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Impell-CLASSI:Program for Soil-Structure Interaction Using Rev 0 to Substructuring Technique
	ML13311A382
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Site:	San Onofre
Issue date:	04/30/1985
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IMPELL -

CLASSI A PROGRAM FOR SOIL-STRUCTURE INTERACTION USING A SUBSTRUCTURING TECHNIQUE Prepared by:

Impell Corporation 350 Lennon Lane Walnut Creek, California 94598 Revision 0 April 1985 8504180242 850415 PDR ADOCK 05000206 P

PDR

CLASSI PROGRAM BACKUP Revision 0 Page i TABLE OF CONTENTS Page 1.0 The CLASSI Program:

General Description 1

1.1 Introduction 1

1.2 CLASSI Substructuring Approach 1

1.3 Determination of Foundation Scattering Matrices and Foundation Input Motion 2

1.4 Determination of Foundation Impedances 3

1.5 Analysis of Coupled Soil-Structure System 3

2.0 The CLASSI Program: An Overview of the Theoretical Formulation 4

2.1 General Equations 4

2.2 Modeling of the Superstructure 4

3.0 Verification Examples 4.0 References 5.0 CLASSI User's Manual

CLASSI PROGRAM BACKUP Revision 0 Page 1 1.0 THE CLASSI PROGRAM:

GENERAL DESCRIPTION 1.1 Introduction In this report, the methodology for the program CLASSI (Continuum Linear Analysis of Soil-Structure Interaction) is described. Much of the CLASSI discussion in this report is found in References 1, 2, 3, 4, and 5. CLASSI is based on a specialized form of substructuring which uses the finite element method to perform the detailed analy sis of the superstructure and uses the continuum mechanis method to calculate the interaction of the foundation with the soil medium and with incident seismic waves. These substructuring procedures are made possible by balancing the forces and moments at the foundation, which serves as the common ground for both the superstructure and the soil medium.

1.2 CLASSI Substructuring Approach The CLASSI substructure approach divides the SSI problem into the following three steps:

a. Determination of the foundation scattering matrices.

b. Determination of the frequency-dependent impedance functions.

c. Analysis of the coupled soil-structure system, using results from steps a and b and the dynamic properties of the structure.

In the first step -- determination of the foundation scattering matrices -- the CLASSI program evaluates the harmonic response of the rigid, massless foundation bonded to the soil and subjected to a given incident seismic wave in the absence of the superstructure.

The free-field motion is then used in conjunction with the complex, frequency-dependent scattering matrix in order to determine the foundation input motion. Details on the development of the founda tion input motion based on scattering matrices for rigid foundations are described in Section 1.3.

In the second step, the foundation impedances corresponding to a rigid foundation on a uniform or layered viscoelastic media are developed. The procedure used for the development of the frequency dependent impedances is described in Section 1.4.

The third step -- analysis of the coupled soil-structure system -

is carried out by CLASSI in the frequency domain. Time history of responses are obtained by inverse Fourier transform techniques.

CLASSI PROGRAM BACKUP Revision 0 Page 2 1.3 Determination of Foundation Scattering Matrices and Foundation Input Motions In the context of the CLASSI approach, the foundation input motion corresponds to the response of the rigid, massless foundation to the seismic environment described by the free-field in the absence of the superstructure. The response of the rigid massless foundation to the seismic excitation can be described by the six-component vector:

AA

f*

Uo (Ax', y' zI AV ey',E z in which A Az,8 represent the translational components of the response, while O, ey. Ez represent the rotational components of the response.

The foundation input motion U is related to the free-field ground motion by means of the complex-valued, frequency-dependent scattering matrix [S(w)]:

U0 = [S(0)]

f(w) where the vector f(w) is the complex Fourier transform of the free field ground motion. At a given frequency, a, each complex number in f(w) corresponds to the amplitude and phase of a wave component of the free-field motion. Each column of the scattering matrix [5(G)]

represents the response of a massless rigid foundation to a given incident wave of unit amplitude. The matrix product [S(o)] f(w) is therefore the response of the rigid massless foundation to a particu lar free-field motion. Thus, in general, the foundation input motion depends on the geometry of the foundation, the characteristics of the soil (material properties and configuration), and the type of wave field assumed for the free-field motion.

For a surface-founded rigid foundation subjected to vertically propa gating shear or compressional waves, the response of the foundation includes only translational components with amplitudes equal to those of the free-field motion on the ground surface. However, if the foundation is embedded, a horizontal component of the control motion consisting of vertically propagating shear waves produces both a horizontal translation and a rocking motion of the massless founda tion. This is primarily due to the scattering of waves from the soil foundation interface and the kinematic constraints imposed on the soil by the rigid foundation.

One resulting effect of embedment on the foundation input motion is that the resulting translational component is modified with respect to the free-field motion. This is in contrast with the case of

CLASSI PROGRAM BACKUP Revision 0 Page 3 surface foundations subjected to vertically incident shear waves, in which the translational response of the rigid, massless foundation has the same amplitude as the free-field motion. The other resulting effect of embedment on the foundation input motion is the presence of a rocking component, which is absent in the case of surface foundations.

1.4 Determination of Foundation Impedances The foundation impedances are complex-valued, frequency-dependent functions which relate the dynamic forces that the foundation exerts on the soil to the resulting soil displacements, i.e.:

Fs(w) = [K(wo)] Us where Fs(w) represents the generalized forces, [K(w)] is the com plex impedance matrix, and Us represents the generalized dis placements. The real part of the complex impedance matrix represents the stiffness of the soil and the imaginary part represents the energy dissipation of the soil, including both radiation and material damping.

For a rigid foundation, the impedances are uniquely defined by a 6x6 matrix relating a resulting set of forces and moments to the six rigid-body degrees of freedom. The foundation impedances depend on the soil configuration and material properties, the frequency of the excitation, and the geometry of the foundation.

1.5 Analysis of Coupled Soil-Structure System The final step in the CLASSI substructure approach is to perform the actual soil-structure interaction analysis. The impedances and scat tering matrices calculated in the previous steps are used to solve the equations of the coupled soil-structure system. For this step, the dynamic characteristics of the structure are used to reduce the effects of the superstructure to six dynamic inertial parameters (modal participation factors) for each mode and a 6x6 rigid-body mass matrix of the structure about a reference point on the foundation where the SSI response is determined. Once the motion of the founda tion has been obtained, the time history response at any level of the structure is computed using Fourier transform techniques.

The method described above permits modeling of the structure to any desired degree of complexity in order to obtain accurate in-structure responses.

CLASSI PROGRAM BACKUP Revision 0 Page 4 2.0 THE CLASSI PROGRAM: AN OVERVIEW OF THE THEORETICAL FORMULATION 2.1 General Equations The formulation presented below is used in CLASSI and is based on References 4 and 5.

Consider the steady-state motion of a rigid massless foundation embedded in an elastic soil medium, subjected to the action of seismic waves and of interaction forces created by the vibration of the total structure. The harmonic motion of the foundation[ U(w)l may be described by six coordinates:

U(w)

= (Ax, Ay, Az' x y' E)T (1)

This generalized displacement vector,{ U1, however, may be represented as the superposition of two displacement vectors (Reference 6)

U(w) =I U

+ U (2)

Where lU*l corresponds to the foundation displacement under the action of the seismic waves (without external forces) andl Uo1 cor responds to the foundation displacement under the action of external forces but in the absence of seismic excitation.

The "foundation input motion," U*3, is related to the generalized driving force, F*, Fy, Fz, Mx, My, Mz, by F (w)} = [Ks] iU},

(3) where [Ks] is the 6x6 foundation impedance matrix. Similarly, the "relative displacement," {Uo3, is related to the interaction force, tFIJ, by I F1} = [Ks] (UQ, (4)

The matrix [Ks] is generally complex and frequency-dependent.

Consider for a moment the case of a single structure placed on a single foundation. The interaction force, FJ, may then be represented as F1J = F t w2[M]U},

(5)

CLASSI PROGRAM BACKUP Revision 0 Page 5 in which a?[Mo]AUI is the inertia force of the rigid foundation, having a mass matrix of [Mo].

The external force, FextT, which is created by the vibration of the superstructure, may be expressed as FexJ 2 [MB(0)]U (6) where [MB(w)] is the frequency-dependent building impedance matrix subjected to base excitation.

Premultiplying, now, equation (2) by [Ks] and combining it with equations (3) and (4), we have

[Ks 1U

= F

+ Fi.

(7)

Hence, substitution of equations (5) and (6) into (7) leads to

[K U

=

F*} + w2[MB(0)]AU1 + w2[M ]4U (8) or, by rearrangement, 2

+ [M

(-w([M0 + [MB(W)]) + [Ks]) U= F (9)

Using equation (9), the foundation motion, U caused by the inter action of seismic waves with the total structure can be determined.

After the unknown, {U}, is determined for each frequency, the com plete deformation and/or stress analysis of the superstructure may be accomplished by simply applying (Uj as the base excitation parameter.

2.2 Modeling of the Superstructure To obtain the matrix [MB(w)] as defined by equation (6), the proce dures described by Lee and Wesley (Reference 5) are used. For base excitation, the equation of motion of the superstructure has the form

-wM] Wt

= iu[C] W + [K] W = 0 (10) in which [M], [C], and [K] are, respectively, the mass, damping, and stiffness matrices that can be formed by standard finite element codes. For the case where six degrees of freedom exist at each node, the relative displacement W may be defined as 1

1 1

1 1 1

N N N N N N T W1 =

Ux, U,

Uz.

Ux, U, Uz x

z x

y z

x, y

x y(11X

CLASSI PROGRAM BACKUP Revision 0 Page 6 while for small vibrations, the total displacement vector Wtj is given by W

= [or]{UI + W,

(12) where fUj is the presently unknown foundation motion defined by equation (1), and [0] is a rectangular matrix defined as

[cf]=

[a21 (13)

[aN in which 1 0 0

0 z -y7 0

1 0 -z 0 x 0

0 1 y -x 0

[

]

0 0

0 1

0 0

(14)

O 0

0 0

1 0

0 0

0 1

2

(-a2[M] + iw[C] + [K]) WI = '2 [M][ct]Ul,

(15) from which the relative displacement, {Wl, may be obtained in terms of the foundation motion, IUf. Assume now that the superstructure possesses classical normal modes and there exists a matrix, [q],

composed of an orthogonal set of eigenvectors which diagonalize [M],

[C], and [K] as follows:

T

[4T][M][4] = [I],

(16)

[T][C][4D] = [ 2wr6

],

(17)

[ T][C][o] = [ 02 (18)

~r The quantitiescor and tr are the modal frequencies and damping values, respectively.

CLASSI PROGRAM BACKUP Revision 0 Page 7 Without further details, it can be shown that the solution( W of equation (15) can be expressed in terms off UT as W3 = [@][X()][4T][M][o]1UI,

(19) in which [X(o)] is the diagonal modal amplification matrix, defined as C2 2&j

[X(A)] =

(20) 1

)+

21 E W2 r c r

~

Before the foundation motion, ku?, and, hence,f WI, can be deter mined, the matrix [MB(w)] must be composed. By summing the inertia forces and moments of each discrete mass of the superstructure, the external forces and moments that the structures exert on the founda tion are F

ext

=

2[o[M]

(21) or, by substituting (12) and (19) into (21),

Fext 2]T[M][] U +

2[()[T[M][]U (22)

Now, let's define

[MBO]

[] T[M][o],

(23) and

[P]T = [a]T (24)

Equation (22) can then be expressed simply as ext

= 0([MBO + [

[X()][0]) I U, (25) in which [MBO] corresponds to the mass matrix for rigid body rota tion and translation about a reference point on the foundation. By comparing equations (25) and (6),

CLASSI PROGRAM BACKUP Revision 0 Page 8

[M B(w)] = [MB 0] + [ffT[X(C0)j[],

(26) thus providing the information necessary for the third subproblem as described.

3.0 VERIFICATION EXAMPLES Introduction This section presents the results of a series of verification examples demonstrating the accuracy of the computer code IMPELL-CLASSI (Refer ence 7). IMPELL-CLASSI performs dynamic soil-structure interaction analy ses of surface-founded structures on a single rigid foundation sitting on a half-space or on a layered viscoelastic system overlying a uniform half-space. The structural model can be of any degree of complexity.

The computer program IMPELL-CLASSI consists of the following three independent modules:

(i) GLAYER, which calculates Green's functions at the surface of a layered viscoelastic half-space.

(ii) CLAF, which calculates the impedance matrix and the input motion vector for the soil foundation system.

(iii) SSIN, which calculates the foundation and structural response in either the frequency or the time domain.

Modules GLAYER and CLAF are used in the first four verification examples to generate frequency-dependent impedance matrices using different founda tion configurations. The generated impedance matrices are subsequently compared to published closed-form solutions (References 8, 9).

In addi tion, all three modules are executed in Verification Examples 5 through 8 to obtain maximum accelerations or response spectra of a structural system. The generated spectra are compared to spectra generated by the EDSGAP (Reference 10) program.

