Manual Bisar 3

(1)

BISAR 3.0

User Manual

This document is CONFIDENTIAL. Neither the whole nor any part of this document may be disclosed to any third party without the prior written consent of Shell International Oil Products B.V., The Hague.

The copyright of this document is vested in Shell International Oil Products B.V., The Hague. All rights reserved. Neither the whole nor any part of this document may be reproduced, stored in any retrieval system or transmitted in any form or by any means (electronic, mechanical, reprographic, recording or otherwise) without the prior written consent of the copyright owner.

Bitumen Business Group May 1998

(2)

1. Introduction

The Windows computer program BISAR 3.0 replaces the DOS version BISAR-PC 2.0. The program is suitable for Windows 3.1, Windows 95 and Windows NT.

In the early 1970s, Shell Research developed the BISAR mainframe computer program1_{, which}

was used in drawing the design charts of the Shell Pavement Design Manual issued in 1978. An abbreviated version of the BISAR program for use on a personal computer2_{was issued in 1987}

as BISAR-PC (Release R 1.0). A PC version comprising all extensive mainframe options was not feasible, because of the lengthy calculations at that time, The PC version was issued to facilitate the use of the design charts and to avoid laborious interpolations. To avoid these limitations, the DOS program BISAR-PC 2.0, issued in 1995, offered all the possibilities of the former mainframe program.

With the release of BISAR 3.0 the full possibilities of the original mainframe BISAR computer program are now available for use in the Windows environment. In addition to the calculation of stresses and strains BISAR 3.0 is capable of calculating deflections and is able to deal with horizontal forces and slip between the pavement layers. This offers the opportunity to calculate comprehensive stress and strain profiles throughout the structure for a variety of loading patterns, including air-crafts. In this way, BISAR 3.0 package is a valuable calculation tool, which can be used for refining the SPDM 3.0*_{designs, to carry out more complicated designs}

(e.g. for cement-bounded base layers or airport designs) and as a stand-alone program for theoretical calculations on elastic multi-layer systems.

To facilitate SPDM related calculations the present BISAR 3.0 version contains options to access with ease the Standard Dual Wheel Configuration and to automatically select important positions in the layer structure under consideration.

The BISAR 3.0 package provides two types of output. The so-called ‘Detailed Report’ contains the same information as the original BISAR mainframe program. The ‘Block Report’ provides an overview of the main results, which in general meets the needs for less complex studies. BISAR 3.0 comprises advanced report layout, improved file and database management. It further includes automatic calculation of the layer number and facilitates selection of positions at a layer interface.

(4)

2. Main Principles of the BISAR Program

With the BISAR program, stresses, strains and displacements can be calculated in an elastic multi-layer system which is defined by the following configuration and material behaviour: 1. The system consists of horizontal layers of uniform thickness resting on a semi-infinite base

or half space.

2. The layers extend infinitely in horizontal directions. 3. The material of each layer is homogeneous and isotropic.

4. The materials are elastic and have a linear stress-strain relationship.

The system is loaded on top of the structure by one or more circular loads, with a uniform stress distribution over the loaded area. The program offers the possibility to calculate the effect of vertical and horizontal stresses (shear forces at the surface**_{) and includes an option to account}

for the effect of (partial) slip between the layers, via a shear spring compliance at the interface. BISAR calculations require the following input:

- the number of layers

- the Young’s moduli of the layers - the Poison’s ratios of the layers

- the thickness of the layers (except for the semi-infinite base layer) - the interface shear spring compliance at each interface

- the number of loads

- the co-ordinates of the position of the centre of the loads

- one of the following combinations to indicate the vertical normal component of the load - stress and load

- load and radius - stress and radius

- (optional) the horizontal tangential component of the load and the direction of this shear load - the co-ordinates of the positions for which output is required.

The centre of the loads and the positions at which stresses, strains and displacements have to be calculated are given as co-ordinates in a fixed Cartesian co-ordinate system. The actual calculations to determine the response of a particular load in terms of stresses, strains and displacements are, however, carried out within a local cylindrical co-ordinate system having the centre of the load as origin. The effect of the simultaneous action of various loads is the sum of the effects due to the action of each separate load. This summation is carried out after

transformation of the results with respect to the underlying Cartesian co-ordinate system. The program calculates the eigen values and eigen vectors of the stress and strain tensors, the principal stresses and strains and the corresponding principal directions. The maximum and minimum principal values represent the maximum and minimum normal stresses and strains. The principal directions denote the normals of the planes through the point under consideration that are free of shear stresses and strains. The maximum shear stresses and strains, acting in planes bisecting the principal directions are equal to half the difference between these principal values. Since these maximum shear stresses can also be considered in failure studies, they are calculated too, together with the midpoints of the Mohr’s stress circles and the total energy density and strain energy density of distortion at the considered position.

BISAR may account for slip between layers. This is incorporated through a shear spring compliance. The standard calculations within BISAR-PC are done with full friction between all the layers. The method to make calculations assuming full or partial slip between all or some of the layers is explained in Appendix 1.

** In calculations dealing with shear forces acting at the loaded surface, no response should be asked for positions at the surface. BISAR does not properly account for that boundary condition and calculated results may be erroneous. In such cases it is recommended to select a position just below the surface of the structure.

