculate the SSI response in the frequency domain using the FDI and KMC models, respectively. (back to top)
The program module CLUSTR reads Tape 4 generated by the program module HOUSE, re-formats the content of the tape and saves the results in a new Tape CLS in preparation for high performance computing (HPC) in the program modules ANALYS and FBASE of MTR/SASSI Linux Enterprise, Super Computing and Cloud Computing Programs. The CLUSTR module does not require input data file or any input other than Tape 4. Tape CLS replaces Tape 4 as input to ANALYS and FBASE modules. No Tape 5 is generated or saved in the ANALYS and FBASE modules; thus, eliminating the need for large storage and I/O.. (back to top)