3.1 Verification Examples by Comparison with Close Form Solutions Verification Example 1: Frequency-Dependent Impedances for Rigid Circular Foundation on a Uniform Half-Space Frequency-dependent impedance matrices were generated for a rigid circular foundation on a homogeneous half-space. The discretization of the circular footing (Radius, R = 65 feet) is shown in Figure 1.1.

A total of 13 square subregions model one quarter of the disk. The properties of the homogeneous half-space are summarized below:

CLASSI PROGRAM BACKUP Revision 0 Page 9 Shear Wave Velocity VS = 1000 ft/sec Poisson's Ratio V = 1/3 Unit Weight of Soil Y= 110 lb/ft 3 Material Damping Ratio of Soil 4= 1.0%

Impedances for all six degrees-of-freedom (three translational x,y,z and three rotational xx, yy, zz) were generated for the following frequencies:

WR f (Hz) w (rad/sec) ao =

0.0 0.0 0.0 0.61 3.84 0.25 1.22 7.69 0.50 1.84 11.54 0.75 2.45 15.38 1.00 3.67 23.08 1.50 4.90 30.77 2.00 6.12 38.46 2.50 7.35 46.15 3.00 8.57 53.85 3.50 9.79 61.54 4.00 11.02 69.23 4.50 12.24 76.92 5.00 Plots of non-dimensional impedance values are shown in Figures 1.2 through 1.5. The closed-form solution values are also plotted on the same graphs for comparison purposes. A list of the plotted values of the IMPELL-CLASSI results is also provided in Tables 1.1 and 1.2. Good agreement is obtained between closed-form and IMPELL-CLASSI results.

Verification Example 2:

Frequency-Dependent Impedances for Rigid Square Foundation on a Uniform Half-Space Frequency-dependent impedance matrices were generated for a rigid square foundation on a homogeneous half-space. The discretization of the square foundation is illustrated in Figure 2.1.

Due to the symmetry of the foundation, only one quarter of the footing was modeled. A total of 25 rectangular subregions were considered in the mesh formulation, as shown in Figure 2.1.

The properties of the half-space are:

Shear Wave Velocity VS = 1000 ft/sec Poisson's Ratio V = 1/3

CLASSI PROGRAM BACKUP Revision 0 Page 10 Unit Weight of Soil Y= 110 lb/ft 3 Material Damping Ratio of Soil

= 5.0%

Impedances were generated for the frequencies shown in the following table. Values of the non-dimensional quantity ao are given, where a =L and L =

and where B and C are defined as shown in Figure 2.1.

wL f (Hz) w (rad/sec) s 0.0 0.0 0.0 1.09 6.82 0.5 2.17 13.63 1.0 3.26 20.45 1.5 4.34 27.27 2.0 5.43 34.09 2.5 6.51 40.91 3.0 7.60 47.72 3.5 8.68 54.54 4.0 9.77 61.36 4.5 10.85 68.18 5.0 11.94 75.00 5.5 13.02 81.81 6.0 14.11 88.63 6.5 15.19 95.45 7.0 16.28 102.26 7.5 17.36 109.08 8.0 18.45 115.90 8.5 19.53 122.72 9.0 20.62 129.53 9.5 21.70 136.35 10.0 The non-dimensional impedance values calculated from IMPELL-CLASSI are plotted in Figures 2.2 through 2.5. A comparison of these values with the closed-form solutions is also demonstrated in the same plots.

All the plotted values are also listed in Tables 2.1 (CLASSI results) and 2.2 (Reference 8).

Good agreement is observed between the two sets of results.

Verification Example 3:

Frequency-Dependent Impedances for a Rigid Rectangular Foundation on a Uniform Half-Space Frequency-dependent impedances were also generated for a rectangular foundation with an aspect ratio of B/C = 4. Figure 3.1 illustrates

CLASSI PROGRAM BACKUP Revision 0 Page 11 the mesh configuration and the dimensions of the footing. Because of the symmetry exhibited by the shape of the foundation, only a one-quarter model was generated with 24 rectangular subregions.

The soil properties used in this example were identical to the soil properties of Example 2. The analyzed frequencies are tabulated below. In the same table values of ao are given, where a=

and L [j-B C V

7r S

a = wL f (Hz) w (rad/sec) 0 Vs 0.0 0.0 0.0 0.54 3.41 0.5 1.09 6.82 1.0 1.63 10.23 1.5 2.17 13.63 2.0 2.71 17.04 2.5 3.25 20.45 3.0 3.80 23.86 3.5 4.34 27.27 4.0 4.88 30.68 4.5 5.42 34.09 5.0 5.97 37.49 5.5 6.51 40.90 6.0 7.05 44.31 6.5 7.59 47.72 7.0 8.14 51.13 7.5 8.68 54.54 8.0 9.22 57.95 8.5 9.76 61.35 9.0 10.31 64.76 9.5 10.85 68.17 10.0 The results of the IMPELL-CLASSI analysis are plotted in Figures 3.2 through 3.5. In the same plots, a comparison is made between results from IMPELL-CLASSI and closed-form solutions of the same problem.

All of the plotted results are also tabulated in Tables 3.1 (CLASSI results) and 3.2 (Reference 8).

Good agreement is obtained between closed-form solutions and IMPELL-CLASSI-generated results.

Verification Example 4:

Frequency Dependent Impedance for Rigid Circular Foundation The circular foundation used in Example 1 was reanalyzed with dif ferent stiffness and damping properties for the soil.

The new soil properties are:

CLASSI PROGRAM BACKUP Revision 0 Page 12 Shear Wave Velocity VS = 2000 ft/sec Poisson's Ratio V = 1/3 Unit Weight of Soil Y = 100 lb/ft 3 Material Damping Ratio of Soil 4 = 5.0%

The foundation mesh was identical to the one used in Example 1. The model is shown in Figure 4.1.

The analyzed frequencies are tabulated below.

(a0 = wR f (Hz) w (rad/sec) 0 0.0 0.0 0.0 1.22 7.69 0.25 2.45 15.38 0.50 3.67 23.08 0.75 4.90 30.77 1.00 7.34 46.15 1.50 9.79 61.54 2.00 12.24 76.92 2.50 14.69 92.31 3.00 17.14 107.69 3.50 19.59 123.08 4.00 22.04 138.46 4.50 24.49 153.85 5.00 Figures 4.2 through 4.5 illustrate the results of the analysis using IMPELL-CLASSI and closed-form solutions.

Table 4.1 contains the results of the IMPELL-CLASSI analysis.

3.2 Verification Examples by Comparison with Other Codes Verification Problem 5:

Structural Model on a Uniform Elastic Half-space In this example, a simple structural model (consisting of two lumped masses) connected to a rigid massless circular footing on homogeneous half-space was analyzed. Figure 5-1 shows the site profile and structural model.

The results of the CLASSI analysis are compared with the results obtained using the SASSI program. The input motion used is composed of vertically propagating shear waves.

CLASSI PROGRAM BACKUP Revision 0 Page 13 The structural frequencies of the model are 5.45 Hz and 13.59 Hz (obtained using Impell's general purpose linear analysis program, EDSGAP).

Comparison of Results Between CLASSI and SASSI A comparison of peak accelerations obtained from the two programs are summarized below:

Peak Acceleration (ft/sec2 Location SASSI CLASSI

% Diff.

Basemat 1.075 1.070 0.5 Node 1 3.117 3.112 0.2 Node 2 4.349 4.338 0.3 Excellent comparison is seen between results obtained from the two methods.

This verification problem verifies the correct formulation of the half-space, as well as the solution of the coupled soil-structure system of equations. Identical results are obtained using SASSI and CLASSI. These two codes employ completely different analytical formulations and solution techniques to solve the SSI problem.

Therefore, this problem benchmarks the two codes.

Verification Problem 6:

Structural Model with Massless Foundation on a Layered Viscoelastic Soil System The same structural model as used in verification Problem 5 is used.

The soil consists of a soil layer, 100 ft thick, overlying a visco elastic half-space. The top soil layer has a material damping ratio of 0.02. The corresponding value for the half-space is 0.01.

The soil model is shown in Figure 6-1.

The system is analyzed for vertically propagating shear waves.

Properties for each layer are shown below.

Soil Material Properties:

Layer 1 Vs= 2000 ft/sec V -

G = V2P V = 4000 ft/sec G = 20002 x 2 = 12.422E6 p

32.2 thickness = 100'

CLASSI PROGRAM BACKUP Revision 0 Page 14 Y= 100 pcf 4-0.02 M-2G 49.689E6 -2

12.422E6 0.333 2(M-G) 2 (49.89E6 -

12.422E6)

Half-Space Vs= 3000 ft/sec V = 6245 ft/sec p

y= 125 pcf G = V2 p

= 30002 125

= 34.938E6 2

2 25 M = Vp = 62452 x

= 151.398E6 p

32.2

= 151.398E6 - 2 x34.938E6 = 0.35 2(151.398E6 - 34.938E6)

Comparison of Results Between CLASSI and SASSI Peak accelerations obtained from CLASSI are compared with those obtained with SASSI in the table below.

Peak Acceleration (ft/sec2)

Location SASSI CLASSI

% Diff.

Basemat 1.061 1.077 1.4 Node 1 3.056 3.102 1.5 Node 2 4.269 4.320 1.2 This problem verifies the solution of a system consisting of a structure sitting on a soil layer overlying a half-space and subjec ted to vertically propagating shear waves. The results are compared with solution obtained by the SASSI Code; both solution are found to be within 2%.

Verification Problem 7:

Structural Model on Foundation with Mass on a Multilayered, Viscoelastic Soil System In this example, the following changes were made to the example in Verification Problem 6:

A soil profile corresponding to a layered site was chosen.

CLASSI PROGRAM BACKUP Revision 0 Page 15 The soil consists of two layers and half-space.

The mass of the foundation was included.

The soil profile is shown in Figure 7-1.

The first and second layers of soil have depths of 20' each. The soil properties for each layer and the half-space are given below.

Layer 1 depth = 20' Vs= 800 ft/sec V = 1600 ft/sec p

V= 100 pcf; 4= 0.06 G = V2 p

= 8002 x 10 1.987577E6 s

32.2 M = 16002 x 100 = 7.9503E6 V=

= 0.333 Layer 2; depth = 20' Vs= 1600 ft/sec V = 3330.7 ft/sec p

Y= 125 pcf G = V2 P

= 16002 x 100

= 9.9378E6 M = 3330.72 x 125 = 43.065E6 X32.2 U= 0.35; 4= 0.04 Halfspace Vs= 3000 ft/sec V = 6245 p

Y= 125 pcf V= 0.35

= 0.01

CLASSI PROGRAM BACKUP Revision 0 Page 16 Mass Matrix (input into CLASSI)

Radius = 42 ft Thickness = 7 ft 150.0 M =

(42) x 7 x 1

32.17 S= 1.809 x 105 lb sec/ft 3

3 bd 3 84(7 )

4 Iyy Ixx T1 2401.0 ft A = A =84 x 7 588 ft2 x

y 2

5 2401 Mass moment of inertia about x & y axes = M2r

= 1.809 x 10 x 588

= 7.386 x 105 lb. sec 2 ft Mass moment of inertia about z axes = 2 x 9.386 x 105 = 1.477 x 106 lb/sec2 ft Comparison of Results Between CLASSI and SASSI Peak accelerations obtained from CLASSI are compared with those obtained with SASSI in the table below.

Peak Acceleration (ft/sec2)

Location SASSI CLASSI

% Diff.

Basemat 1.634 1.711 4.5 Node 1 4.063 4.237 4.1 Node 2 5.395 5.589 3.5 In conclusion, the SSI solution of a system consisting of a structure sitting on a multilayered, viscoelastic system has been analyzed using the CLASSI code, and results compared with SASSI results. The maximum difference is observed to be 4.5%. This is acceptable given the completely different formulations and implementation of the SASSI and CLASSI methodologies.

CLASSI PROGRAM BACKUP Revision 0 Page 17 Verification Example 8:

Single Square Foundation on Viscoelastic Halfspace -- Full Model This verification problem is developed to compare the SSI responses obtained from CLASSI with those obtained from EDSGAP. Because of the use of a high value for shear wave velocity for the soil, a direct comparison with results from a fixed base analysis is feasible. For this purpose, a full 3-0 structural model was developed. The structure is founded on a square rigid basemat on a viscoelastic half-space. This model is shown in Figure 8-1.

The structural model has eccentric lumped masses to develop full 3-0 behavior. Other relevant parameters for the half-space are:

Shear Wave Velocity Vs = 10000 ft/sec Poisson's Ratio V = 0.35 Unit Weight Y = 100 lb/ft 3 Hysteretic Damping p = 5.0%

A 0.67g acceleration time history was used for the SSI analysis in the horizontal x-direction. The control motion consists of verti cally propagating shear waves and is applied in the free field at the ground surface level.

The masses used are shown in Table 8.1.

The stiffness properties of the beams used are shown in Table 8.2.

The table below presents a comparison of maximum basemat accelera tions and structural peak accelerations obtained from CLASSI and EDSGAP at three locations. Response spectra was also generated at the same locations. These are shown in Figures 8.2, 8.3 and 8.4.

The results show excellent correlation between the two analyses.

Comparison of Accelerations from CLASSI and SASSI Maximum Accelerations (g)

Node No.