(5)

The detailed output comprises the following information for each selected position in the structure under consideration:

• for each load separately (all expressed in terms of the cylindrical co-ordinate system for the loading):

- the components of the stress tensor (normal and shear) - the components of the strain tensor (normal and shear) - the components of the displacement vector

• for the combined action of all loads (all expressed in terms of the fixed Cartesian co-ordinate system:

- the components of the stress tensor (normal and shear) - the components of the strain tensor (normal and shear) - the components of the displacement vector

- the principal values and directions of the stress tensor - the principal values and directions of the strain tensor - the maximum shear stresses and strains

- the midpoint of the Mohr’s stress circles - the strain energy of distortion

- the total strain energy.

A full description of the fundamentals behind the BISAR program is given in the user guide of the first program (External Report AMSR.0006.73). Essential parts of this document remain available to interested parties for reference to the theoretical basis of the elastic multi-layer model.

(6)

3. System Requirements

The minimum requirements for the computer system to run BISAR 3.0 are as follows:

Part Description

Computer IBM (or compatible) PC with a 486DX2-50 MHz or higher processor Operating system Windows 3.1, Windows 95, Windows NT 3.51, Windows NT 4.0 Memory 4 MB of memory (8 MB recommended for Windows 95, 16 MB

recommended for Windows NT)

Disk-drive The program is supplied on CD-ROM. On request it is available on two high density diskettes of 1.44 MB

Hard disk 6 MB of available disk space Screen VGA display or better

Mouse Microsoft Mouse or compatible pointing device Printer Any Windows compatible printer

(7)

4. Installing BISAR 3.0

4.1 Installation from CD-ROM In Windows 3.x

• Start Windows (or close all running programs if Windows is already started)

• Place the CD-ROM in your CD-ROM drive

• Select File/Run from the Program Manager

• Type: D:\BISAR3\SETUP (where D: is the drive letter assigned to your CD-ROM drive)

• Press the [Enter] key

• Follow the instructions in the section “Installation Screens (CD-ROM)” below

In Windows 95/NT

• Start Windows 95/NT (or close all running programs if Windows 95/NT is already started)

• Place the CD-ROM in your CD-ROM drive

• Select Run from the Start menu

• Type: D:\BISAR3\SETUP (where D: is the drive letter assigned to your CD-ROM drive)

• Follow the instructions in the section “Installation Screens (CD-ROM)” below

Installation Screens (CD-ROM)

(8)

Installation is complete when the following window is displayed:

4.2 Installation from diskettes In Windows 3.x

• Start Windows (or close all running programs if Windows is already started)

• Place the disk labelled “BISAR 3.0 Disk 1 of 2” in Drive A:\

• Select File/Run from the Program Manager

• Type: A:\SETUP

• Follow the instructions in the section “Installation Screens” below

In Windows 95/NT

• Start Windows 95/NT (or close all running programs if Windows 95/NT is already started)

• Place the disk labelled “BISAR 3.0 Disk 1 of 2” in Drive A:

• Select Run from the Start menu

• Type: A:\SETUP

(9)

Installation Screens (diskettes)

Once the installation of BISAR 3.0 has started, the following screen will be displayed:

It is recommended that BISAR 3.0 is installed in a directory called BISAR3, however, a different directory may be specified. Pressing the OK button starts the process of installing the

BISAR 3.0 files into the specified directory.

As files are installed, a progress meter is updated as shown below:

When the following screen is displayed, remove DISK 1 and replace it with DISK 2 before pressing the OK button.

(10)

Installation is complete when the following window is displayed:

Installation Troubleshooting

If installation appears to be extremely slow, or if problems are encountered as installation progresses, files may be manually copied to your hard disk and installed from there. To do this, follow the instructions below.

• Using File Manager (in Windows 3.x) or Windows Explorer (in Windows 95) to create a temporary directory on your hard disk.

• Copy all of the files from both BISAR 3.0 installation disks to this temporary directory.

• Run the BISAR 3.0 SETUP program from this temporary directory.

Once installation has completed, the temporary directory may be removed.

Network Installation

Although BISAR 3.0 may be installed on and run from a network, it is not recommended since the internal database is not designed for multi-user access.

(11)

5. Use of BISAR 3.0

Each BISAR 3.0 project (run) can deal with ten separate sets of input. A single set of input is defined as a system. Within each system the program can deal with ten layers and ten circular loads. The use of more systems in one BISAR project facilitates studies into the effect of certain parameters e.g. variation of modulus or thickness by extending the number of positions.

The way to indicate the positions (the co-ordinates in the layer structure where calculation results are asked) has been improved. It is no longer necessary to provide the layer number, which is now calculated automatically from the Z-co-ordinate. For positions at the interface between two layers, the program offers the opportunity to select a specific layer or to choose for calculating the results at the same position in both layers. Stresses, strains and displacements can usually be calculated at ten positions per system. This number is extended when interface positions are selected for both layers.

The original BISAR mainframe program contained an option to select between the a ‘rough’ and the ‘smooth’ calculation method. The ‘rough’ method was introduced to speed-up mainframe computer calculations. With the present fast PC’s, the ‘rough’ calculation method has become obsolete and the ‘smooth’ method is standard for all the calculations within BISAR 3.0.

To facilitate SPDM related calculations the present BISAR 3.0 version contains options to easy access the Standard Dual Wheel Configuration and to automatically select important positions in the layer structure under consideration.

The output of BISAR 3.0 comprise two types of reports. The ‘Detailed Report’ contains the same information as the output of the original mainframe program, but in an improved lay-out. A shortened report, the so-called ‘Block Report’ comprises normal stresses, normal strains and uniaxial displacements at each selected position in the structure. The results in the ‘Detailed Report’ and the ‘Block Report’ can be copied to the Windows clipboard for importing the results of the calculation into commercial Windows programs for preparing graphics etc.

