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Program CONAN

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  • Appendix E

    Program CONAN (CONe ANalysis) user's guide

    The methods described in this book are implemented in an executable program named 'CONAN' (CONe ANalysis), available from the book website, http://www.civil.uwa.edu.au/~deeks/conan/. The program executes the analysis procedures much faster than the MATLAB environment, but the logic of the procedures is identical to those described in Appendix E This appendix is a self-contained user's guide for the program CONAN. Familiarity with dynamic-stiffness coefficients and effective foundation input motion is necessary, but no detailed understanding of the strength-of-materials approach to foundation vibration analysis is required to use the program. The appendix commences with an overview of the program. This is followed by a detailed description of the preparation of input data for the program, including guidance for the construction of suitable layered models. Execution of the program is then described. The final section provides suggestions regarding the use of the results of the program.

    E.1 Program overview

    CONAN is an executable program that can be used to compute the dynamic-stiffness coefficients and/or the effective foundation input motion for surface and embedded foundations. The site may be horizontally layered, and the foundation may be partially or fully embedded. The wall and horizontal base of the foundation are assumed to be rigid (providing accurate results when the foundation is very stiff in comparison to the site, which is usually the case). The foundation is also assumed to be axi-symmetric. If this is not the case, an equivalent radius must be used. The radius of an embedded foundation may change with the depth.

    An input text file is first prepared describing the site and the foundation. The format of this text file is defined in Section E.2. The text file can be prepared using the Microsoft Windows' text editor 'Notepad', which can be accessed through the 'Accessories' submenu of the 'Programs' submenu of the Windows' 'Start' menu, or any other software package capable of creating and modifying text files (which are normally named with a file extension 'txt').

    The CONAN program is then executed, and the input text file describing the problem is pro- cessed. A simple menu is used to direct the program, indicating which coefficients to calculate, which range of frequencies to process, and whether to normalise the results or not.

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  • Program CONAN (CONe ANalysis) - user's guide 171

    The program stores the results into an output text file, and also displays them on the screen as they are calculated. The output text file can also be opened with Notepad, and the results can be printed or transferred to another software package (such as MATLAB or EXCEL) for further processing.

    E.2 Problem description

    Every site is taken to consist of an upper homogeneous half-space (which may have zero shear modulus and density), a number of homogeneous layers of finite thickness (this number may be zero), and a lower homogeneous half-space (which may have infinite shear modulus and density), as illustrated in Fig. E.1. For convenience the upper and lower half-spaces are referred to as 'layers', even though they have infinite thickness. It is possible to specify an upper half-space with infinite shear modulus and density and/or a lower half-space with zero shear modulus and density, although such situations are unusual.

    The radius of the foundation is specified at each layer interface. To simplify the problem description, the foundation radius at the interface immediately below a layer is included in the description of that layer. This radius is specified as zero where the interface is below or above the foundation. If two adjacent interfaces have non-zero radii specified, the radius of the foundation is assumed to vary linearly between them. However, if the radius is non-zero at one interface and zero at the next, the foundation is assumed to extend only to the interface with the non-zero radius.

    For each layer of the site (including any homogeneous half-spaces) the material properties of the soil must also be specified.

    Each line of the input text file describes one layer of the site, and commences with a character or word indicating the type of layer present. Three characters ('F', 'R' and 'H') or the corresponding words ('FREE', 'RIGID' and 'HALFSPACE') are used to specify the properties of the upper and lower half-spaces, and are only used on the first and last lines of the input file.

    ~, (Upper half-space) Interface 1

    _ Layer n _ ,~

    Figure E.1 General description of layered full-space

    Layer 2

    Layer 3

    Layer j

    Interface 2 Interface 3

    < ~ Interface j-1

    Interface j

    ! Interface n-1

  • 172 Foundation Vibration Analysis: A Strength-of-Materials Approach

    'F' or 'FREE' designates a free surface, or a half-space with zero shear modulus and zero density. It is usually used to describe the upper half-space on the first line of the input file. The radius of the foundation on the interface (which in the case of the upper half-space is the free surface of the site) is specified as the second item.

    'R' or 'RIGID' designates a rigid half-space with infinite shear modulus and infinite density. It is usually used to describe an underlying rock layer on the final line of the input file. The foundation radius in this case is specified as zero, and is ignored in the computations.

    'H' or 'HALFSPACE' designates a homogeneous half-space. It is usually used on the last line of the file to describe the underlying half-space, but may also be used on the first line of the file for the analysis of foundations embedded in a full-space. When describing an underlying half-space, the foundation radius is specified as zero and has no effect. However, when used to describe an upper half-space, the foundation radius is significant. After the foundation radius, the input file line specifies the shear modulus (G), Poisson's ratio (v), density (p) and hysteretic damping ratio (() of the soil.

    'L' or 'LAYER' designates a layer of finite thickness, and cannot be used on the first or last line of the input file. The letter or word is followed by the foundation radius at the interface below the layer, the shear modulus (G), Poisson's ratio (v), density (p) and hysteretic damping ratio (() of the soil, and the thickness of the layer (d).