CLASSI EDSGAP 2

0.549 0.667 5

1.065 1.027 8

1.497 1.454

CLASSI PROGRAM BACKUP Revision 0 Page 18

4.0 REFERENCES

1. J.E. Luco, Linear Soil-Structure Interaction, Lawrence Livermore National Laboratory, Livermore, California, UCRL-15272, 1980 (included in Reference 2).

2. J.J. Johnson, Soil-Structure Interaction: The Status of Current Analysis Methods and Research, Lawrence Livermore National Laboratory, Livermore, California, UCRL-53011, NUREG/CR-1780, 1981.

3. Wong, H.L, Dynamic Soil-Structure Interaction, Earthquake Engineering Research Laboratory, EERL 75-01, California Institute of Technology, Pasadena, California, 1975.

4. Wong, H.L., Luco, J.E., "The Application of Standard Finite Element Programs in the Analysis of Soil-Structure Interaction."

5. Lee, T.H., Wesley, D.A., "Soil-Foundation Interaction of Reactor Structures Subjected to Seismic Excitation." Proceedings 1st Conference Structural Mechanics in Reactor Technology, Berlin, Germany, Paper K 3/5.

6. Luco, J.E., Wong, H.L., Trifunac, M.D., " A Note on the Dynamic Response of Rigid Embedded Foundations," International Journal of Earthquake Engineering and Structural Dynamics, 4, pp. 119-128.

7. IMPELL-CLASSI, User's Manual, Version 0, Impell Corporation.

8. Wong, H.L., and Luco, J.E., "Tables of Impedance Functions and Input Motions for Rectangular Foundations," Report No. CE 78-15, Dept. of Civil Engineering, University of Southern California, December 1978.

9. Veletsos, A.S., and Verbic, B., "Vibration of Viscoelastic Founda tions," Earthquake Engineering and Structural Dynamics, Vol. 2, pp.87-102, April 1973.

10. EDSGAP, User's Manual, Version 3/1/80, Impell Corporation.

Y

12) (137 (9)

(10) (11)\\

(5s()

(7)

(8S

( ) (2)

(3)

(4) o.a o.aE. ~

~~-4~

f= 65 ft.

NOTE: BASEMAT IS ASSUMED RIGID AND MASSLESS FOR THIS PROBLEM Figure 1.1 Verification Problem 1:

Foundation Model

F H E SYM6OL

0 CU1RR SPUN1)S TJ JGRkEE OF FPE[ IOM NU M R

THE SYMBOL

+

CU KESPONJS TA] DEGRLL (F

F REFEOM NUMfilR 2

THE SYMBUL X CURRtSPINDS Ti DEGREE uF FREEDOM NUMEER 3

.1002+02 1---------------------------------------------------

1%

1 0

+

IMPELL-CLASSI I

xI I

X I

.750E+01 1

1 L

Reference 4 I

I II I

I S

x x

I I

'X I

I.

\\

I

.500E+01 I

I K

K I

I I

'~' + - - -

- + -

-I I

I I

XI I

I I

II

[

x x

I

.250E+01 I

I I

I LI I

I I

I

[

I I

I

0.

1---------------------------------------------------------------------------------------------------I U.

50+01

.L30E+02 FREQUtNCY Figure 1.2 Verification Problem 1:

Comparison of Impell-CLASSI vs. Reference Impedances for Circular Foundation

THE SYMd0L 0 CORRt-SPONjS Tj CFGRcE JF FREt JOM NUMIlt 4

THE SYMdOL

CORRESPON3S TU DFGRI-E UF FREE)UM NUM'[R 5

.IOOE +o 1--------------------------------------------------

0

+ IMPELL-CLASSI I

Reference ci

.750E+01 I

I I

II II I

I I

I

.500E+01 I

0 I

I I

.20E0 z1 FN Figure 1.3 Verif ication Problem 1: Comparison of Impell-CLASSI vs. Ref erence Imoedances for Circular Foundation

)AMP ING, iH IMAGINARY RAtT U

THE SYMBOL U CORKEPONDS TO DcGRFE OF hRELDOM NUMBEi2 R I

THE SYMdOL + CuiRI-5PONJS TU DEGRE-OF FREFO0M NUNRER 2

THE SYMBOL X CURkLSPUNDS TO DEGREE (OF FREEDOM vUMBER 3

1%

. 100E+02 I----------

I--------------

I II I

I 01

+

IMPELL-CLASSI x

Reference I I

.750E+U1 I

IL IL I

I X

I 1_

lx I

I

-x x-I

.500E+01 I

x x

I I

[20E0 I

I I

I

+

I ---------

I I

I

.250E+01 I

I

[

I I

(

I 1

I I

I

).

X------------------------------------------------I------------------------------------------------------------I G.

. 00E+'L

.130IE+.02 FREQUCY Figure 1.4 Verification Problem 1:

Comparison of Impell-CLASSI vs. Reference Impedances for Circular Foundation

) A MP IN G, TilA L

-1 K.7TP-FNK10 THE SYMBOL L) COIrPJNDS IT1 i I-GRUi O

FREEDOM NUMijE R THE SYMBOJL CdPlRL-IVJN4JS TO flEGkEFL ijF F REFIM NiJM5L 5

/

.E+01 I

I 0

+ IMPELL-CLASSI I

I I

Reference 9

I I

.150E+01 I

II I

-I I

.E I

,+

.10E+0I I

I I

1

1.

V I

I I

I 1

I I

]

I I

I

- I 3*

x 25001

. L0E+0

0.

r UEC Fiue1.ieifiainErbem14opaio oOmel-LSI s

efeec ImeacsfrCrclrFudto

SUMMAKT OF IMPRi1vT TFcAS STIFFNESS TERMS FAR D.O.P.S 1

2 3

4

%0.

0.000

.485Et+0

.485F+01

.613F+0

412+ut.412"01

537F+0L 40=

249

.48 3F+1

.4d3E+0)1

.609F*01

.405-OL1

.406E+01

.531F+01 4

.498

480E+01

.463E*01

59,4E+01

.389Ef+01

3j.9Eto

.514E+ut

.751

.47!j:+0L

.475E+01

.574F+0i

.3t67E01

.3b7E#(OL

.490E+01 A0=

L.001 4tPL+0L

.4b8E+O

.552F+01

.344t+01

.344E+U

.465E+01 40=

1.499

.453C+01

.453F+01

.4BLE+01

.304L+01

.304

-1.19E+01 40=

2.001

.440E+01

.440E#0L

.395t*01

.2n9.+ 01

.2096+01

.380E+0L 40=

2.499

.432E+01

.432+0 1

.319E+01

.235L+01

.235t+01

.349E+01 AD=

3.00Z

.429E*01

.4?9L01.273L+01

203E+01

.203E+0L

.125E+01 4o=

3.500

.425E+UL

.425E+01

.265L.+0

.173t*01

.173E*0L

.309E+01 43-3.998

.a418E+01

.418V+01

.zd5E+01

.14BE +01

.143E*01

.302E+0L.

43=

4.501

.405E*0I

.405E+01

.312F+01

.131E+01

.300E+01 40=

4.999

.390E+01

.33ot*01

.121E+01

.300E+OL DAMPING TkMS FOR D.O.F.S 1

2 3 4 5 6 40-0.000 U.

a.

0.

D.

0.

40

.249

.322E+01

.322F+01

.53bE+01

.399E+00

.394E00

.482E+00 40=

.498

.302E+01

.302t-+01

.511E+01

.355E+00

.355'E+00

.384E+00 k3.

.751

.297E+01

.297E+0l

.506Et0L

.46 LLtoU

.#51t000

.471E+00 40=

1.001

.296E+01

.296F+01

.507E+01

.589F+00

.539E+00

.597E+00 40=

1.499

Z98E+01

298E+01

.521E+01

.807E+00

.841[+00 40=

2.001

.303t+uL

.303E0*l

.546E+01

.964E+00

.103E+01 40=

2.499

.307E+0L

.3071:+01

.57bE+01

.108F+01

.1086+01

.L18E+0i 40=

3.002

.309E+01

.3090+01

.605E+01

.11L+01

.116aE*OL

.130E+0L 40=

3.500

.309E+0L

.309E+01

.627E+01

.127F+01

.127E+01

.139E+01 40-3.998

.308E+01

.639E+01

.135F+01

.135E+01

.14b(E+OL 40-4.501

.308+0L

.30812*01

.643E+01

.143E+01

.500E+01 4J-4.999

.309E+01

.643E+01

.149E+01

.149Et0L

.152E+0L Table 1.1 Verification Problem 1:

Impell-CLASSI Impedances for Circular Foundation

y I =65ft 0.14.1 21 22 23 24 25 0.15.

16 17 18 19 20 0.221 11 12 13 14 15 I = 65 ft 0.231 6

7 8

9 10 0.261 1

2 3

4 5

0.261 0.231 0.22 0.1510.144 Figure 2.1 Verification Problem 2:

Foundation Model (Quarter Model)

S TI F N S, -

-T F. L -?A X rHE SYMBOL (I COJKRESPANMS T1 DEGRE OF F:

)fOM

'UMet.R I

rHE SYMBOJL + CiUIRRISPOWIS TA tuGI:E~ IF kc 1r0m, NU Pti r R

[HE SYMBOL X CURKESPONUS TJ DEGREE OF FREFUOM NUMHER 3

.100E +02 I-----------------

I I

01 I

O

+

IMPELL-CLASSI x

Reference 8

.750E+01 I

Ix xI I

I II I"I IN II x I I \\

II I\\I

-- +-

+'

I

.250E+01 R

Part) fd I

I I

x I

I XI I-------------------I-------------------------------------------------I X

. LLO.:u

.220E +02 FIGURE 2.2 Verification Problem 2:

Comparison of IMPELL-CLASSI vs. Reference 8 Impedances (Real Part) for Square Foundation (B/C

= 1)

THL SYMROL 0 CiR LtSPJN0S TO D: GR-r THE SYMBOL

CORRSPONDS TO DEGRLE OF FRFLOOM NUMbt R 7

THE SYMdUL X CURRESPUNJS T]

OEGREE OF FREE)OM NUMBEIR b

.100E+02 I-------------------------------------------------------------------------------------------------

I

.I 0

+

IMPELL-CLASSI L

X S----

Reference 8 I

I I

I

.750E+01 I

I I

II I

I I

Is I

.500E+01 1

0-I I

~

I I

x x

x l_

I I

.250E+01 I

I I

C.

.LLOE+02

.220E*02 FREQUENCY FIGURE 2.31 Verification Problem 2:

Comparison of IMPELL-CLASSI vs. Reference 8 Imoedances (Real Part) for Sauare Foundation (B/C = 1)

)AiP ING, I-iE IMAGINARY PART OF THE U

N r-THL SYMBdL G CUkRESPJN0S TJ OEGRDE UF FREEDOM NUMBER I

THE SYMBOL

CORRESPlNJS TO DEGREE JF FREEDOM NUMbtR

?

THE SYMBUL X CURRE)PNDS TO DEGREF OF FREEDOM NUMBER 3

.IOOE+02 I -----------

I I

1 I

0 I

0

+

IMPELL-CLASSI xI I

I I

I Reference 8

' I I

.750E+01 I

I I

I 1

I I

I

(

-- )

K-

-V I

1 I

I I

.50 E+01 I

1 I

]

I I

I

]

I I

+-------

I I

+

+-----

+----+-------------

+-----------+----------

4 I

.250E+01 1

I I

J1 1

I I

I F;.