The BISAR 3.0 package is based on SI-Units. The units with their prefixes are displayed in the columns of the input screens. In contrast to previous versions (BISAR Mainframe and BISAR-PC 2.0) the ‘Detailed Report’ also includes display of units, be it without the prefixes used in input windows and Block Report. The actual units and their prefixes for input and output in BISAR 3.0 are listed in Appendix III.

BISAR 3.0 comprises modules for input, calculations and reporting / displaying results. The program does not contain a module for interpretation of results and comparisons with specific material properties (e.g. fatigue relations) or specific design criteria. Such interpretation is possible with the SPDM 3.0 program, the computerised Shell Pavement Design Manual, although SPDM is more limited in the number of layers and positions to be considered. To analyse stress and strain profiles for user defined structures and loading patterns it is recommended to use the BISAR 3.0 facility to copy and paste output to other Windows

programs. Copy and paste to a graphics program can be used to find e.g. the maximum asphalt stresses and strains (not necessarily at the bottom of the asphalt). The facility is also

(12)

6. Starting BISAR 3.0

The program is started by double-clicking the BISAR icon: and the main window appears with the following pull-down menus

• Project • Help

The options for the Project pull-down menu are:

• New • Open • Previous Calculations • Delete • Compact Database • Repair Database • Exit

New and Open are used for the actual calculations. New is used to set-up a new project while Open is used to edit input of already existing projects. These options are explained in

section 10 of this manual.

Previous Calculations is used to access the reports (output) of previous projects. Delete is

used to for deleting input with the following options:

• Project Input

• Loads

• Layers

• Positions

Details for Previous Calculations and Delete are given in section 7.

Compact database and Repair Database are used to maintain the internal BISAR databases

(see section 7)

Exit closes the application.

When opening a New or existing project (Open) following additional pull-down menus become available: • Edit • Copy From • Results • Window • Help

Edit is used to undo all changes within project input data. Copy From is used to copy input

data from system to system. Results is used to start the calculations.

The Window pull-down menu offers the possibility to use the well-known general Windows options:

• Cascade

• Windows

for arranging and selecting the various windows.

The Help menu offers the general Windows Help options

• Contents

• Search For Help On

(13)

Help is also always available when pressing F1, except within Block Report and Detailed

(14)

7. File and Database Management

Input and output (reports) are stored in an internal BISAR 3.0 database. In this way, the user is not troubled with the management of separate input and output files on his computer via the File Manager or the Windows Explorer. This set-up implies that all file management has to be done within the BISAR program. It allows the use of narrative descriptions (long names) for the various database parts.

The structure of the internal database is as follows:

Project Contains input data (Loads, Layers and Positions) for a certain Project (maximum 10 Systems).

Previous Calculations Contains input and output for a certain Project (Block Report, Detailed Report, Block Table, Detailed Table).

Loads Contains user defined Load configurations, which can be saved and retrieved when preparing input for a certain Project.

Layers Contains user defined Layer / structure configurations, which can be saved and retrieved when preparing input for a certain Project.

Positions Contains user defined Positions, which can be saved and retrieved when preparing input for a certain Project.

Editing existing Projects input data

To edit existing input data in order to define a new Project is done via Project, Open from the main BISAR window:

(15)

resulting in display of a window like

to select a certain project for editing e.g.

which allows all options for Systems, Loads, Layers and Positions as explained for starting a New Project (see section 10.1)

(16)

Deleting Input Data

The option to delete specific Project input, Load configurations, Layer structures and series of positions can be approached via Delete.

Note that this option is only available when all projects are closed.

After selecting Project Input, Loads, Layers or Positions a following window (or similar) is displayed to delete a certain item

(17)

Accessing and Deleting Previous Calculations

The content of Previous Calculations can be assessed via Project, Previous Calculations resulting in display of a window like

Via this way it is possible to select project output

• for browsing and printing by choosing Block Report or Detailed Report (see Section 9) • for copy to clipboard and pasting to any Windows application by clicking Block Table or

Detailed Table

• to Delete specific output.

Database Maintenance

Under certain circumstances (e.g. loss of power in the middle of a calculation) it is possible that the BISAR 3.0 database is corrupted. If this occurs then the following message will be displayed when attempting to open or save projects:

Selecting the Repair Database option will remove any corruption of data which might have occurred and BISAR 3.0 operation will continue normally.

When projects and results are deleted from the BISAR 3.0 database, the space that they once occupied is not automatically reclaimed. The Compact Database option manually reclaims this space. Please note that if used infrequently, database compaction can take one or two minutes to complete.

(18)

Saving Project Input and Calculations

Project Input can be saved at any time through use of the Project menu options:

(19)

8. Working with Tables

Whenever the Block Table or Detailed Table button is selected from the Calculated Data window is selected, a table of calculated results is displayed. The following example shows a Block Table:

The Block (or Detailed) Table provides a convenient way to view a large number of results (up to 2000). Horizontal and vertical scroll bars will appear, if necessary, to allow navigation when more results have been calculated than can be displayed in the Table window.

The Table is initially displayed with all results selected (highlighted). Pressing the Copy to

Clipboard button will copy the selected results to the clipboard so that they may be pasted into

another application. For example, copying the results and pasting them into a spreadsheet application would allow the graphing of results etc.