    For each type of layer, different items on the same line are separated by spaces or tabs. It is necessary to use a consistent set of units for r, G, p and d. Newtons, metres and kilograms are usually most convenient, although kilonewtons, metres and tonnes are useful alternatives. The dynamic-stiffness coefficients will be computed in the set of units used for the input data.

    Two examples are now presented illustrating how the input text files are prepared. The first example consists of a surface foundation on a layered site, as illustrated in Fig. E.2. The cor- responding input file is presented in Listing E.1. The second example consists of an embedded

    GI=0 1~

    < G2=28.125x106 N/m 2 ~ / 1.0 m /~/ 1.0 m < > < p2=1800 kg/m 3 ~2=5~ > <

    < > / ,: G3=14"063x106 N/m2 v3=0"3:> I 0.5 m p3=1800 kg/m 3 ~3=5% ,/ <

    / G4=5.625x106 N/m 2 v4=0.333 p4=1600 kg/m 3 ~4=5%

    Figure E.2 Example 1 - Surface foundation on layered site overlying homogeneous half-space

  • Program CONAN (CONe ANalysis) - user's guide 1'/3

    F 1.0 L 0.0 28. 125e6 0.25 1800 0.05 i. 0 L 0.0 14. 063e6 0.30 1800 0.05 0.5

    H 0.0 5.625e6 0.333 1600 0.05

    Listing E.1 Text input file for Example 1

    F 1.0 L 1.0 28.125e6 0.25 1800 0.05 0.i

    L 1.0 28. 125e6 0.25 1800 0.05 0.1 L 1.0 28. 125e6 0.25 1800 0.05 0.1

    L 1.0 28. 125e6 0.25 1800 0.05 0.1

    L 1.0 28.125e6 0.25 1800 0.05 0.i L i. 0 28. 125e6 0.25 1800 0.05 0.1

    L i. 0 28. 125e6 0.25 1800 0.05 0.1

    L 1.0 28 .125e6 0.25 1800 0.05 0.i

    L I. 0 28. 125e6 0.25 1800 0.05 0.1

    L 1.0 28.125e6 0.25 1800 0.05 0.i

    L i. 0 14. 063e6 0.30 1800 0.05 0. 0625

    L i. 0 14. 063e6 0.30 1800 0.05 0. 0625

    L i. 0 14. 063e6 0.30 1800 0.05 0. 0625

    L i. 0 14. 063e6 0.30 1800 0.05 0. 0625

    L 0.0 14. 063e6 0.30 1800 0.05 0.25

    L 0.0 5. 625e6 0. 333 1600 0.05 i. 0 R 0.0

    Listing E.2 Text input file for Example 2

    foundation in a similar site, but with an underlying rock layer. The situation is illustrated in Fig. E.3. In this case the embedded foundation is discretised in the vertical direction, with the actual layers subdivided into fictitious layers such that the thickness d of each layer satisfies (Eq. 5.1a)

    yrc d < (E.1)

    - 5o9

    o9 represents the highest frequency the dynamic model must accurately be able to represent, and c designates the appropriate wave velocity (in general the shear-wave velocity Cs = v /G/p) . This procedure is described in Section 5.1.

    E.3 Using CONAN

    The program is executed in the Windows environment by double-clicking on the CONAN icon. The user is first prompted to enter the name of the input text file containing the problem description.

  • 174 Foundation Vibration Analysis: A Strength-of-Materials Approach

    G,:0 \

    i ! G2=28.125x106 N/m 2 ~-- ~ i ~2 22: ..=o25 ~-- . . . . . . . . . i , i- --! 92 =1800 kg/m3 ~2 =5~ ~__---ZZZZZZZ.~ ! ~Z 2Z:

    G~=~4 O63x~O~ Wm' .~=o 3 ~-----------':'~-- i !-========--

    . . . . . . . . . . I . . . . . . . . . . . . . G4=5.625x106 N/m 2 L , ] i v4=o.333 \ I ( p4=1600 kg/m 3 ~4=5 % ~ I r . ~

    G5= oo p5 =

    Figure E.3 Example 2 - Foundation embedded in layered site overlying rigid base

    0.5m

    .0m

    1.0 rn

    The full name of the file should be entered, including the 'txt' extension, if present. The contents of the text file are echoed to the program window for checking.

    A menu controlling the execution of the program is then presented. Each item in the menu is addressed separately in the following paragraphs.