. LLO'-+UZ,

.220E+402 FIGURE 2.4 Verification Problem 2:

Comparison of IMPELL-CLASSI vs. Reference 8 Impedances (Imaginary Part) for Square Foundation (B/C = 1)

)AMPING, frI IMAINARY PART UF THE IiPEDANC c iaL-T LE I

U I

THE SYMBOL 0 LRktSP;]NjS T

DELGREF OF FkEEDOM NUMIiER 4

THE SYMBiUL CURRESPANDS TO DFGkEF OF FRi-EEDM NUMBER 5

THE SYMbOL X CURRESPJNDS Ti DEGREE OF FREEDJUM NUMBER b

.200E+01 I-------------------------------------------------I-------------------------------------------------

0

+

IMPELL-CLASSI Lx XI Reference 8 I

I I

~x-----

+ 1

.150E+01 I

,-+

1 1

I

. 100E +0 1 I

I I

.7 1

I I

I R

I I

I

[

I

.50 +0 I

I I

I FIGURE 2.5 Verification Problem 2:

Comparison of IMPELL-CLASSI vs. Reference 8 Impedances (Imaainary Part) for Sauare Foundation (B/C =1)

S'JMMARY iF IMPORTANT TLRMS STIFFNESS T[ RMS FJR D.OI.FS 1 2 3

4 5

40=

0.000

.4P,8L-+0L

.86L+01

.616E+01

.424*0+1

.429E+01

.j71E+01 40=

.502

.478E+01

.47FUuL.592E*0L

.4041+01

.404E+01

.545E+01 40=

1.000

.4b3c+01

.4b3E+,1

.542E+01

.360L+01

.36OE+01

.495E*01 40=

1.502

.44 7K:+01

.447F+01

.'72F+01.319F+01

.319E+01

.4481E+01 40=

2.000

.435L-+01

.435E+01

.4002+01

.2t51+01

.285E+01

.411E+01 40=

2.502

.428E:+0 1

.428E+,1

.341E+0L

.254E+01

.254E*01

.382E+01 40=

3.000

.424E+01

.424+01

.303F+01

.228E+01

.2282t01

.363E+01 40=

3.502

.417E#01

.417L+01

.285E+01

.2041+01

.204E+01

.352E+01 A= 4.000

.407F+0L

.407E+01

.281E+01

.185L+01

.145E+01

.350E+01 40=

4.502

.393+01

.393F+01

.28E+01

..169E+01

.169E+01

.352E+UL 40=

5.000

.377E+01

.28dE+01.157L+01

.157E+01

.355E+01 40=

5.502

.362E+01

.362L+01

.282E+01

.150F+01

.150E+01

.356E+01 4u=

6.000

.35LE+0L

.351E+01

.274E+01

.148E+01

.354E+01 A0=

6.502

.342.E+0

.342E+01

.257E+01

.148F+01

.148+01

.350E+01 40=

7.000

.33tut+01

.33tF+01

.230F+01

.150E+01l

.150E+01

.343E+01 40=

7.502

.329E+01

.330E+01

.194E+01

.152E+01

.337E+01 A=

8.000

.322E01.3221+01

.153E+01

.152E+01

.331E+01 40=

8.502

.313E+01

.110E+01

.149E+01

.325E+01 AO=

9.000

.302E+01

.301E+01

.709E+00

.1421+01

.142E+01

.319E+01 40=

9.502

.290E+01

.291E+01

.390E+00

.1321+01

.132E+01

.312E+01 40= 10.000

.279E+01

.148L+00

.120E+01

.304E+01 DAMPING TERMS FOR 0.U.F.S 1

2 3

4 5

b 40=

0.000

0.

U.

0.

3.

0.

40=

.502

.384E+01

.3841+0L

.61E+01

.105F+01

.105E+01

.132E+01 40=

1.000

.339E+01

.564E+01

.951U+00

.951E+00

.L10E+01 40=

1.502

.326E+01

.328L+01

.562E+01

.106E+01

.120E+01 40=

2.000

.325E+01

.325E+0L

.575E+01

.116E+01

.116+01

.132E+01 40=

2.502

.323E+01

.593E+01

.124E+01

.1421E+01 40=

3.000

.320E+01

.608E+01

.131E+01

.151E+01 40=

3.502

.317E+01

.619E+01

.137r+01

.137E+01

.157E+01 40=

4.000

.314E+01

.314E+0L

.624E+01

.142t+01

.142E+01

.161E+01 40=

4.502

.312E+01

.3121+ol

.626E+01

.147E+01

.163E+01 40=

5.000

.311E+01

.311F+01

.625E+01

.1501+01

.150E+01

.163E+01 40-5.502

.312c+01

.3121+01

.622E+01

.1531+01

.153E+01

.162E+01 40=

6.000

.312E+01

.3121+01

.619E+01

.155F+01

.15oE+01

.161E+01 4=

6.502

.312t*01

.312L.01

.61!)E+01

.1571+01

.157E+01

.L60E+01 40=

7.000

.312E+01

.312+01

.613F+01

.15UE+01

.158E+01

.160E+01 40=

7.502

.312E0L

.312E+01

.611L+01

.155E+01

.158E*01

.160E+01 40=

8.000

.311E+01

.3111+01

.610E+01

.157E+01

.159E+01 40=

d.502

.31LL+01

.611E+01

.155F+01

.156E+01

.159E+01 40=

9.000

.310!1+01

.310E+01

.613E+01

.15!3+01

.156E+01

.159E+01 43=

?.502

.310L+01

.310E+0L

.614E+01

.155E+01

.159E+01 40= 10.000

.310t+01

.310F+01

.616E+01

.155E+01

.155E.01

.158E+01 TABLE 2.1 Verification Problem 2: IMPELL-CLASSI Impedance Functions For Square Foundation (B/C = 1)

TABLE 2.2 POISSON's RATIO = 1/3, B/C = 1, DAMPING 5%

AO K11 K15 K55 K22 K24 K44 K33 K66 b.0 489+l 489+0

-399+0 -399-1 435+1 435+0 489+1 489+0 3yq+v 397-1 435+1 435+o 619+1 ulwo+0

>77+1 577+d 0.5 400+1 193+1

-472+0 -552-1 410+1 535+0.

4166+1 1,3+1.

472+0 552-1 41i+1 535+0 595+1 311+1 552+1 671.+d 1.0 4bb+1 341+1

-527+0 229-1 364+1 967+t6 465+1 341+1 527+f6 -229-1 364+1 967+o 544+1 569+1 501+1 111+1 1.5 449+1 495+1

-549+d 127+v 323+1 162+1 449+1 495+1 549+0 -127+0 323+1 162+1 475+1 d60+1 454+1 183+1 2.6 437+1 654+1

-533+0 25io+0 289+1 237+1 437+1 654+1 533+0 -25b+v 269+1 237+1 443+1 116+2 416+1 269+1 2.:

431+1 812+1

-467+0 373+0 258+1 317+1 431+1 812+1 467+k) -373+0 258+1 317+1 345+1 159+2 367+1 363+1 3.o 427+1 966+1

-353+0 468+0 232+1 401+1 427+1 966+1 353+0 -46d+@

232+1 401+1 310+1 184+2 368+1 461+1 3.5 421+1 112+2

-210+0 512+0 2d9+1 4d9+1 421+1 112+2 2140 -512+0 2019+1 489+1 295+1 219+2 359+1 559+1 4.w 411+1 126+2

-671-1 499+0 190+1 560+1 411+1 126+2 671-1 -499+0 190+1 580+1 293+1 252+2 357+1 654+1 4.5 398+1 141+2 524-1 43+0 175+1 673+1 39d+1 141+2

-524-1 -438+0 175+1 673+1 297+1 2d4+2 3bu+1 744+1 5.w 363+1 157+2 131+0 346+0 165+1 767+1 383+1 157+2

-131+0 -346+0 165+1 767+1 306+1 315+2 364+1 827+1 5.j 370+1 173+2 165+0 243+d 161+1 861+1 37+1 173+2

-165+0 -243+0 160+1 861+1 302+1 345+2 366+1 9oi6+1 6.6 361+1 ld9+2 158+k) 151+0 160+1 951+1 361+1 189+2

-156+d -151+0 160+1 951+1 305+1 375+2 365+1 tob3+1 6.5 354+1 265+2 122+0 854-1 163+1 114+2 354+1 205+2

-122+0 -653-1 163+1 114+2 292+1 404+2 362+1 1d6+2 7.6 349+1 220+2 735-1 492-1 167+1 112+2 349+1 220+2

-734-1 -491-1 167+1 112+2 2bd+1 433+2 357+1 114+2 7.5 345+1 236+2 253-1 392-1 170+1 121+2 345+1 236+2

-252-1 -392-1 170+1 121+2 239+1 4b3+2 353+1 122+2 8.1 339+1 251+2

-133-1 512-1 172+1 128+2 339+1 251+2 135-1 -512-1 172+1 12d+2 2w4+1 493+2 349+1 130+2 8.5 332+1 266+2

-391-1 765-1 171+1 135+2 332+1 266+2 394-1 -765-1 171+1 135+2 169+1 524+2 344+1 137+2 9.k) 323+1 2d1+2 1 189+0 167+1 143+2 323+1 211+2 471-1 -199+0 167+1 143+2 138+1 556+2 341+1 145+2 9.5 314+1 297+2

-377-1 140+0 159+1 150+2 314+1 297+2 381-1 -140+0 159+1 150+2 116+1 58,+2 334+1 153+2 10.0 305+1 312+2

-138-1 164+0 150+1 158+2 306+1 312+2 142-1 -164+0 150+1 158+2 161+1 621+2 329+1 161+2

Y

= 260ft 19 20 21 22 23 24 13 14 15 16 17 18 7

8 9

10 11 12 1

2 3

4 5

6

-~x 0.25.

0.20X 0.20-9 0.151 0.129

0. Op Figure 3.1 Verification Problem 3:

Foundation Model (Quarter Model)

THE SYM3OL +

CURki SP.]N S Ti D1 G141 0

FR tt uA U

r THE SYMBOL X CURE SPANDS Ti UEGIKE-OF FRE IOM NUM!L k

. 100E +02 I ---------------------------- - - -

I I

I 0

+

IMPELL-CLASSI I

x I

I X

1 1

Reference 8 I

I I

.750E+UL I

I I

LI I

LI x

.500EO

+0 L 0

I I

I A---

I

-X--

I 0.~~~~

X50[0.I0E0 I

XI I

I I

0.

550E 0o

110E402 FRlt QUE NlY FIGURE 3.,Q Verification Problem 3:

Comparison of IMPELL-CLASSI vs. Reference 8 Impedances Real for Rectangular Foundation (B/C = 4)

THE SYMBUL LUkk1'SPJN1)S TJ Of G~I-E THE SYMBOL X CIlkkESPONDS TO DEGktE OF FkEbJUM NIJMt

.200E+02 I ------------------------------------------------- 1I-------------------------------------------------1 I

I 0

+

IMPELL-CLASSI I

X 1

1 I

I Reference 8 I

- * -I I

I I

I

.150E+02 I

I I

II I

I I

I£ I

I It I

KI I

x

\\

I

.100E+02 I

I 1

-- 5 I

I I

I IN I

I I

. I

OE.

+0 I I

I I

I FIGUREO

3.

VeiiainPolm3Ioprsn fIPL CAS s

eeec I

I I

I--

0 0

0 I.1-------------------

I

.50:+'"

.110tLO+02 FIGURE 3.3 Verification Problem 3:

Comparison of IMPELL -CLASSI vs. Reference 8 Impedances Real Rectangular Foundation (B/C = 4)

rFM SYMBiUL X CUkktSP3NDS TI LtGREL OF

&kiFOLOM 'UMuI R

3 I

0 0

+

IMPELL-CLASSI I

x I

X II I

Reference 8 I

I

.750E+U 1

19 II I

1I t

.500E+01 I

I I

0 I

I 250E +0 1 1

I IN II II II II II S--------I I

I I

I U..51)0[

+01 1 10k +02 FIGURE 3.4 Verification Problem 3:

Comparison of IMPELL-CLASSI vs. Reference 8 Impedances (Imaginary Part) for Rectangular Foundation (B/C =4)

THE SYMBOL

Cu~kzSP~jNijS Tq UF 11F FhkA:DIIM 1UMHI R

THE SYMBOL X CURKtiPINUS Tr) UL SREE OF PWLF DOM NUMBSER

.1 0 +0 1--------------------------------------

I I

0

+

IMPELL-CLASSI I

x II Reference 8 II II

.750E+01 I

1 I

I I

I

/*

I I

x

_,g X

It IX I

I I

I

.2S0E+01 I

I II I

I I

I II I

[

1 1

q1 I

I I

I U.J i

I

~---------------..........

0*

.0E+OL

.L10E+02 FIGURE 3.5 Verification Problem 3:

Comparison of IMPELL-CLASSI vs. Reference 8 Impedances (Imaginary Patt) 'for Rectangular Foundation (B/C = 4)

SUMMARY

31 IMPURTANT TEkRS STIFFNESS TLRMS FOR U.U.F.S 1

2 3

4 i

A0=

U.000

.510i *0to1

.5731 +01

.6 tE +0 1

. 1771 +01

. 137:"-+02

.1I14E +,;

40=

. 498

!)051-+0)1 7 3 F+401 701: +0 1

.1721 +01

.1U23F002

. LG6F+C.,2 N0=

1.005

.5 01+ 01

.598 +01

.6191.01

.163F+01

.10 E*U2

.Y4dE+0L 40=

1.502

.'95L +0L

.031iE+(L

.bf,'9+0L

.154E+01

.472E+01

.900E+01 40=

2.000

.4830.1

.655E+01

.633E+01

.L5F +01

.922+01

.906E+0L 40=

2.498

.467E+0L

.6571-+01

. 513L+01

.1371 +01

.ob7E+01

.927E*01 40=

2.995

.452E+01

.653E.01

.521F+01

.129U+0L

.b021E01

.930F+0L 40=

3.5U2

.4371+o1

.648E+01

.4u71+01

.122E+01

.741L+01

.917E+01 40=

4.000

.424E+0L

.640E+0L

.403E+01

.114+U1

.b)2E+OL

.904E+01 40 4.498

.412E+01

.630+01.356E+01

.107E+01

.b43E+01

.H9t+0L 40s 4.996

.403E+01

.b20E+01

.3LbE+01

.997E +00

.595E+01

.876E+01 40=

5.502

.395E+01

. 00t

+U1

.27E+01

.926E+00

. 52E+01

.616.1+01 40=

t.000

.38d1+01

.5951+01

.263E+01

.850E+0C

.521E+01

..49E+01 43=

6.498

.382E+01

.58LE+01

.255E+0L

.79E+uO

.q99E+01

.336E+01 4D=

6.996

.376E+01

.567E+01

.246E+01

.734E+uO

.487E+01

.82lE+01 40=

7.502

.369E+01

.552E+01

.238E+01

.678U+00

.481E+01

.805E+01 40=

8.000

.301+01.535L+01

.231E+0L

.6291+00

.470lE+01

.789E+01 40=

8.498

.351e+01

.520E+01

.223F+0L

.5871+00

.467E+01

.773E+01 40=

8.996

.340E+0L

.504F+01

.215E+0L

.552E+00

.454E+01

.756E+01 40=

9.503

.326E+01

.489E+01

.209E+01

.524U+00

.440E+01

.741E+01 40= 10.000

.315E+01

.47E+.01

.196E+01

.503F+00

.426E#01

.72bE+01 DAMPING TERMS FOR D.O.F.S 1

2 3

4 5

6 A0=

0.000

0.