(20)

9. Printing in BISAR 3.0

Whenever a report is created in BISAR 3.0 (by pressing the Block Report or Detailed Report button) a preview window similar to the following is displayed:

The arrow buttons at the top of the preview window enable you to move backwards and forwards in your report. The action of those buttons is as follows:

Moves you to the first page of the report Moves you to the previous page

Moves you to the next page

Moves you to the last page of the report

Cancels page formatting. For long reports, page formatting may take a few moments. If you want to stop the page formatting, press this button. Previews the page to be printed

Sends your report to the printer

NOTE: You can also use the keyboard to move around in the print window. [Ctrl]+[Home] moves you to the first page, [Pg Up] moves you to the previous page, [Pg Dn] moves you to the next page, [Ctrl]+[End] moves you to the last page, and [Esc] closes the print window.

(21)

Print Preview

The magnifying glass button is the print preview button. This button lets you see each page in its entirety, as it will print. When you Click this button, the program displays the page that’s currently in the preview window, reduced in size so the entire page fits in the window at one time.

Printing to the printer

To send the displayed report to the printer, click the printer button. A screen similar to the following will be displayed. Note that BISAR 3.0 will print the report on your default printer. To select a different printer in Windows 3.x use the printers option in the control panel. To select a different printer in Windows 95, use the printers option in My Computer.

The print range option allows you to print all or just part of your report. Select ALL to print the entire report or specify a page range for a partial report.

The default number of copies printed is 1, however this may be changed by specifying a different number in the copies box.

The Collate Copies option determines how multiple copies of a report are printed. To print multiple copies of a multiple page report in the order 1,1,1,2,2,2,3,3,3, etc. leave this option empty. To print multiple copies of a multiple page report in the order 1,2,3...,1,2,3…, etc. then select this option. Note that certain printers do not respond to this collating option and will always print a report in the order 1,2,3…,1,2,3…, etc.

(22)

10. Performing BISAR Calculations

10.1 Outline of Input and Output

When starting a new project (run) via Project and New the following input window appears:

A new project is ’untitled’ and a project name can be given after completing the input and starting the calculations. The default number of Systems (maximum 10) is set at 1. The input panels for a certain system are made active via Tabs. The System Description box offers the possibility to give narrative details. Per system the input panels for Loads, Layers and

Positions can be made active.

The load characteristics can be given in three modes: • Stress and Load

• Load and Radius (default)

• Stress and Radius.

The example below shows typical input data for a Super Single Wheel in the Load and Radius mode (next page).

(23)

It is possible to Save and Retrieve user defined load configurations in the internal database*_.

(24)

Corresponding structure data have to be given in the Layer panel e.g.

The number of layers can be varied between 1 and 10. The checkbox Full Friction Between

Layers is active as default.

BISAR offers the opportunity to study the effect of full and partial slip between certain layers in the structure via the so called Shear Spring Compliance parameter. The use of this option is explained in section 10.3 and Appendix 1.

The next step is to provide the co-ordinates of Positions in the structure where output is desired. It is not possible to select positions without defining the structure first.

The Position panel below shows (by way of example) the co-ordinates below the centre of the load at the top of the surface, in the middle of the top layer, the interface between layer 1 and 2, a position in layer 2 and the interface between layer 2 and 3. With this new version of BISAR it is no longer required to input the layer number. This number is now automatically calculated and displayed when typing the Z - co-ordinate of the position.

A proper choice of the layer number is very important because at the interface discontinuities may occur. Discontinuities may for instance occur in

• vertical strains and horizontal stresses when the modulus on both side of the interface is different

(25)

When a Z- co-ordinate is positioned at an interface the layer number is indicated in the format 1/2. The panel offers the possibility to select the desired layer number or to choose both by clicking the Select Layer button

(26)

By clicking the Number of Systems indicator in top of the input panel, the number of systems for a certain project can be extended up to 10. In that case more system indicators become available e.g. system 2, starting with empty data fields:

(27)

Via Copy From and (in this case) selecting System 1, the already provided content of

System 1 is copied to System 2, and can be adjusted where required. In many cases, the user would define new positions in order to obtain extended stress and strain profiles for a given load configuration and a certain layer structure.

Calculations are started by selecting Results and Calculate or by pressing F5

and the following message is displayed:

Here the user has the opportunity to save the input data and to give a description (name) to the project input by pressing Yes:

(28)

After pressing OK, the calculations are performed and the following window is displayed:

The output of the calculations can be accessed as (see also sections 8 and 9) • Block Report

• Detailed Report • Block Table

• Detailed Table

The Detailed output contains the same extended information as produced by the original BISAR mainframe computer program. The Block output compiles the main results. The Report function prepares for browsing and printing.

When using the Table option a following window is displayed, in which the data is selected and ready for Copy to Clipboard. This option gives the opportunity to copy and paste data to any other Windows application.

(29)

Closing the Table and the Calculated Data window results in the display of

After confirmation via Yes the calculation results are saved under the same name as the project input and may be reassessed through use of the Previous Calculations options in the Project menu.

Undo All Changes on the Edit menu will cancel all changes since the last time Project Input

was saved.

(30)

10.2 Input Arrangements for the Standard Dual Wheel

BISAR 3.0 includes the possibility to perform extensive calculations the Standard Dual Wheel Configuration (80kN standard axle) as used in the Shell Pavement Design Manual and the SPDM 3.0 computer program.

Within the SPDM package the use of BISAR is limited with respect to the number of layers and the number of positions. Use of the new BISAR Standard Dual Wheel Arrangements offers the possibility to analyse stress and strain profiles in much more detail and to study more complex structures (up to ten layers, including e.g. high modulus cement-bound base-layers).

