PLAXIS Hoek and Brown

download PLAXIS Hoek and Brown

of 26

  • date post

    10-Dec-2016
  • Category

    Documents

  • view

    236
  • download

    17

Embed Size (px)

Transcript of PLAXIS Hoek and Brown

  • June 2009 / CGG_IR011_2009

    Client:

    Computational Geotechnics Group

    Institute for Soil Mechanics and Foundation Engineering

    Graz University of Technology

    Plaxis

    P.O. Box 572

    2600 AN Delft

    The Netherlands

    Ao. Univ.-Prof. Helmut F. Schweiger

    M.Sc. Ali Nasekhian

    Validation Report of Hoek-Brown

    Model Implemented in Plaxis

  • COMPUTATIONALGEOTECHNICSGROUP 1

    Project-Nr.: CGG_IR011_2009

    Validation Report of Hoek-Brown Model

    Implemented In Plaxis

    Client:

    Plaxis P.O. Box 572 2600 AN Delft The Netherland

    Ao. Univ.-Prof. Helmut F. Schweiger M.Sc. Ali Nasekhian

    Computational Geotechnics Group Institute for Soil Mechanics and Foundation Engineering Graz University of Technology

    Graz, am 18.June 2009 Helmut F. Schweiger

  • COMPUTATIONALGEOTECHNICSGROUP 2

    CONTENTS

    1 SCOPE OF THE REPORT .. 3

    2 VALIDATION SCHEME ........... 3

    3 HOEK-BROWN MODEL (HB-MODEL) . 4

    4 TRIAXIAL TEST . 6 4.1 Stress path and yield surface check ..... . 6 4.2 Comparison with lab data... 8 4.3 HB-model in compression and extension mode...... 10

    4.4 HB-Model and safety factor 13

    5 EVALUATION HB-MODEL IN BOUNDARY VALUE PROBLEMS.... 14

    5.1 Circular opening under hydrostatic pressure .. 14 5.2 Slope stability .... 19

    6 REFERENCES ........ 23

    7 APENDIX A: PLAXIS FILES . 24

  • COMPUTATIONALGEOTECHNICSGROUP 3

    1 SCOPE OF THE REPORT

    The objective of this report is to validate the Hoek-Brown model implemented in Plaxis using an

    MMTFILE to assign input parameters instead of the normal Plaxis interface. To do this, first a

    validation scheme was provided as given in section (2) to evaluate different aspects and features of

    the Hoek-Brown model based on reliable references. This scheme incorporates both, element tests

    and boundary value problems. In element tests several properties of an elastic perfectly plastic model

    such as elastic part, limit strength of material, stress path, drained and undrained conditions have

    been assessed. Afterwards, an analytical solution of a circular tunnel under hydrostatical stress has

    been compared to the results of the numerical model using the Plaxis HB-model. Accordingly, both the

    stress and displacement field of a boundary value problem have been checked.

    2 VALIDATION SCHEME

    The validation scheme is divided into 3 parts. First, a triaxial test is modelled numerically and

    according to HB properties of the intact or jointed rock (mentioned in the references) a compression or

    extension test is performed and the results are compared with theoretical Hoek-Brown curves or with

    other user-defined HB models such as FLAC, as well as experimental data obtained from lab tests. In

    the second and third part of this scheme two boundary value problems including a simple slope and a

    circular deep tunnel under hydrostatic pressure have been considered. The validation scheme is

    briefly explained in the following.

    a. Triaxial Test

    The following items have been taken into account:

    Whether HB-model complies with the theoretical (1- 3) curves or not?

    Comparison with lab data

    (Madhavi, 2004)

    Comparison with other user-defined model implemented in FLAC (using FISH).

    (Madhavi, 2004)

    Modelling triaxial compression and extension test to check whether shear strength

    reduction scheme works or not (c- reduction). (Benz et al., 2008)

    Hard rock mass Fair quality Poor quality

  • COMPUTATIONALGEOTECHNICSGROUP 4

    b. Boundary Value Problem Simple Slope

    Comparison between Bishop, MC and HB with two different slope angles (35.5 and 75) under

    drained and undrained conditions in terms of F.O.S. (Benz et al. 2008)

    The following items will be checked:

    Arclength control Ignore undrained behaviour c- reduction

    c. Boundary Value Problem Circular opening under hydrostatic pressure (2D)

    Plastic radius around the opening stress and displacement field (ur,,r)

    (Carranza 2004, Carranza et al. 1999 & Sharan 2008)

    3 HOEK-BROWN MODEL (HB-MODEL)

    The Hoek-Brown model is an elastic perfectly plastic model with non-associated flow rule. Deformation

    prior to yielding is assumed to be linear elastic governed by the elastic parameters E and n. The yield

    function f for the Hoek-Brown model is given by:

    a

    cibciHB smfwithff )(

    ~)(~ 3331 +==

    which is derived from the generalized Hoek-Brown failure criterion.