U.

0.

U.

0.

43=

.498

.412E+0L

.513E+01

.740E+01

.393F+00

.447E01

.323E+OL

40.

1.005

.356t+01

.446E*01

.6t,3E+01

.275L+00

.502E+01

.333E+01 40=

L.502

.335E+01

.404E+01

.62ZE+01

.262E+00

.556E+01

.371E+01

40.

2.000

.324E+01

. 37LE+OL

.598E+01

.2b5E+00

.57oE+01

.384E+01 40=

2.498

.319t+01

.351E+01

.588L+01

.275F+00

.582+01

.376E+01 40=

2.995

.317E+.1

.340E+01

.5371-01

.2841+00

.590E+0L

.365E+01 40=

3.502

.316E+01

.332E+01

.569E+01

.293E+00

.594E+01

.357E+01 40=

4.000

.316E+01

.326E+0L

.595E+GL

.301F+00 b07E+01

.354E+01 40=

4.498

.316+01

.323C*01

.602E*01

.30-U+00

.613E+01

.351E+01 40=

4.99b

.31bE+0L

.3231+01

.609E+01

.31 1 +00

.bl4E01.349E+01 40=

5.502

.316E+OL

.317E+0L

.61bE+01

.3241+00

.626E+01

.347E+01 40=

b.000

.316E+01

.620E+01

.331E+00

.632E+01

.346E+01 40=

6.498

.315E+01

.314E+01

.623E+01

.338+00.b37E+01

.345E+01 AD=

6.99t

.315E+01

.313E+0L

.625L+01

.3451+00

.b40E+01

.344E+01 40=

7.502

.319E+01

.313E+01

.f26E+01

.353U+00

.b43E+01

.344E+01 40=

8.000

.313E+0L

.312E+01

.627U+01

.359E+00

.b43E+01

.343k401 40=

8.498

.312E+01

.312L+01

.627E+01

.3o8[+00

.bq3E+01

.343E+01 4D=

8.996

.312E+01

.3121+01

. t20E+01

.371V+00

.b43c+01

.343+0L 40=

9.503

.312r+01

.312E+OL

.b15E+01

.377E+00

.b42E+01

.343E01 40=

10.000

.311E+01

.312E+01

.624E+01

.381F+00

.642E+01

.343F+01 TABLE 3.1 Verification Problem 3:

IMPELL-CLASSI Impedances Functions for Rectangular Foundation (B/C = 4)

TABLE 3.2 PoissoN's RATIO = 1/3, B/C = 4, DAMPING = 5%

A0 K11 K15 K55 K22 K24 K44 K33 K66 0.4 567+1 507+0

-547+0 -547-1 136+2 136+1 570+1 570+0 306+d 30*-1 172+1 172+0 679+1 679+w 113+2 113+1 0.5 503+1 2d4+1

-654+f 737-1 123+2 220+1 571+1 254+1 355+0 a90-1 168+1 190+0 668+1 366+1 105+2 168+1 1.0 499+1 352+1

-539+0 291+0 186+2 496+1 516+1 442+1 424+0 d25-1 159+1 263+d 66t+1 657+1 945+1 330+1 1.5 44+1 497+1

-340+0 348+0 973+1 828+1 634+1 600+1 476+0 329-1 150+1 376+0 665+1 923+1 857+1 551+1 2.0 482+1 641+1

-215+0 285+0 923+1 114+2 654+1 734+1 499+0 -3d6-1 142+1 589+

635+1 11d+2 904+1 761+1 2.5 467+1 768+1

-17+

220+o 869+1 144+2 656+1 868+1 503+8 -903-1 134+1 656+8 5u6+1 145+2 125+1 932+1 3.0 452+1 939+1

-191+0 200+0 804+1 175+2 653+1 101+2 501+0 -148+d 126+1 b16+0 530+1 174+2 927+1 10d+2 3.5 437+1 189+2

-193+0 206+0 744+1 2a8+2 648+1 115+2 490+0 -209+0 119+1 979+w 471+1 204+2 i15+1 124+2 4.0 423+1 125+2

-189+0 228+0 694+1 240+2 641+1 129+2 468+0 -271+0 111+1 115+1 412+1 233+2 to2+1 140+2 4.5 411+1 140+2

-167+w 263+0 644+1 273+2 631+1 143+2 433+0 -329+

14+1 133+1 359+1 26b+2 de9+

156+2 5.0 401+1 156+2

-119+0 291+1 593+1 307+2 620+1 158+2 386+O -382+d 967+0 151+1 318+1 381+2 o7q+1 173+2 5.5 392+1 172+2

-588-1 293+0 549+1 341+2 60.9+1 172+2 334+0 -427+d 896+0 170+1 286+1 335+2 0>n+1 10+2 6.0 387+1 187+2

-b34-2 271+8 519+1 376+2 597+1 1U7+2 269+d -462+8 o27+0 1.98+1 274+1 3bd+2 647+1 2kb+2 b.5 381+1 2u3+2 231-1 240+0 498+1 411+2 584+1 202+2 28u+0 -4u6+o 761+8 21u+1 264+1 401+2 o33+1 222+2 7.o 376+1 218+2 3dg-1 211+0 486+1 445+2 570+1 217+2 127+d -406+0 6io+v 232+1 256+1 434+2 lo+1 23b+2 7.5 369+1 233+2 459-1 190+0 480+1 479+2 556+1 231+2 536-1 -494+0 639+b 253+1 251+1 4b+2 dd2+1 255+2 d.0 362+1 248+2 519-1 178+d 475+1 511+2 541+1 246+2

-181-1 -477+d 587+0 276+1 248+1 407+2 7d6+1 272+2 8.5 352+1 263+2 640-1 167+0 465+1 543+2 525+1 262+2

-841-1 -446+0 540+0 2!9o+1 245+1 528+2 77+1 286+2

.k 341+1 278+2 794-1 152+0 453+1 575+2 509+1 277+2

-141+

-483+8 501+0 321+1 241+1 55:9+2 753+1 3d5+2

.9.5 329+1 2!#3+2 9ud-1 129+0 439+1 607+2 494+1 292+2

-187+0

-352+0 470+o 345+1 23b+1 589+2 737+1 322+2

10.

317+1 3dd+2 925-1 184+0 425+1 639+2 479+1 308+2

-226+8

-295+d 446+0 3bb+1 226+1 619+2 722+1 339+2

Y (9) (10)(

111)

(5)

(6)

(7)

(8,

1) 2 (3)

(4) o1a on o

E--4-4--4 f = 65 ft.

NOTEt BASEMAT IS ASSUMED RIGID AND MASSLESS FOR THIS PROBLEM Figure 4.1 Verification Problem 4:

Foundation Model

THE SYMaOL U CuRRLSPONJS TO UEGREL OF FkFVUflM L

THE SYMBOL

+ COkRESPANOS TI DEGRFE IF FNEEuIIM NUMBIR 2

THE SYMBOL X CUkkESPJNUS TII DEGREE OF FREEOM NUMEtiR 3

5%

.100E+02 I1---------- -

11 0

+

IMPELL-CLASSI I

I x

1 II I

I Reference I

I I

x

.750E+0l I

II I1 I

I I+

-X.

I I

I

+

xI

.500E+01 I

I x.x I

LI

.2505+01+02

(-

X LI I

~

I 1

x I

1I Fiur 4.2.-

VeiiainPolm4Ioprsno melCAS s

eeec I

f C

I I

II 3

I----------------------------------------1------------------------------

U.

. L 25E +02

.250E+02 FM JUENCY Figure 4.2 Verification Problem 4:

Comparison of Impell-CLASSI vs. Reference Impedances for Circular Foundation

THE SYMBOL 0 CIkRILSPJNUS TU DEGkIA U

r0 THE SYMBUL

+ CURRESPJNUS T3 DEGREE OF FREE00M NUMBER 5

5%

.100E+02 I -----------

I I

I 0

+

IMPELL-CLASSI I

I I

Reference II

.750E+01 1

KI I

I I

I

.500E+01 I

I I

LI I

I I+I I

I 0*

. L.

+0)?

.250E+02 F4R:OUENCY Figure 4.3 Verification Problem 4: Comparison of Impell-CLASSI vs. Reference Imoedances for Circular Foundation

THE

'iYMIbJL 0 CU'iKR S~jNS Ti flEGkVE OP EKEEUJOM 4UMn! R I

THE SYMBOL

CURRtSPIN)S T I UEGREE AF FRekLJM NUMIBE.R 2

THE SYMBOL X CURKESPONi5L)S TI OthGREE OF FREDOOM NUMBER 3

5%

.100E*0 I ------------------------------------------------------------------------------------------------

I I

0II II

+

IMPELL-CLASSI x

I X

Reference

.750E+01 I

I xI X

A. X X

I

.2500E+01 I

I

+

I I

e -

I I

I

.20E0 I

1:+o 5E0 1

I I

~

Fiur 4-.-4 VeiiainPolm4Ioprsno melCA s

eeec I

I II I

I I

.-----------------------------------------------------------------I-----------------------------------------------.........

0*

.25640;2

. 250E +021 FRE&QUIENCY Figure 4.4 Verif ication Problem 4:

Comparison of Impell-CLASSI vs. Ref erence Impedances for Ci rcul ar Foundation

THE SYMiIOL U CUIRR SPJNDS TO ;OCGkb OjF V F, U

r HE.j YMBOL

+ CORRE SP' )N'JS TJ D)EtoRFE OF F-Rt DOJM NUMid I I----------- ------------------------------------------------- 1 5%

.500E+U1.

1 0

I

+

IMPELL-CLASSI II Reference I

I I

.375E+01 I

I I

II I

I I

I

. Z50E+01 I

+I

+I I

I I

I I-I t

LI I

I I

U.

x 1

0.~~~20 xo+020 zseo FRE:QUENLY Figure 4.5 Verification Problem 4:

Comparison of Impell-CLASSI vs.

Reference Imoedances for Ci rcul ar Foundation

SU4MARY IF IMPORTA4T TERIS STIFFNESS TERMS FOR D.0.F.S 1

2 3

4 5

0=

0.00

.45Et01

.485E+01

.613E+0+

.412r01

.412E+01

.5371-+0 1 43=

.249

.41IF+uL

.46jt01.6041tI

.40[t*01

.A06601.531Etu 40=

.500

.475ctol

.751+01

.5d utU

.it,91+0CI

.339E+01

.j1q*01 40=

.799

.467E+0L 67Lt*1

.5v4E+01

.3b7E+01

.3blfO1

.q91E+01 AO=

1.001

.t57E+U1

.457U+0L

.533E+01

.34510-01

.345E*01

.466E+01 40=

1.499

.437:+kL

.437f+01

.453E+01

.303101.303+01

.419E+01 40=

1.999

.4H6 +01

.418+-40)1

.362L +01

.265F+01

.265E +01

.378E+01 40=

2.499

.404E-01

.404bE+0L

.278F+01

.2301+01

.230E+01

.344E+01 40=

3.000

.393E+0L

.393E+01

.2U01+01

.19tolU

.196E+01

.317E+01 40=

3.500

.32?E+01

.382E+0-L

.194*LiUL

.L65F+01

.165E+01

.29bE+Ul 40=

4.000

369E+01

.369E+01

.191f+01

.137E+01

.286E+01 40=

4.501

.351E+01

.351E+UL

.18IE+0L

.1E+

01

.116C+01

.779E+0L 40=

5.001

.332+01

.332F+01

.205E+01

.10?1#01

.102E+01

.273E+01 DAMPING TERMS FUR D.O.F.S 1

2 3

4 5

6 40=

0.000

0.

D.

0.

a.

0.