The Standard Dual Wheel load configuration can be directly chosen by clicking the Use

Standard Dual Wheel checkbox

(31)

After defining a certain layer structure e.g.

the program gives the possibility to directly select relevant positions for the combination of Standard Dual Wheel and the given layer structure by clicking Select Positions for Standard

(32)

This implies that the following positions are automatically selected:

• all positions underneath the load position between the wheels and load position under a wheel for

– the top of the undermost (infinite thick) layer – the bottom of all the other layers.

Because all these positions are by definition at an interface, it is possible to select both interface positions and/or the same position in the layer above the interface.

This facility accommodates structures up to five layers. For structures with more layers, the automatic section of positions will apply to the top of the undermost layer and the bottom of the four top layers. It is of course possible to extend the number of positions when the load configuration and the layer structure is copied to a new system within the project.

(33)

10.3 Calculations with Shear Spring Compliance

The BISAR calculations outlined in Section 10.1 assume full friction (perfect adhesion) between all layers of the structure under consideration. One of the possibilities of BISAR is the capability to account for (full or partial) slip. This type of calculation is made with aid of the shear spring compliance. Detailed information on the theoretical background and the use of the shear spring compliance parameter is given in Appendix 1.

Shear spring compliance values are provided in the input panel for Layers:

In this case a reduced spring compliance value of 15 m (for the interface of layers 2/3 and 3/4 is chosen as 100 times the radius of the load. As explained in Appendix 1 this value approximates full slip. The corresponding load itself is defined in the Loads input screen:

(34)

The user can choose between input of the standard and reduced shear spring compliance in the Layers input screen. There is an automatic link between the two compliance modes. By clicking Standard Spring Compliance the value corresponding to the provided reduced spring compliance value (via modulus and Poisson’s ratios) is directly displayed

(35)

11. BISAR 3.0 Reports

11.1 The Block Report

An example of the content and layout of the Block Report is presented on the next pages. In this Block Report, the input and output for one system is compiled on one page. The output comprises the normal stresses and strains and uniaxial displacements at each selected position in the structure. These normal stresses and strains are denoted by XX, YY, ZZ according to the directions in the fixed Cartesian co-ordinate system. The uniaxial displacements are

(36)

BISAR 3.0 – Block Report

Example Project

System: 1: Positions Between the Wheels and Under a Wheel

Structure Loads

Modulus of Vertical Horizontal (Shear) Shear

Layer Thickness Elasticity Poisson’s Load Load Stress Load Stress Radius X-Coord Y-Coord Angle

Number (m) (MPa) Ratio Number (kN) (MPa) (kN) (MPa) (m) (m) (m) (Degrees)

1 0.300 5.000E+03 0.35 1 2.000E+01 5.774E-01 0.000E+00 0.000E+00 1.050E-01 0.000E+00 -1.575E-01 0.000E+00 2 0.200 1.000E+03 0.35 2 2.000E+01 5.774E-01 0.000E+00 0.000E+00 1.050E-01 0.000E+00 1.575E-01 0.000E+00 3 0.150 8.000E+02 0.35

4 2.000E+02 0.35

Stresses Strains Displacements

Position Layer X-Coord Y-Coord Depth XX YY ZZ XX YY ZZ UX UY UZ

Number Number (m) (m) (m) (MPa) (MPa) (MPa) µstrain µstrain µstrain (µm) (µm) (µm)

1 1 0.000E+00 0.000E+00 1.500E-01 -1.475E-02 -9.446E-02 -1.290E-01 1.269E+01 -8.831E+00 -1.815E+01 0.000E+00 0.000E+00 9.900E+01 2 1 0.000E+00 0.000E+00 3.000E-01 1.919E-01 1.409E-01 -5.623E-02 3.246E+01 1.868E+01 -3.454E+01 0.000E+00 0.000E+00 9.516E+01 3 2 0.000E+00 0.000E+00 3.000E-01 1.416E-02 3.954E-03 -5.623E-02 3.246E+01 1.868E+01 -6.257E+01 0.000E+00 0.000E+00 9.516E+01 4 3 0.000E+00 0.000E+00 6.500E-01 2.704E-02 2.539E-02 -1.327E-02 2.849E+01 2.572E+01 -3.953E+01 0.000E+00 0.000E+00 7.978E+01 5 4 0.000E+00 0.000E+00 6.500E-01 1.399E-03 9.881E-04 -1.327E-02 2.849E+01 2.572E+01 -7.054E+01 0.000E+00 0.000E+00 7.978E+01 6 1 0.000E+00 -1.575E-01 1.500E-01 -2.084E-02 -3.776E-02 -2.388E-01 1.519E+01 1.062E+01 -4.366E+01 0.000E+00 -1.366E-01 9.778E+01 7 1 0.000E+00 -1.575E-01 3.000E-01 1.834E-01 1.450E-01 -5.453E-02 3.034E+01 1.999E+01 -3.389E+01 0.000E+00 -3.101E+00 9.284E+01 8 2 0.000E+00 -1.575E-01 3.000E-01 1.319E-02 5.514E-03 -5.453E-02 3.035E+01 1.998E+01 -6.108E+01 0.000E+00 -3.101E+00 9.284E+01 9 3 0.000E+00 -1.575E-01 6.500E-01 2.563E-02 2.317E-02 -1.262E-02 2.743E+01 2.327E+01 -3.712E+01 0.000E+00 -3.920E+00 7.845E+01 10 4 0.000E+00 -1.575E-01 6.500E-01 1.314E-03 6.976E-04 -1.262E-02 2.743E+01 2.327E+01 -6.660E+01 0.000E+00 -3.920E+00 7.845E+01

