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MechaRock International Consultants

http://www.mecharock.com/


• About us

• Main activities

Software DISROC®

Consulting services

MechaRock International Consultants is an association of engineering consultants and experts around the world sharing their experience and numerical tools in the field of modelling and design of civil engineering structures, geotechnical and mining projects in rock formations and petroleum geomechanics.

www.mecharock.com

About us

• About us

• Main activities

Software DISROC®

Consulting services


5

Finite Element Method for modelling engineering structures Finite Element Method is the most powerful numerical method for modelling mechanical, hydraulic and thermal behaviour of engineering structures and is widely used in various softwares:

Most of geotechnical projects are designed by Finite Element Method, and software using this method are highly appreciated by engineers if the .

However, in presence of fractures and discontinuities, other software based on Finite Difference or Distinct Element methods seems to be needed, even if these methods or software are less efficient or pleasant to use (time duration, geometry, outputs…).

Necessity of a suitable FE software for rock masses design => DISROC®

Main activities: Software development : DISROC ®

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Joint Elements for fractures in Finite Element Method

c

nA

n( )= +f tg c

Rockjoint, Masonry mortar

Fracture

Contact interface

Joint Element (Goodman 1976)

1 2

3 4

With appropriate parameters, joint elements can reproduce the behavior of fractures, rockjoints, interfaces and contact surfaces.

However, their use in presence of a great number of discontinuities or fractures poses the difficulty of Conform Finite Element mesh creation.

Zero thickness Joint Element was proposed by (Goodman 1976) for modeling discontinuities in the Finite Element Method.

With appropriate parameters, joint elements can reproduce the behavior of fractures, rockjoints, interfaces and contact surfaces.


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e

s

e

Joint : K n , K t,c , f

Conform Finite Element mesh generation for fractured medium

DISROC® is the first Finite Element code especially conceived for fractured rocks. Its powerful meshing tool Discrac® allows easily creating a conform mesh and special Joint Elements for fractured media.

s


8

DISROC®Architecture

GID is a powerful pre and post processor developed by Cimne: www.gidhome.com

DisrocFP generates fractured rock mass

Discrac allows joint elements creation

DISROC® is the calculation module

GeometryBoundary conditions

Mesh

GIDPost Process

GID

DiscracWinDisroc

DISROC®

input file

Fracture generationParameters

output file


http://www.gidhome.com/

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Functionalities of DISROC® : Hydro-mechanical behavior of rock masses

DISROC® has the following main functionalities:

• Elastic-plastic modeling of rocks, rock-joints and rockbolts with incremental loading

• Incremental multistage excavation of underground openings and rock cuttings

• Stability of rock slopes under seismic loads (horizontal and vertical upward acceleration)

• Analysis of block fall down risk in tunnels in blocky rockmasses

• Homogenization of fractured rock mass mechanical properties: Determination of the effective elastic parameters Determination of equivalent permeability Simulation of effective stress-strain curve to determine effective strength properties

• Modeling rock bolts, bars and cables in fractured rock

DISROC® is interfaced with the powerful pre and post-processor GID (www.gidhome.com) that allows easily defining the geometry and materials model, generating mesh, and displaying the calculation results in the form of contours and curves, etc.



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Modelling fractured rocks with DISROC®

With DISROC® it becomes easy to model geotechnical projects like dams, tunnels, bridges and rock cuttings in fractured rocks.

Rock Slope Stability

Tunnel in fractured rock


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b Bolt

Fracture

Bolting fractured rockHomogenization of fractured rock properties

Bolts are very often used to reinforce and stabilize fractured rocks, but are difficult to model when they cross fractures:

DISROC® is the only Finite Element software capable to model properly rock bolts crossing fractures.


Effective elastic properties of fractured rock masses are very often needed for projects design:

DISROC® has a “Large scale Homogenization” module for determination of effective parameters of fracture rock masses (deformation modulus, cohesion, angle of internal friction).

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Modeling bolts and anchors in DISROC®

41110 :Elastic-plastic bolt + elastic-plastic bolt/roc contactNb = 8Param1 = E (bolt elastic modulus)Param2 = Kt (bolt/rock contact shear stifness )Param3 = Kn (bolt/rock contact normal stifness )Param4 = Knt = Ktn (bolt/rock contact ns stifness )Param5 = Ys (bolt elastic limit)Param6 = c (bolt/rock contact cohesion)Param7 = (bolt/rock contact friction angle)Param8 = s0 (bolt pres-stress)

Complete models for bolts, anchors and bars are available in Disroc with full integration of the grout behavior by an elastic-plastic interface model.

b Bolt

Bolts can cross fractures. The model of intersection allows discontinuity of rock displacement at the two side of the fracture with continuity of the bolt rod.Disroc® is the only Finite Element software allowing this modeling.