0 40=

.249

.78E+01

.478E+01

.739E+01

.172E+01

.221E+01 40=

.500

.3801+01

.380E+0L

.610E+01

.IOLE+01

.101E+01

.124E+01 40=

.749

.349r+01

.349F+.L

.5721+01

.869>+00

.839E+00

.103E+0L 40=

1.001

.335F+01

.5570OL

.901E+00

.90tE+00

.101E+01 40=

1.499

.324F+01

.3241+01

.553E+01

.100,+01

.100E+01

.L10E+0L 40=

1.999

.322E+01

.322U+01

.569E+01

. 1101,+01

.110OE+01

.121F+01 40=

2.499

.322E+01

.3220+01

.592E+01

.118E+01

.11dEL.131E+01 40=

3.000

.321E+01

.3211+0L

.616>+01

.12bE+01

.12b+01

.L40E+01 40=

3.500

.3191#01

.319F+01

.634*101

.133L+01

.133E+01

.147F+01 43=

4.000

.318E+01

.644E+01

.140E+01

.152E+01 40=

4.501

.j1I7+01

.317E+01

.648E+01

.14oF+01

.146E+01

.156E+01 40=

5.001

.317E*0L

.317E+01

.648E+01

.152E+01

.152E+0L

.157E+01 Table 4.1 Verification Problem 4:

Impell-CLASSI Impedances for Circular Foundation

STRUCTURAL PROPERTIES ELEMENTS (8) z Ixx = lyy = 1.0 J = 1.0 As = 0.0 E = 0.6667 X 108 2

M 3.0 x 10 4 V = 0.3

= 0.001 MI

= 3.9 x 104 RIGID BASEMAT 7 fe HALFSPACE Vs = 2000 ft/sec.

Vp = 4000 Ft/sec.

Y = 100 lb/ft 3 V = 0.33

!f= 0.0001 Figure 5.1 Verification Problem 5:

Site and Structural Model

HFSPACE, 'Y= 125 pct, Vs = 3000 fps, Vp = 6245 fps 6= 0.01 p=

125

= 3.88 32*17 vu= 0.35 Figure 6.1 Verification Problem 6:

Site Model

Layer 1, y= 100 pcf, Vs =80uups 20' Vp = 1600 Ips, =0.06 Layer 2. Y= 125 pCf, Vs = 1600 fps 20' Vp = 3330.7 fps&= 0.04 HALFSPACE, Y= 125 pCf'. Vs 3000 fps Vp = 6245 fps,

= 0.01 Figure 7.1 Verification Problem 7:

Site Model

28 8

18 27 7

17 26 6

16 25 5

15 24 4

14 2 _ RIGID BEAMS (TYP) 3 13 RIGID BASEMAT HALF SPACE SOIL Vs = 1000ft/sec b = 100 lbs/ft3 1)t Pro. 35 S=5%

Figure 8.1 Verification Problem 8:

Site and Structural Model

2.0 EDSGAP (Fixed-Base)

IMPELL-CLASSI (Vs= 10,000 fps) z 1 0 LU 0 0a 1

I 1I I

i I

I I

0. 2 0.5

1.

2.

5.

10.

20.

50.

FREQUENCY (HZ)

FOUNDATION NODE, 2X (TRRNSLRTION)

SURFACE FOUNDRTION X-DIR INPUT MOTION 5% ORMPING SPECTRA CLRSSI/SSSI VERIFICATION EDSGP RNRLYSIS (FIXED BRSE)

Figure 8.2

6.0 EDSGAP (Fixed-Base)

IMPELL-CLASSI 5.0 (s

10,000 fps) 3.0

-J CI Q^

UI 1.0 0.2 0.5

1.

2.

5.

10.

20.

50.

FREQUENCY (HZ)

M.IDOLE NODE, 5X. (TRRNSLRTION)

SURFACE FOUNDATION, X-OIR INPUT MOTION 5% DAMPING SPECTRA CLRSSI/SRSSI VERIFICATION CLPSSI ANALYSIS (RIGID SOIL)

Fiqure 8.3

10.0 EDSGAP (Fixed-Base) 9.0

IMPELL-CLASSI 8.0

= 10,000 fps) 7.0 6.0 zi CD 3.0 LuJ

-j LUJ 4.0 3.0 2.0 1.0 20.5

1.

2.

5.

10.

20.

50.

FREQUENCY (HZ)

TOP NODE, 8X (TRANSLATION)

SURFACE FOUNDATION, X-OIR INPUT MOTION 5% ORMPING SPECTRA CLASSI/SPSSI VER.IFICRTION CLASSI RNRLYSIS (RIGID SOIL)

Figure 8.4

NODE I MASS (K-SEC 2/FT) 13 46.63 14 46.63 15 62.17 16 62.17 17 77.71 18 93.25 23 46.63 24 46.63 25 62.17 26 62.17 27 77.17 28 93.25 Total Mass = 777.12 K-SEC2/FT BASEMAT MASS TOTAL TRANSLATION MASS

=

298.14 K-SEC2/FT TOTAL M.0.I. ABOUT HORIZONTAL AXIS

= 161500.0 K-SEC2-FT TOTAL M.O.I.

ABOUT VERTICAL AXIS

= 318000.0 K-SEC2-FT Table 8.1 Verification Problem 8:

Structural and Foundation Masses

SIIFFNESS BEAM I Al A2 A3 3

I1 12 1

129.0 64.5 64.5 330800.0 185400.0 165400.0 2

129.0 64.5 64.5 330800.0 185400.0 165400.0 3

129.0 64.5 64.5 330800.0 185400.0 165400.0 4

170.0 85.0 85.0 365000.0 202600.0 182600.0 5

170.0 85.0 85.0 365000.0 202600.0 182600.0 6

170.0 85.0 85.0 365000.0 202600.0 182600.0 where:

Al = Axial area (FT2)

A2 = Local axis 2 shear area (FT2)

A3 = Local axis 3 shear area (FT2)

J =

Torsional constant (FT4 )

I = Moment of inertia about axis 1 (FT4) 12 = Moment of inertia about axis 2 (FT4)

Table 8.2 Verification Problem 8:

Structural Stiffnesses

5.0 -

IMPELL-CLASSI USER'S MANUAL

CLASSI PROGRAM BACKUP Page 1 5.1 -

PROGRAMS AND SUBROUTINES LIST GLAYER Program for the calculation of Green's functions at the surface of a layered viscoelastic half-space.

GLI Subroutine to read the properties of the soil layers and allocate the core space for the Green's function calculation.

GL2 Subroutine to normalize the dimensionless parameters and to coordinate the calculation of the integrals.

GL3 Subroutine to check the accuracy of the interpolation table for the option IFITER=l KPICK1 Subroutine to select the integration sample points to meet the error requirements.

STATIC Subroutine to compute the static analytical results for a half space with the properties of the top layer.

LAYFRQ Subroutine to convert the amplitudes of the upgoing and downgoing waves and the source terms to displacements at the surface.

CINT Subroutine to compute the coefficients for quadratic interpolation.

CINTR Subroutine to integrate by multiplying integrands by Bessel coefficients.

RFLTRS Subroutine to compute the reflection and transmission coefficients for the layered viscoelastic half-space when K. less or equal to KASYMT.

ASYRT Subroutine to compute the reflection and transmission coefficients for the layered viscoelastic half-space with K is larger than KASYMT.

FRQCFF Subroutine to compute the frequency-dependent reflection and trans mission coefficients for P and S waves when LOWFRQ is not in effect.

LOWFRT Subroutine to compute the frequency-dependent reflection and trans mission coefficients when LOWFRQ is in effect.

GENCFF Subroutine to compute the generalized transmission and reflection coefficients.

CONA2T Subroutine to convert the amplitudes of P and S waves into displacements at the surface.

CLASSI PROGRAM BACKUP Page 2 LWVFA2T Subroutine to convert the amplitudes of (P-S) and (GMASQ

P-S) waves into displacements at the surface.

BESSEL Subroutine to generate Bessel functions of the 1st kind of order zero and one.

IXNCS Subroutine to integrate (K-Kl) ** N

COS (K

R) and (K-K1) ** N

SIN (K

R) on the interval Kl to K2 for N = 0, 1, 2.

BESASY Subroutine to generate P and Q functions in Hankel asymptotic expression.

E Complex function to generate the expanded term in CEXP (Z) = 1 + E(Z FG Complex function to generate the expanded form in CSQRT (1-Z) = 1 -

(Z/2) * (1 + FG).

CEXPD Complex function to generate the complex exponential.

STATZO

Subroutine to compute the static integrand for a half-space with the properties of the top layer.

GHALF Program for the calculation of Green's function in an elastic half-space.

GHO1 Subroutine to check the accuracy of the interpolation table for the option IFITER = 1.

GHO Subroutine to calculate the Green's function by numerical integration.

GH1 Subroutine to calculate the root of the Rayleigh function.

GH2 Subroutine to calculate the Bessel's functions.

GH3 Subroutine to integrate the real function F by Simpson's rule.

GH31 Utility function for GH3.

GH311 Utility function for GH3.

GH32 Utility function for GH3.

GH33 Utility for GH3.

GH4 Subroutine to integrate the complex function F by Simpson's rule.

GH41 Utility complex function for GH4.

GH42 Utility complex function for GH4.

CLASSI PROGRAM BACKUP Page 3 CLAF Program for the calculation of the impedance matrix and the input motion vector for the soil foundation system.

CLAF 2 Subroutine to read the input data and to coordinate the calculation of the impedance matrix and of the driving forces.

CLAF 21 Subroutine to define the limits for digital plotting.

CLAF 22 Subroutine to round-off the limits to ten's multiple of 2, 5, or 10.

CLAF 23 Subroutine to generate the digital plots.

CLAF 3 Subroutine to set up the compatibility conditions for the incident waves.

CLAF 31 Subroutine to calculate the average of the free field motion in a subregion.

CLAF 4 Subroutine to set up the influence matrix.

CLAF 41 Subroutine to calculate the influence functions.

CLAF 42 Subroutine to calculate the three displacements at a point due to uniform loads at a rectangular subregion.

CLAF 43 Subroutine to calculate the static part of the influence function.

CLAF 5 Subroutine to set-up the matrix equations and to solve them.

CLAF 51 Subroutine to form the total forces from the calculated stresses.

COMSOL Subroutine to solve complex systems of linear equations.

SSIN Program for the calculation of foundation and structural response in either the frequency or the time domain.

SSIOl Subroutine to read the initial parameters to prepare the program for dynamic core allocation.

SSIO2 Subroutine to coordinate the soil-structure interaction calculations.

SSI1 Subroutine to write error messages when the allowed core is exhausted.

SSI2 Subroutine to transform matrices and vectors to the reference coordinate system.

SSI31 Subroutine to compute all the structural properties to create the MBO and BETA matrices.

CLASSI PROGRAM BACKUP Page 4 SS132 Subroutine to read the structural properties when the option IFCAL 0 is used.

SS14 Subroutine to compute the impedance matrix and driving force vector by interpolation.

SS15 Subroutine to compute the dynamic part of the building effective mass matrix.

SSI6 Subroutine to perform the inverse Fourier transformation to obtain the time series for each selected location.

SSI7 Subroutine to compute the response of the upper levels from the motion of the basement level.

RFFT Subroutine to compute the finite Fourier transformation.

RFFTI Subroutine to compute the inverse finite Fourier transformation.

FOUR1 Subroutine including the Cooley-Tukey fast Fourier transformation algorithm.

COMSOL Subroutine to solve complex systems of linear equations.

CLASSI PROGRAM BACKUP Page 5 5.2 -

INTERNAL FILES System Unit GLAYER 1

Storage of Green's function tables in binary form GHALF 1

Storage of Green's function tables in binary form CLAF 1

Green's function tables in binary form 10 Storage of impedance matrices and input motions SSIN 10 Impedance matrices and input motions 2

Results of SSI Analyses 11 Scratch File 4

Reserved for reading geometry data 7

Reserved for reading mass matrix 8

Reserved for reading frequencies, damping, and mode shapes 9

Reserved for reading ground motion accelerograms or spectra

CLASSI PROGRAM BACKUP Page 6 5.3 -

CLASSI USER'S MANUAL DATA FOR GLAYER ALL UNITS MUST BE CONSISTENT CARD 1 Columns Format Data Description of Data 1-5 15 NFRQ Total number of frequencies at which the Green'-s function table is to be calculated.

6-10 15 NLY Number of layers (including the underlying half-space) in the soil medium.

11-15 15 IFITER Code defining the procedure to apply for computing the Green's function.

= 0 The Green's function table is computed using the prescribed increment of DR.

= 1 The Green's function table is computed by iteration; the increment of DR is optimized by the program.

16-20 15 LLLL Initial number of points for the Green's function table when the automatic procedure is selected (IFITER = 1). The recommended values are 8 for low frequencies and 16 or more for intermediate to high frequencies.

21-15 IS IPRNT Code for printing the Green's function table.

= 0 The Green's function table is not printed.

= 1 The Green's function table is printed.

CARD 2 Columns Format Data Description of Data 1-10 E10.3 RI Initial radius for the Green's function table.

This value is usually set to zero.

11-20 ElO.3 RE Final radius for the Green's function table. This value must be larger than the maximum distance between two arbitrary points of the foundations.

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- DATA FOR GLAYER (Cont'd)

CARD 1 This card is to be provided only when IFITER = 0, i.e. when the user has to specify the increment values DR.

Columns Format Data Description of Data 1-10 E1O.3 DRMIN Minimum increment value DR to be used in the calculation of the Green's function table. This value governs the total core space needed.

CARD 2 This card is to be provided only when IFITER = 1, i.e. when the automatic procedure is selected.

Columns Format Data Description of Data 1-5 15 NITER Maximum number of iterations allowed. This param eter is used to prevent nonconvergent iterations, and to determine the site of core memory required if the maximum number of iterations is performed.