Calculated: 02-Dec-1997 13:18:52 Print Date: 02-Dec-1997 Page: 1

(37)

BISAR 3.0 – Block Report

Example Project

System: 2: Position Outside the Loads

Structure Loads

Modulus of Vertical Horizontal (Shear) Shear

Layer Thickness Elasticity Poisson’s Load Load Stress Load Stress Radius X-Coord Y-Coord Angle

Number (m) (MPa) Ratio Number (kN) (MPa) (kN) (MPa) (m) (m) (m) (Degrees)

1 0.300 5.000E+03 0.35 1 2.000E+01 5.774E-01 0.000E+00 0.000E+00 1.050E-01 0.000E+00 -1.575E-01 0.000E+00 2 0.200 1.000E+03 0.35 2 2.000E+01 5.774E-01 0.000E+00 0.000E+00 1.050E-01 0.000E+00 1.575E-01 0.000E+00 3 0.150 8.000E+02 0.35

4 2.000E+02 0.35

Stresses Strains Displacements

Position Layer X-Coord Y-Coord Depth XX YY ZZ XX YY ZZ UX UY UZ

Number Number (m) (m) (m) (MPa) (MPa) (MPa) µstrain µstrain µstrain (µm) (µm) (µm)

1 1 0.000E+00 -3.150E-01 1.500E-01 -1.583E-02 -6.004E-02 -6.675E-02 5.710E+00 -6.227E+00 -8.040E+00 0.000E+00 -6.995E-01 8.742E+01 2 1 0.000E+00 -3.150E-01 3.000E-01 1.222E-01 6.552E-02 -3.354E-02 2.219E+01 6.901E+00 -1.985E+01 0.000E+00 -5.374E+00 8.537E+01 3 2 0.000E+00 -3.150E-01 3.000E-01 9.982E-03 -1.345E-03 -3.354E-02 2.219E+01 6.901E+00 -3.657E+01 0.000E+00 -5.374E+00 8.537E+01 4 3 0.000E+00 -3.150E-01 6.500E-01 2.192E-02 1.736E-02 -1.087E-02 2.456E+01 1.687E+01 -3.078E+01 0.000E+00 -7.118E+00 7.478E+01 5 4 0.000E+00 -3.150E-01 6.500E-01 1.088E-03 -5.138E-05 -1.087E-02 2.456E+01 1.687E+01 -5.619E+01 0.000E+00 -7.118E+00 7.478E+01

(38)

11.2 Detailed Report

Examples of the layout of ‘Detailed Report’ pages are presented on the next pages.

The first page of a System contains the input (layer structure and load configuration). The next pages contain the detailed output per selected position (one position per page).

In contrast to previous versions (BISAR Mainframe and BISAR-PC 2.0) the ‘Detailed Report’ includes display of units, be it without the prefixes used in input windows and Block Report. The actual BISAR calculations to calculate the response of a load in terms of resulting stresses, strains and displacements at a certain position are carried out within a local cylindrical co-ordinate system (see section 2 and Appendix 2).

The following characteristics are given for each position

- the X, Y and Z - co-ordinates in the fixed Cartesian co-ordinate system - the distance between load-axis and position

- the angle θ(theta) as an (indirect) measure for the radial direction of the position for the individual combination of load and position (see Appendix 2)

- for each load the displacements, normal and shear stresses and strains expressed in directions of the local cylindrical co-ordinate system with the centre of the load as origin - the combined action of all the loads is expressed in terms of the (fixed) Cartesian

co-ordinate system

- total stresses, strains and displacements

- principal values and directions of total stresses and strains. The local cylindrical co-ordinate system is chosen such that

- the origin is at the centre of the load at the surface of the layered structure - the vertical direction is parallel to the Z-axis of the fixed Cartesian system

- the radial direction and the tangential direction are in a horizontal plane perpendicular to the vertical direction

The meaning of various notations for stresses (and similar for strains) is illustrated in Figure 1, which contains examples of the notation for type and direction of normal and shear stress within the fixed Cartesian co-ordinate system and a local cylindrical co-ordinate system. The origin for the latter system is indicated as O’ (the X’-, Y’- and Z’- axes in Figure 1 are respectively parallel to the X-, Y- and Z-axes of the fixed Cartesian system).

X

XX

rr

r

Z

XY

shear

normal

Fixed XYZ-system

Local cylindrical system

normal

Y

O

X'

Z'

Y'

O'

σ

r

η

shear

η

σ

(39)

BISAR 3.0 – Detailed Report

Example Project

Layer Young’s Poisson’s Shear Spring Number Thickness (m) Modulus (Pa) Ratio Compliance (m3/N)

1 0.300 5.000E+09 0.35 0.000E+00 2 0.200 1.000E+09 0.35 0.000E+00 3 0.150 8.000E+08 0.35 0.000E+00

4 2.000E+08 0.35

Load Normal Shear Radius of Load Position Load Position Shear Number Stress (Pa) Stress (Pa) Loaded Area (m) X (m) Y (m) Direction (°)

1 5.774E+05 0.000E+00 1.050E-01 0.000E+00 -1.575E-01 0.000E+00 2 5.774E+05 0.000E+00 1.050E-01 0.000E+00 1.575E-01 0.000E+00