    Figure 1 Hoek-Brown failure criterion in principal stress space (left) and in the deviatoric plane (right)

  • COMPUTATIONALGEOTECHNICSGROUP 5

    The Hoek-Brown failure criterion was introduced in the early eighties to describe the shear strength of

    intact rock as measured in triaxial tests (Hoek & Brown 1980). The failure criterion for intact rock

    defines the combination of major and minor principal stresses (1 and 3) at failure to be:

    ciici m

    331 1++=

    (1)

    In the equation above, ci is the unconfined compressive strength of the rock and the coefficient mi is a

    parameter that depends on the type of rock (normally 5 mi 40). Both parameters, ci and mi, can be

    determined from regression analysis of triaxial test results). The Hoek-Brown failure criterion was later

    extended to define the shear strength of jointed rock masses. This form of the failure criterion, that is

    normally referred to as the generalized Hoek-Brown failure criterion, is

    a

    ciici sm )(

    331 ++=

    (2)

    The coefficients mb, s and a in equation (2) are semi empirical parameters that characterize the rock

    mass. In practice, these parameters are computed based on an empirical index called the Geological

    Strength Index or GSI. This index lies in range 0 to 100 and can be quantified from charts based on

    the quality of the rock structure and the condition of the rock surfaces (Marinos & Hoek 2000). In the

    latest update of the Hoek-Brown failure criterion, the relationship between the coefficients mb, s and a

    in equation (2) and the GSI is as follows (Hoek, Carranza-Torres, & Corkum 2002)

    =D

    GSImm ib 1428100exp

    (3)

    =D

    GSIs39100exp

    (4)

    ( )3/2015/61

    21 += eea GSI

    (5)

    In equations (3) and (4) D is a factor that depends on the degree of disturbance to which the rock has

    been subjected due to blast damage and stress relaxation. This factor varies between 0 and 1.

    The model parameters are listed in Table (1).

  • COMPUTATIONALGEOTECHNICSGROUP 6

    Table 1 Parameters for the HB-Model ____________________________________________________________________ Nr. Name Unit Description ____________________________________________________________________ 1 Gref [kN/m2] Elastic Shear Modulus 2 - Poisson`s Ratio 3 ci [kN/m2] Unconfined Compressive Strength 4 mi - Hoek-Brown Parameter 5 GSI - Geological Strength Index 6 m - Power Law Exponent 7 Pref - Reference Stress 8 D - Disturbance Factor ____________________________________________________________________

    4 TRIAXIAL TEST

    4.1 Stress path and yield surface check

    Modelling a triaxial test numerically is a simple way to check whether the implemented material model

    is able to model the strength of a rock sample according to the Hoek-Brown criterion and its input

    parameters. To do so, properties of an average quality rock mass were chosen which are given below.

    ci=80 MPa

    mi=12

    GSI=50

    Gref=3600000 kN/m2

    n=0.25 ; D=0

    Figure 2 Triaxial test modelled in Plaxis with prescribed displacement

  • COMPUTATIONALGEOTECHNICSGROUP 7

    Hoek-Brown Element Test Results

    0

    10

    20

    30

    40

    50

    60

    0 10 20 30 40 50 60

    p' (MPa)

    q' (M

    Pa)

    Drained-Plaxis ResultsFailure EnvelopeUndrained-Plaxis results

    3

    1

    3=5

    .2M

    Pa

    3=1

    .7 M

    Pa

    3=1

    .1 M

    Pa

    Undrained

    Figure 3 Hoek-Brown failure criterion and HB-model results in (p-q) space

    Comparison between FEM model and Hoek_Brown failure envelope

    0

    10

    20

    30

    40

    50

    60

    70

    80

    90

    -5 0 5 10 15 20 25

    Minor principal stress (MPa)

    Maj

    or p

    rinci

    pal s

    tres

    s (M

    Pa)

    HB Failure Envelope Plaxis Results

    3=0

    .050

    MPa

    3=1

    .1

    3=5

    .2 3=

    10.1

    3=1

    7.1

    Figure 4 Hoek-Brown failure criterion and HB-model results in terms of principal stress

  • COMPUTATIONALGEOTECHNICSGROUP 8

    A prescribed displacement method was applied to simulate the vertical loading in the triaxial test.

    Incremental multipliers and additional steps of the loading p