Warning:

Storage requirements increase in propor tion to 2**NITER. The recommended value for this parameter is 6.

CARDS 4 One or several cards must be provided in order to define the shear wave velocities for the NLY layers at a rate of 8 values per card.

Columns Format Data Description of Data 1-10 E10.3 BETA Shear wave velocities for soil layers in ascending 11-20 ElO.3 layer number, starting from surface layer.

21-30 E10.3 31-40 E1O.3 41-50 E1O.3 51-60 E10.3 61-70 E10.3 71-80 E10.3

CLASSI PROGRAM BACKUP Page 8 DATA FOR GLAYER (Cont'd)

CARDS 5 One or several cards must be provided in order to define the soil mass densities for the NLY layers at a rate of 8 values per card.

Columns Format Data Description of Data 1-10 E10.3 RHO Soil mass densities for soil layers in ascending 11-20 ElO.3 layer number, starting from surface layer.

21-30 E10.3 31-40 E10.3 41-50 ElO.3 51-60 E10.3 61-70 ElO.3 71-80 E10.3 CARDS 6 One or several cards must be provided in order to define the Poisson's ratio for the NYL layers at a rate of 8 values per card.

Columns Format Data Description of Data 1-10 E10.3 POISON Poisson's ratio for soil layers in ascending 11-20 E10.3 layer number, starting from surface layer. Must 21-30 E10.3 be a non-zero value.

31-40 E10.3 41-50 E10.3 51-60 E10.3 61-70 E10.3 71-80 E10.3 CARDS 7 One or several cards must be provided in order to define the damping ratio for the NYL layers at a rate of 8 values per card.

Columns Format Data Description of Data 1-10 E10.3 DAMP Damping ratio for soil layers in ascending layer 11-20 E10.3 number, starting from surface layer.

21-30 E10.3 31-40 E10.3 41-50 E10.3 51-60 E10.3 61-70 E10.3 71-80 ElO.3

CLASSI PROGRAM BACKUP Page 9

- DATA FOR GLAYER (Cont'd)

CARDS 8 One or several cards must be provided in order to define the thickness for the NYL layers at a rate of 8 values per card.

Columns Format Data Description of Data 1-10 E10.3 TH Thickness of the soil layers in ascending layer 11-20 E10.3 number, starting from surface layer. Since the 21-30 E10.3 last layer is the underlying half-space, it is 31-40 E10.3 not necessary to specify a thickness for it.

41-50 E10.3 51-60 E10.3 61-70 E10.3 71-80 E10.3 CARDS 9A These cards are to be provided only when IFITER = 0, i.e. when the user has to specify the increment values DR. NFRQ cards must be provided (one per frequency at which the Green's function table is computed).

Columns Format Data Description of Data 1-10 E10.3 FRQ Frequency at which the Green's function table is to be computed. If a zero frequency is specified, the program will use a value of 0.01 instead (values in Hertz). If NLAYER = 1, input the maximum frequency only. If NLAYER 1, input frequencies in ascending order.

11-20 ElO.3 DR Increment of radius to be used in the calculation of the Green's function table. This value of the increment must be chosen so that the interpolated values have adequate accuracy. DR may be specified different for each frequency (the higher frequencies require a smaller increment).

CARDS 98 These cards are to be provided only when IFITER = 1, i.e. when the automatic procedure has been selected. NFRO cards must be provided.

Columns Format Data Description of Data 1-10 E10.3 FRQ Frequency at which the Green's function table is to be computed. If a zero frequency is specified, the program will use a value of 0.01 instead (values in Hertz).

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- DATA FOR CLAF

- ALL UNITS MUST BE CONSISTENT CARD 1 Columns Format Data Description of Data 1-10 E10.3 G

The reference shear modulus of the soil medium (first layer). It is used to normalize the dimensionless impedance and scattering matrices.

11-20 ElO.3 VS The reference shear wave velocity of the reference soil medium (first layer). It is used to normalize the dimensionless frequency AO = W*CL/VS.

21-30 E10.3 CL Characteristic length of a reference foundation. It is used to render dimensionless both the frequency and the impedances. If CL is chosen to represent the overall dimension of the foundation, e.g. the radius of a circle or the width of a rectangle, the impedance functions will usually have the order of lO**O or 10**l.

G, VS, CL values are used only to generate non-dimensional variables. Arbitrary figures may be input but data on cards 6, 7, and 8B must be consistent with them.

CARD 2 Columns Format Data Description of Data 1-5 15 NUMFRQ Total number of frequencies at which the imped ances and driving forces are to be calculated.

6-10 15 NGRN Maximum number of points for all Green's function tables calculated by GLAYER.

11-15 15 IFCVAR Code defining whether the wave parameters (see card 8B) are frequency-dependent or not.

= 0 Wave parameters are independent of frequency.

= 1 Wave parameters are frequency-dependent.

16-20 15 IPRNT Code for printing the calculated results.

= 0 The calculated results are not printed.

= 1 The calculated results are printed.

CLASSI PROGRAM BACKUP Page 11 DATA FOR CLAF (Cont'd)

ALL UNITS MUST BE CONSISTENT CARD 2 (Cont'd)

Columns Format Data Description of Data 21-25 15 IPLOT Code for plotting (digital plotter) the calculated results.

= 0 The calculated results are not plotted on the computer output.

= 1 The calculated results are not plotted on the computer output.

26-30 15 IDIM Code for normalizing the results.

= 0 The calculated results are printed in dimensionless form.

= 1 The calculated results are printed in physical units. The results stored for further use will always be in dimensionless form.

CARD 3 Columns Format Data Description of Data 1-5 15 IFDOF Array of six numbers specifying which degrees of 6-10 15 freedom of the foundation are wanted. The 11-15 15 applicable code is as follows:

16-20 15 1 = X, 2 = Y, 3 = Z, 4 = XX, 5 YY, 6 = ZZ 21-25 15 26-30 15 CARD 4 Columns Format Data Description of Data 1-5 15 NP Number of rectangular subregions required to form the foundation surface.

6-10 IS NTYPE Number of different types of subregions used. A type of subregion is characterized by a set of (X, Y) dimensions; in order to use the same type, both the X and Y dimensions of the subregion must be identical.

CLASSI PROGRAM BACKUP Page 12 DATA FOR CLAF (Cont'd)

ALL UNITS MUST BE CONSISTENT CARD 4 (Cont'd)

Columns Format Data Description of Data 11-15 15 IFSX Code specifying symmetry of the foundation about the X axis.

= 0 The foundation is not symmetrical about the X axis.

= 1 The foundation is symmetrical about the X axis.

16-20 15 IFSY Code specifying symmetry of the foundation about the Y axis.

= 0 The foundation is not symmetrical about the Y axis.

= 1 The foundation is symmetrical about the Y axis.

21-25 15 NCASE Number of incident waves forms to be considered.

If no input motion is to be calculated, NCASE must be specified as zero.

26-30 15 IMP Code specifying whether the impedances must be computed.

= 0 The impedances are not calculated.

= 1 The impedances are calculated.

31-35 15 NLAYER Number of layers (including the underlying half space) in the soil medium. (See NLY, card 1 of GLAYER.)

CARD 5 Columns Format Data Description of Data 1-6 F6.3 SCALE Scale factor for convenience of input. The values of XB, YB, XH, and YH will be divided by this factor.

CLASSI PROGRAM BACKUP Page 13 DATA FOR CLAF (Cont'd)

ALL UNITS MUST BE CONSISTENT CARD 6 One card must be provided per rectangular subregion required to form the foundation surface.

Columns Format Data Description of Data 1-6 F6.3 XB X coordinate of the centroid of the subject subregion, divided by CL.

7-12 F6.3 YB Y coordinate of the centroid of the subregion, divided by CL.

13-17 15 LET Index specifying the type of subregion, i.e. the set of (X,Y) dimensions of the subregion.

CARDS 7 One card 7 must be provided per type of rectangular subregion, i.e., per set of (X,Y) dimensions.

Columns Format Data Description of Data 1-6 F6.3 XH X dimension of the subject type of subregion divided by CL.

7-12 F6.3 YH Y dimension of the subject type of subregion divided by CL.

CARD 8 CARDS 8A One card 8A must be provided for each frequency at which impedances and input motions must be computed. Thus NUMFRQ cards 8A must be provided.

Columns Format Data Description of Data 1-10 ElO.3 FRQ Frequency at which impedances and input motions must be computed. If the soil medium is layered, these frequencies must be the same as those used in the Green's function program. If the soil medium is a half-space, the frequencies must be lower than the maximum frequency used in the Green's function program. Value is in Hertz.

A zero value does not default to 0.01 (see cards 9A & 9B of GLAYER).

CLASSI PROGRAM BACKUP Page 14 DATA FOR CLAF (Cont'd)

- ALL UNITS MUST BE CONSISTENT CARD 8B One set of cards 8B must be provided for each frequency if IFCVAR = 1, i.e.,

if wave parameters are frequency-dependent. If the wave parameters are not dependent on the frequency, only the first set of cards 8B is sufficient. Each set of cards 8B must include one card per incident wave, i.e., NCASE cards must be provided per set.

Columns Format Data Description of Data 1-10 FlO.4 BOC Ratio of shear wave velocity VS (card one) to apparent wave velocity. For layered soil medium, this ratio will usually be frequency-dependent.

11-20 F10.2 TH Horizontal angle measured in degrees from the X axis to the axis of propagation of the incident wave (positive direction goes from X axis to Y axis).

21-28 F8.3 UL Complex amplitude for the longitudinal component of 29-36 F8.3 the incident wave. First field is for the real part, second field for imaginary part.

37-44 F8.3 UT Complex amplitude for the transverse component of 45-52 F8.3 the incident wave.

53-60 F8.3 UV Complex amplitude for the vertical component of 61-68 F8.3 the incident wave.

Note:

if IFCVAR = 0, the sequence is 8A/8B/8A/8A/8A/...

if IFCVAR = 1, the sequence is 8A/8B/8A/8B/8A/8B/...

Note:

UL, UT, UV are measured on the soil surface, i.e. UV refers to Z axis, and if TH = 0, UL refers to X, UT refers to Y.

CLASSI PROGRAM BACKUP Page 15 DATA FOR SSIN

- ALL UNITS MUST BE CONSISTENT CARD 1 Columns Format Data Description of Data 1-10 E10.3 G

The reference shear modulus. It is taken to be the modulus of the top layer.

11-20 E1O.3 VS Shear wave velocity of the reference soil layer.

21-30 E10.3 CL Characteristic length of the reference foundation (same values as for CLAF).

CARD 2 Columns Format Data Description of Data 1-5 15 NFDN Number of foundations in the soil structure inter action problem. Only one allowed with present version of CLAF (specify NFDN = 1).

6-10 15 NTSTR Total number of structures in the soil structure interaction problem (several structures may be fixed to the same foundation).

CARDS 3 For each foundation in the soil structure interaction problem, a set of cards 3 must be provided. Cards 3 are of two types; a set of cards 3 includes one of each type. (NFDN Sets).

CARD 3.1 Columns Format Data Description of Data 1-5 15 NSTR Number of structures fixed to the subject foundation.

6-10 15 NDFD Number of degrees of freedom of the foundation.

The most general case would include all six degrees of freedom.

11-15 15 IFTIMP Index specifying whether the impedances and driving force vectors need to be transformed into new coordinate system.

CLASSI PROGRAM BACKUP Page 16

- DATA FOR SSIN ALL UNITS MUST BE CONSISTENT CARD 3.1 (Cont'd.)

Columns Format Data Description of Data

= 0 Impedances and driving forces need not to be transformed.

= 1 Impedances and driving forces must be transformed (in that case, all six degrees of freedom must be provided for the foundation).

16-25 E10.3 XF Coordinates of the origin of the local system 26-35 E10.3 YF measured with respect to the reference coordinate 36-45 E10.3 ZF system of the foundation. XF, YF, and ZF are the distances of the translational transformation.

46-55 E10.3 QF Rotation about the Z axis of the local system measured in degrees counter-clockwise to the reference coordinate system.

CARD 3.2 Columns Format Data Description of Data 1-5 15 ITDOF Array of six integer constants specifying which 6-10 IS degrees of freedom of the foundation are 11-15 15 considered. The applicable code is as follows:

16 15 21-25 15 1 = X, 2 = Y, 3 = Z, 4 = XX, 5 = YY, 6 = ZZ 26-30 15 CARDS 4 For each foundation in the soil structure interaction problem, a set of cards 4 must be provided. Each set includes several subsets.

The following sketch illustrates the structure of set 4.

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- DATA FOR SSIN -

CONT.

Set 4 One subset Several cards 4.1.1 4.1 One card 4.1.2 One or several One card 4.2.1 subsets 4.2 One card 4.2.2 One card 4.2.3 One card 4.2.4 Option 1 One or several cards 4.2.5.1 IFCAL = 1 One or several cards 4.2.5.2 One or several cards 4.2.5.3 One or several groups of cards 4.2.5.4 Option 2 One or several groups of cards 4.2.6.1 IFCAL = 0 One or several cards 4.2.6.2 One or several cards 4.2.6.3 One or several cards 4.2.6.4 SUBSET 4.1 Subset 4.1 includes several cards 4.1.1 (the number depends on the number of degrees of freedom of the foundation) and one card 4.1.2.