(40)

BISAR 3.0 – Detailed Report

Example Project

Position Number: 1 Layer Number: 1 X Coord (m): 0.000E+00 Y Coord (m): 0.000E+00 Z Coord (m): 1.500E-01

LoadDistance to Displacements (m) Stresses (Pa) Strains

No. Load Axis (m) Theta (°) Radial Tangential Vertical Radial Tangential Vertical Rad./Tang. Rad./Vert. Tang./Vert. Radial Tangential Vertical Rad./Tang. Rad./Vert.Tang./Vert. 1 1.575E-01 9.001E+01 9.993E-07 0.000E+00 4.950E-05 -4.723E+04 -7.377E+03 -6.449E+04 0.000E+00 -7.877E+04 0.000E+00 -4.415E-06 6.345E-06 -9.075E-06 0.000E+00 -2.127E-05 0.000E+00 2 1.575E-01 -9.001E+01 9.993E-07 0.000E+00 4.950E-05 -4.723E+04 -7.377E+03 -6.449E+04 0.000E+00 -7.877E+04 0.000E+00 -4.415E-06 6.345E-06 -9.075E-06 0.000E+00 -2.127E-05 0.000E+00

Total Stresses (Pa) XX: -1.475E+04 YY: -9.446E+04 ZZ: -1.290E+05 YZ: 0.000E+00 XZ: 0.000E+00 XY: 0.000E+00 Total Strains XX: 1.269E-05 YY: -8.831E-06 ZZ: -1.815E-05 YZ: 0.000E+00 XZ: 0.000E+00 XY: 0.000E+00 Total Displacements (m) UX: 0.000E+00 UY: 0.000E+00 UZ: 9.900E-05

Principal Values and Directions of Total Stresses and Strains

Normal Normal Shear Shear X Y Z

Stress (Pa) Strain Stress (Pa) Strain Comp. Comp. Comp.

Maximum: -1.475E+04 1.269E-05 1.0000 0.0000 0.0000

Minimax: -9.446E+04 -8.831E-06 0.0000 1.0000 0.0000

Minimum: -1.290E+05 -1.815E-05 0.0000 0.0000 1.0000

Maximum: 5.711E+04 1.542E-05 0.7071 0.0000 -0.7071

-7.186E+04 0.7071 0.0000 0.7071

MiniMax: 3.985E+04 1.076E-05 0.7071 -0.7071 0.0000

-5.461E+04 0.7071 0.7071 0.0000

Minimum: 1.726E+04 4.660E-06 0.0000 0.7071 -0.7071

-1.117E+05 0.0000 0.7071 0.7071

Strain Energy (J): 1.494E+00 Strain Energy of Distortion (J): 9.266E-01

(41)

12. Error Messages

The following error messages apply:

Entry of Loads in Stress and Load Mode

Field Actual Error Message

Vertical Stress The Vertical Stress Value must be greater than 0 and less than 10000 Vertical Load The Vertical Load Value must be greater than 0 and less than 10000 X Coordinate The X Coordinate Value should be between -99.9999 and 999.9999 Y Coordinate The Y Coordinate Value should be between -99.9999 and 999.9999 Horizontal Stress The Horizontal Stress Value should be between 0 and 9999.999 Shear Direction The Shear Direction Value should be between 0 and 999.9

Entry of Loads in Load and Radius Mode

Vertical Load The Vertical Load Value must be greater than 0 and less than 10000 Radius The Radius Value must be greater than 0 and less than 1000 X Coordinate The X Coordinate Value should be between -99.9999 and 999.9999 Y Coordinate The Y Coordinate Value should be between -99.9999 and 999.9999 Horizontal Load The Horizontal Load Value should be between 0 and 9999.999 Shear Direction The Shear Direction Value should be between 0 and 999.9

Entry of Loads in Stress and Radius Mode

Vertical Stress The Vertical Stress Value must be greater than 0 and less than 10000 Radius The Radius Value must be greater than 0 and less than 1000

X Coordinate The X Coordinate Value should be between -99.9999 and 999.9999 Y Coordinate The Y Coordinate Value should be between -99.9999 and 999.9999 Horizontal Stress The Horizontal Stress Value should be between 0 and 9999.999 Shear Direction The Shear Direction Value should be between 0 and 999.9

Validation of Layers

Thickness The Thickness Value should be greater than 0 and less than 100 Modulus of Elasticity The Modulus of Elasticity Value should be greater than 0 and less than

1E20

Poisson’s Ratio The Poisson’s Ratio Value should be greater than 0 and less than 1 Spring Compliance The Spring Compliance Value should be between 0 and 1E+10

Validation of Positions

(42)

Appendix 1

BISAR Calculations with Slip between Layers (Shear Spring Compliance Concept)

A1.1 Theoretical Background

One of the possibilities of BISAR is the capability to account for (full or partial) slip. This type of calculation is made with aid of the shear spring compliance, a parameter which should not be confused with the well-known friction coefficient.

Within BISAR, it is not possible to use the ‘classic’ friction coefficient, because its value differs for static and dynamic conditions. Use of this parameters would require BISAR to be able to cope with discontinuities (step functions). The mathematics behind the BISAR model, however, assumes continuous relations for all its parameters.

To solve this problem, the designers of BISAR have developed the concept of shear spring compliance. In this approach the interface between two (horizontal) pavement layers is represented by an infinite thin inter-layer of which the strength is described by means of a spring compliance. Physically it assumes that the shear stresses at the interface cause a relative horizontal displacement of the two layers, which is proportional to the stresses acting at the interface.