    1 Dynamic-stiffness coefficient. This option computes the dynamic-stiffness coefficient at one or more excitation frequencies for a chosen degree of freedom. When this option is chosen, the user is prompted to enter the degree of freedom. This is specified using a single character. 'H' indicates the horizontal degree of freedom, in which case the rocking degree of freedom (for an embedded foundation) is constrained to be zero. 'V' indicates the vertical degree of freedom, while 'T' indicates the torsional degree of freedom. 'R' indicates the rocking degree of freedom, but also computes the dynamic-stiffness coefficients for the horizontal degree of freedom and for the cross-coupling between the horizontal and rocking degrees of freedom. The user is then prompted to enter the first excitation frequency (in rad/s), followed by the last excitation frequency. If these are not identical, the frequency interval at which computation is required (the frequency step) is requested. The user is then asked whether or not normalisation of the results is required. If 'N' is entered, for 'No', the results are output in dimensional form, tabulated against excitation frequency w specified in rad/s. If 'Y' is entered, for 'Yes', the static-stiffness coefficient K for the foundation is computed first, and used to decompose the dynamic-stiffness coefficient into the form S (a0) = K [k (a0) + ia0 c(ao) ]. The static-stiffness coefficient is output, while k(ao) and c(ao) are tabulated against the real part of dimensionless frequency, a0 -- o~ro/cs. If for an embedded foundation the radius varies, the largest radius is used for r0. The material properties of the layer below the upper half-space are used to determine Cs, ignoring hysteretic damping. Finally the user is requested to enter the name of

  • Program CONAN (CONe ANalysis)- user's guide 1'/3

    the output text file. As the results are computed, they are written both on the screen and to this output text file.

    2 Effective foundation input motion. When this option is chosen, the user is requested to select between the horizontal 'H' and vertical 'V' degrees of freedom by entering the appropriate single character code. This degree of freedom indicates the direction of the ground motion generated by the earthquake. For a horizontal earthquake the computed effective foundation input motion consists of both horizontal and rocking motions, while for a vertical earthquake it consists of vertical motion only. The user is then requested to enter the control point location. This is the position where the control motion (free field) is to be specified, and can either be on the surface of the site (taken to be at the interface beneath the upper half-space) or on the free surface of a fictitious rock outcrop (taken to be at the interface above the lower half-space). The first, last and step frequencies (in rad/s) are then specified as described for the dynamic- stiffness coefficient. The user is asked whether or not normalisation of the results is required. The normalisation just causes the excitation frequency for the output to be selected as a0 in dimensionless terms in the final tabulation. The dimensionless frequency a0 is determined as described for the dynamic-stiffness coefficient. Whether or not normalisation is specified, the effective foundation input motion is normalised by the control motion amplitude. Finally, the user is requested to enter the name of the output text file. As the results are computed they are written both on the screen and to this text file.

    3 Both. This option computes both the dynamic-stiffness coefficient and the effective foundation input motion for a range of frequencies. The degree of freedom is limited to horizontal 'H' and vertical 'V' motion. When the character for horizontal motion is entered, horizontal, rocking and coupled dynamic-stiffness coefficients are computed, along with horizontal and rocking effective foundation input motions. In the case that the character for vertical motion is entered, only the dynamic-stiffness coefficient and effective foundation input motion for vertical motion will be computed. The control point location, the frequency range for computation and whether or not normalisation of the results is required must also be specified, as described above.

    4 Read new model description from file. This option discards the current site description and reads a new problem description from another input text file specified by the user. The option allows analysis of multiple models without having to execute the program separately for each one.

    5 Change the calibration method (currently ). This option indicates the calibration method for the cone aspect ratios currently being used in the analysis. By default is 'half-space', but this can be changed to 'full-space' by selecting this option. For details regarding the two calibration methods the reader should refer to Section 3.6. Selecting the option again will change the calibration method back to 'half-space'. The option thus 'toggles' the calibration method.

    6 Change reference point (currently ). This option changes the point on the embedded foundation where the horizontal and rocking degrees of freedom are defined when computing the horizontal, rocking and coupling dynamic-stiffness coefficients. This is the point at which the structural model will be connected when a dynamic soil-structure interaction analysis is undertaken. By default is 'bottom', but this can be changed to 'top' by selecting this option. The option toggles between 'bottom' and 'top'.

    7 Change internal soil treatment (currently ). This option changes how the soil inside the foundation is treated during the analysis. By default is 'excavate', indicating that the soil is analytically excavated, as described in Section 5.3. However, in some situations, such as the suction caisson addressed in Section 7.3, the soil is not excavated. This option toggles the treatment between 'excavate' and 'none'.

    8 Quit. This option exits the program.

  • 176 Foundation Vibration Analysis: A Strength-of-Materials Approach

    E.4 Further processing of results

    The results from CONAN are saved in an output text file, the name of which is specified by the user. Columns are separated by tab characters, so the file can easily be transferred into a spreadsheet program, such as Excel. Real and imaginary components are tabulated in consecutive columns. The data can be transferred to the MATLAB environment by copying from the output file, then performing a 'Paste special...' in MATLAB, choosing the option to paste the columns as real vectors. Columns containing real and imaginary components must be combined together to form complex vectors before use. This procedure is discussed further in Appendix F.8.

    Alternatively, further programs can be written that access the output file to obtain the dynamic stiffness of the foundation and then provide a higher level of structural modelling than that discussed in this book.

    For simpler problems analysis can be performed in the Excel environment, although the descrip- tion of vibration with real quantities must be used (Appendix A. 1), as complex numbers cannot be handled readily.