CARDS 4.1.1 Columns Format Data Description of Data 1-10 E10.3 FIM Mass matrix of the foundation. This matrix is a 11-20 E10.3 square matrix whose dimension is equal to the 21-30 E10.3 number of degrees of freedom of the foundation.

31-40 E1O.3 One card must be provided per row of the matrix.

41-50 E10.3 51-60 E1O.3 CARD 4.1.2 Columns Format Data Description of Data 1-5 15 IFTR Index specifying whether the mass matrix of the foundation needs to be transformed into a new coordinate system.

= 0 The mass matrix of the foundation need not to be transformed.

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- DATA FOR SSIN - CONT.

CARD 4.1.2 (cont).

Columns Format Data Description of Data

= 1 The mass matrix must be transformed (in that case, the foundation must have all six degrees of freedom active).

6-15 E10.3 X

Coordinate of the origin of the local system 16-25 ElO.3 Y

measured with respect to the reference coordinate 26-35 ElO.3 Z

system. X, Y, Z are the distances for the translational transformation.

36-45 ElO.3 Q

Rotation about the Z axis of the local system measured in degrees counter-clockwise to the reference coordinate system.

SUBSET 4.2 One subset 4.2 must be provided for each structure fixed to the foundation.

Each subset 4.2 must include 4 mandatory cards (cards 4.2 1 4.2.2, 4.2.3, and 4.2.4) and a set of cards selected among two optional sets cards 4.2.5 or 4.2.6).

CARD 4.2.1 Columns Format Data Description of Data 1-5 IS NMODE Number of fixed base normal modes for the subject structure.

6-10 15 NDOF Number of components of base excitation to be considered in the soil structure interaction analysis for this structure.

11-15 15 IDOF Array of six integer constants specifying which 16-20 15 components of the base excitation must be con 21-25 15 sidered in the analyses. The applicable code 26-30 15 is as follows:

31-35 15 1 = X, 2 = Y, 3 = Z, 4 = XX, 5 = YY, 6 = ZZ 36-40 15

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CONT.

CARD 4.2.2 Columns Format Data Description of Data 1-5 15 IFTRAN Index specifying whether the dynamic matrices of the structure must be transformed into a new coordinate system.

= 0 The mass matrix of the foundation need not to be transformed.

1 The mass matrix must be transformed.

6-15 E10.3 X

Coordinates of the origin of the local system 16-25 E10.3 Y

measured with respect to the reference coordinate 26-35 E10.3 Z

system. X, Y, Z are the distances for the translational transformation.

36-45 E10.3 Q

Rotation about the Z axis of the local system measured in degrees counter-clockwise to the reference coordinate system.

CARDS 4.2.3 Columns Format Data Description of Data 1-5 IS IFCAL Index specifying the option selected by the user to define the structural data.

= 0 The structural matrices MBO and BETA are not calculated but read in on cards. (This option is convenient for simple analytical beam models.)

= 1 The structural matrices MBO and BETA are computed from the structural data obtained from a discrete structural analysis.

6-10 15 ISSI5 System unit number to read the geometry data (structural nodes coordinates and constraint condition of the nodes).

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CONT.

CARDS 4.2.3 (continued)

Columns Format Data Description of Data 11-15 15 ISSI6 System unit number to read the banded mass matrix of the structure. This data is not used when the option IFCAL = 0 has been selected.

16-20 15 ISSI7 System unit number to read the modal frequencies, modal damping, and mode shapes of the structure.

This data is not used when the option IFCAL = 0 has been selected.

21-25 15 ND Total number of degrees of freedom in the mathe matical model of the structure. This data is not used when the option IFCAL = 0 has been selected.

26-30 15 NNODES Total number of nodes in the mathematical model of the structure. This data is not used when the option IFCAL = 0 has been selected.

31-35 15 NBAND Half bandwidth of the mass matrix of the structure.

For lumped mass calculations, the half bandwidth is equal to 1. This data is not used when the option IFCAL = 0 has been selected.

CARD 4.2.4 Columns Format Data Description of Data 1-5 15 NKEEP Number of degrees of freedom of the structure for which the dynamic response must be computed and stored.

CARD 4.2.5 These cards must be provided only when the option IFCAL = 1 has been selected, i.e., when the dynamic matrices MBO and BETA must be calculated by the program from the structural data provided. Some of those structural data will be read from units ISSIS, ISSI6, and ISSI7 as defined on card 4.2.3.

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CONT.

CARD 4.2.5.1 (to be read from cards)

Columns Format Data Description of Data 1-5 15 KPCOM Index number of degrees of freedom of the struc 15 ture's model where the dynamic response must be IS computed and stored. The index number of a degree of freedom corresponds to the order at which the structural data (modal displacements and mass) are provided for this degree of freedom. NKEEP indexes 75-80 15 must be provided on those cards, NKEEP being defined on card 4.2.4.

CARDS 4.2.5.2 (to be read from unit ISSIS)

One card or data string is to be provided per node in the mathematical model of the structure, i.e., NNODES cards must be provided.

Columns Format Data Description of Data 1-10 FlO.5 X

Coordinates of the node.

11-20 FlO.5 Y

21-30 F10.5 Z

31-32 612 IFCOOR Array of six number constants specifying the con straint conditions of the node in each of the six components. A value 0 is used to express that the corresponding degree of freedom is free, and a value 1 to express that the degree of freedom is fixed.

CARDS 4.2.5.3 (to be read from unit ISSI6)

As many cards, or data strings, must be prepared in order to define the mass matrix of the structure at a rate of 8 values per card. The matrix must be defined in diagonal form, i.e., diagonal terms, then first line parallel to diagonal, etc..

Columns Format Data Description of Data 1-10 E10.3 MMX Mass matrix of the structure.

11-20 E10.3 21-30 E10.3 (ND

NBAND values) 71-80 E10.3

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CONT.

CARDS 4.2.5.4 (to be read from unit ISSI7)

For each node of the structure, a group of cards 4.2.5.4 of both types defined below must be provided, one of type A and as many of type B as needed to define the mode shape. (NMODE Sets)

Columns Format Data Description of Data TYPE A:

1-10 El.3 WN Modal circular frequency defined in radians/second.

11-20 E10.3 DAMP Modal damping in fractions.

TYPE B:

1-10 ElO.3 T

Modal displacements defined sequentially at a rate 11-20 E10.3 of 8 values per card or data string.

21-30 E1O.3 71-80 E10.3 CARDS 4.2.6 These cards must be provided only when the option IFCAL = 0 has been selected, i.e., when the dynamic matrices MBO and BETA are provided by the user. This option should be selected only for simple analytical beam models. All data area read from unit ISSIS.

CARDS 4.2.6.1 Two cards, one of type A and one of type B must be provided for each mode of the structure (NMODE cards)

Columns Format Data Description of Data TYPE A:

1-10 ElO.3 WN Modal circular frequency defined in radians/second.

11-20 ElO.3 DAMP Modal damping in fractions.

TYPE B 1-10 ElO.3 BETA For each mode, the row of the modal participation factors corresponding to that mode must be provided. The dimension of that row is equal to the number of components of base excitation to be considered for the structure.

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- DATA FOR SSIN - CONT.

CARDS 4.2.6.2 As many cards 4.2.6.2 must be prepared to define the MBO matrix at a rate of 8 values per card. (NDOF cards)

Columns Format Data Description of Data 1-10 E1O.3 BMASS Static mass matrix MBO entered row by row.

11-20 ElO.3 21-30 E10.3 71-80 E10.3 CARDS 4.2.6.3 One card 4.2.6.3 must be provided per mode of the structure. (NMODE cards)

Columns Format Data Description of Data 1-10 E10.3 SMODE Modal displacements at the degrees of freedom where the dynamic responses must be computed and stored.

NKEEP values of modal displacements must be

.8 provided where NKEEP is defined on card 4.2.4.

71-80 E10.3 CARDS 4.2.6.4 One or several cards 4.2.6.4 must be prepared per component of the base excitation to be considered for the structure. (NDOF cards)

Columns Format Data Description of Data 1-10 E10.3 ALKP Row of the matrix defined at the degrees of freedom where the dynamic response must be computed and stored. A set of NKEEP values must be provided at a rate of 8 values per card.

71-80 E10.3

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CONT.

CARD 5 Columns Format Data Description of Data 1-5 15 LFT Index specifying the mode of definition of the ground motion and the type of analysis.

= 1 Real time analysis, NCOM time histories of accelerations.

= 2 Frequency analysis, NCOM real, or complex Fourier spectra must be provided; results will be Fourier spectra.

= 3 Mixed analysis, NCOM complex Fourier spectra must be provided; results will be time histories of accelerations.

6-10 IS NCOM Number of components of ground motion (maximum 3) to be combined simultaneously in the analysis.

This parameter causes the same number of driving force tables to be combined together as the total excitation for the foundations; each component is weighted by the Fourier amplitude and phase of the corresponding component of the accelerograms.

11-15 15 NCASE Number of cases of incident waves calculated while deriving the impedance matrices (see CLAF, card 4).

16-20 15 NSTART Component of the input motion table at which the program should start reading. This parameter allows to skip a number of input motion data. NSTART 1.

21-25 15 IEXTPR Index specifying whether extrapolation and input motions beyond FMAX of the impedance tables is allowed or not.

= 0 Extrapolation beyond FMAX is not allowed.

= 1 Extrapolation beyond FMAX is allowed.

26-30 15 ISSI8 System unit number to read the input time histories of acceleration or Fourier spectra.

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CONT.

CARDS 6 Cards 6 are to be provided only when the option LFT = 1 has been selected, i.e., for a real time analysis. Two cards must be provided.

CARD 6.1 Columns Format Data Description of Data 1-10 ElO.3 DT Increment in time (equally spaced) of the acceleration time histories.

11-20 E10.3 SCALE Scale factor for the input acceleration to obtain the correct physical unit for the problem.

21-25 15 NPOINT Number of points in the input acceleration. All NCOM components of time histories must have the same number of points.

26-30 15 NFFT Number of points to use the Fast Fourier Transfor mation. NFFT must be equal to 2 raised at a posi tive power. IF NFFT is greater than NPOINT, zeros will be used to fill the end of the accelerogram.

If NFFT is smaller than NPOINT, only NFFT values will be considered.

CARD 6.2 Columns Format Data Description of Data 1-6 F6.2 FMIN Minimum frequency in cycles/second in the impedance tables generated previously.

7-12 F6.2 FMAX Maximum frequency in cycles/second in the impedance tables. FMIN and FMAX should cover the frequency band of strong motion interest.

(See cards 8 of CLAF.)

CARDS 7 Cards 7 are to be provided only when the option LFT = 2 has been selected, i.e., for a frequency analysis. Two cards must be prepared.

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CONT.

CARD 7.1 Columns Format Data Description of Data 1-10 E10.3 DW Increment in frequency (equally spaced) in radians/second of the input Fourier spectra.

11-15 15 NFRQ Number of frequency points at which the spectra are provided and at which the response spectra are calculated.

16-20 15 IFCMPX Index specifying whether the input Fourier spectra are real or complex.

= 1 Input Fourier spectra are real.

= 2 Input Fourier spectra are complex.

21-25 15 IFCNST Index specifying whether the input Fourier spectra are constant over the range of interest.

= 0 Input Fourier spectra are not constant. The spectra must be read in for all NFRQ points.

= 1 Input Fourier spectra are constant (this option, together with IFCMPX = 1, is useful for determining the transfer functions of the soil structure interaction system, if the input spectra are set to 1).

CARD 7.2 Columns Format Data Description of Data 1-6 F6.2 FMIN See explanations for card 6.2.

7-12 F6.2 FMAX

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CONT.

CARDS 8 (to be read from unit ISSI8)

Cards 8 are used to input the ground motion accelerograms or Fourier spectra.

NCOM sets of cards or data strings must be prepared. NPOIT accelerations or NFRQ spectral values (in case complex spectra are used, 2

NFRQ spectral valves) must be provided for each of the NCOM components of ground motions.

Columns Format Data Description of Data 1-10 E10.3 ACC Accelerations or spectra values for complex spectra; the two values must be provided together.

In case the IFCNST = 1 option has been selected, only one value (2 for complex spectra) must be 71-80 E10.3 provided.

CLASSI PROGRAM BACKUP Page 28 ISSIl = 5 Input Data File ISSI2 = 6 Output Data File ISSI3 = 1 Scratch Disk or Tape File ISSI4 = 4 Scratch Disk or Tape File. File in which final results are stored.

ICLA4 = 10 Impedances from CLA ISSI5 = 15 Geometry (IFCAC = 1), Frequencies, modal damping, modal participation factors, mode shapes (IFCAC = 0)

ISSI6 = 16 Structural Mass Matrix (IFCAC = 1)

ISSI7 = 17 Modal Frequencies, Modal dampings, Mode shapes (IFCAL = 1)

ISS 8 = 9 Input time histories of accelerations or Fourier Spectra.

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4.0 REFERENCES

SUMMARY

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