The physical definition of the standard shear spring compliance, AK, is given by relative horizontal displacement of layers

AK = [m3_/N]

stresses acting at the interface

which relation is treated mathematically through the parameter α, defined as

in which

a = radius of the load, m

E = modulus of the layer above the interface, Pa

ν = Poisson’s Ratio of that layer

α = friction parameter, with 0 ≤ α ≤1

(α= 0 means full friction, α= 1 means complete slip). The reduced shear spring compliance,ALK expressed in m, is defined as

One of the values of AK and ALK is input for the BISAR program. The value of α, called interface friction, used in all computations is derived from the input (either AK or ALK).

The friction parameter αshould not be considered as a classic friction coefficient. The interface friction parameter depends on the diameter of the applied load and is therefore not a pure material property. Within calculations with loads of different diameters, different values for α apply for one ALK or AK value as physical characteristic for a specific layer interface. It is

AK α= 1 + ν AK + . a E α ALK = .a 1 – α

(43)

therefore formally not correct to express a percentage of slip as a proportion of the spring compliance for full slip.

On the other hand, it remains difficult to assign or justify a specific value for AK (ALK).

Therefore, it is recommended to always perform a series of calculations with different values for ALK as a kind of sensitivity analysis. A numerical variation in ALK from zero to, say, 100 times the radius of the loaded area covers the range from full friction to (practically) full slip (α= 0.99). The physical meaning (see above definition of AK) of such input values should be considered in connection with the moduli of the layers in the structure and the corresponding shear spring compliance (AK) values, with aid of the relation

1 + ν AK = ALK .

(44)

Appendix 2

The radial direction within fixed and local co-ordinate systems

The input for BISAR is expressed in terms of a fixed Cartesian co-ordinate system (X,Y,Z). The actual BISAR calculations, however, to determine the response of a load at a certain position in terms of resulting stresses, strains and displacements are carried out in a local cylindrical co-ordinate system (r,θ,z) for each load. An outline of both systems is given in Figure 2-1. L is the centre of a load in the X-Y plane at the top of the structure and is the origin of the local cylindrical system. P corresponds to an arbitrary position in the structure, with P’ as projection of P on the surface plane.

Fixed XYZ-system

Local cylindrical system

P

P'

X

Z

Z'

L (x

_L

,y

_L

,0)

P' (x

_P

,y

_P

,0)

P (x

_P

,y

_P

,z

_P

)

L (0,0,0)

P' (r,

Θ

,0)

P (r,

Θ

,z

_P

)

Y

O

O'

P'

P

L

r

Θ

Figure 2-1 Outline of coordinate systems within BISAR.

O

Y

X

L

r

P'

η

Θ

Tangential

direction

_{Radial direction}

xP

xL

yP

yL

(x

P

,y

P

,0)

(r,

Θ

,0)

Figure 2-2 Outline of the directions in the cylindrical coordinate system for a specific combination of load and position (loading without shear force).

(45)

The so-called ‘Detailed Report’ contains a value for the angle θ(theta), which is internally used by BISAR. This appendix explains the relation between the radial direction with respect to the fixed Cartesian Co-ordinate system (defined by the user) and the radial direction used and reported by BISAR.

The situation in case of vertical loading, without applying any shear force, is outlined in Figure 2-2.

The radial direction for a load and position combination with respect to the fixed Cartesian Co-ordinate system is given by the (internal BISAR) value η, the angle between the intersection line of position and the centre of the load with the positive X-axis.

In case of vertical loading

θ= η

so the BISAR output θ(theta) is equal to the direction with the (fixed) positive X-axis of the user defined Cartesian co-ordinate system.

When applying a horizontal shear force on the loading, the situation is more complex, because the value of θin the output now also depends on the direction of the horizontal loading. The situation is illustrated in Figure 2-3.

The radial direction (angle θin the Detailed Report) used to perform the calculations within the local cylindrical co-ordinate system is now taken with respect to the direction of the shear force. This direction is indicated by ψ, the angle between the shear direction and the positive X-axis (input in the load screen). In other words, the value for θvaries with varying shear direction,

0 Y

X

L

r

P'

η

Θ

Tangential

direction

Radial direction

Shear direction

xP

xL

yP

yL

Ψ

(x P,yP,0) (r,Θ,0)

Figure 2-3 Outline of the directions in the cylindrical coordinate system for a specific combination of load and position (loading with shear force).

(46)

Appendix 3

Overview of Units and Prefixes

Parameter Units

Input Screens Block Report Detailed Report

Load kN kN

-Radius m m m

Stress MPa MPa Pa

Co-ordinates m m m

Shear Direction degrees degrees degrees

Thickness m m m

Modulus MPa MPa Pa

Poisson’s Ratio - - -Spring Compliance m3_/N _m3_/N _m3_/N - (reduced) m m m Strains - µm/m m/m Displacements - µm m Distance to load - - m Theta - - degrees Strain Energy - - J - of Distortion - - J

(47)

References

1. D.L. de Jong, M.F.G. Peutz and A.R. Korswagen, Computer Program BISAR, Layered systems under nornal and tangential surface loads, AMSR.0006.73.

2. R.C. Koole, C.P. Valkering and F.D.R. Stapel, Development of Pavement Design Program for Use on Personal Computer, Paper presented at the 5thConference of Asphalt Pavements for Southern Africa, Swaziland, 5th-9thJune 1989.