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Representing bolt stresses in DISROC®

F

FEM mesh for the sample, bolt and fracture

Axial force SL in the bolt represented in two different ways. SL passes by a local maximum when crossing the fracture.

SL (MN)

SL

Deformation at the roof of a bolted tunnel

Weight

SL (MN)

Axial force SL in the bolt represented in two different ways. SL passes by a maximum when crossing the fracture.

Pull out test on a bolt crossing a fracture

FEM mesh for the rock,Bolt and fracture

SL


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Materials models in DISROC®

A great variety of classical constitutive models are available in DISROC for rocks, fractures, joints and rockbolts.

• Solid materials:

Elastic-plastic behavior:- Linear isotropic or anisotropic elasticity- Mohr-Coulomb, Drucker-Prager, Hoek & Brown plastic

failure criteria

• Discontinuities: fractures, faults, rock joints and interfaces

- Linear or non linear Barton-Bandis elasticity- Mohr-Coulomb (Cohesion, friction angle) yield criterion

• Rockbolts and cables

- Elastic and plastic limit for steel rod,- Elastic stiffness, cohesion and friction angle for rock–grout

interface

b Bolt

Fracture

Joint : K n , K t,C , f


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Displaying results in DISROC®

Stress vectors on rock joints Normal stress on rock joints

A variety of different representations of the results are possible, specially those concerning rock joints and fractures.Example: Deformation of the fractured REV

under shear stress sxy :

Ux displacement


• About us

• Main activities

Software DISROC®

Consulting services


TunnelsSlope stablityDams HomogeneizationMasonry structures

Consulting services

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I. Tunnels design

Modeling fractures and bolts with DISROC® is very easy.The following tunnel/road project includes:• a rock mass with two sets of fractures (possibly non persistent)• non persistent fractures (cracks) on the tunnel’s wall,• rock bolts to stabilize the rock slope and the rock cut over the road.

All these elements are easily introduced in the Finite Element model created by DISROC®.

Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting

Main activities: Consulting services - TUNNELS

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Meshing with Disrac ® : The Finite Element mesh created by the software GID (www.gidhome.com) is transformed by the module Discrac® to generate specific elements for fractures, bolts and cables.

The meshing tool integrates:• Intersecting fractures (a)• Non persistent fractures (b)• Rockbolts passing through fractures (c)

b (c)(a)

(b)




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The project includes a tunnel and a rock cutting for a road in a fractured sedimentary formation. The formation is constituted of alternate layers of two limestones varieties. The interfaces between layers are modeled as fractures (Fracture1). Two faults are present in the formation (Fracture2). Modeling passes through the following stages.

I) The fractures are generated stochastically (Fracture1)and faults are placed in the model with their known position (Fracture2) .

II) Other lines defining the soil profile, the tunnel contour, the cutting contour and the rock bolts are introduced in the model.

road

Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting


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Tunnels : Modeling stagesIII) A conform Finite Element mesh is created by DISCRAC®+GID. Specific joint elements for fractures and bolt elements for rockbolts are created automatically. The material properties are assigned to limestone layers, fractures and rock bolts.

In this example, the limestone varieties 1a, 1b, 2a, 2b are identical to Limestone1 and Limestone2 and are introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting.


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In situ stress (syy) before excavation

Vertical displacement Uy due to tunnel excavation Rock bolts are placed (activated) in the model at this stage with a pre-stress SL = 0.1 T

Vertical stress (syy) after tunnel excavation

IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and boundary conditions, modeling excavation stages, displaying results…

SL


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Vertical stress (syy) after rock cutting Vertical displacement showing uplift after rock cutting

Vertical displacement details showing fractures opening Bolts stresses change when crossing fractures and attain a maximum value of 2 T.


Case study 3 - Tunnels

A double line tunnel in a sedimentary rock mass


Tunnels

Tunnel in a blocky rockmass

Displacement at the roof of the tunnel versus the excavation ratio

Calculations diverge before total excavation and can not go beyond the excavation ratio of 0.9.

The displacement field at this stage shows the existence of instable blocks at the roof of the tunnel.

Instable blocks at the roof of the tunnel

0

2

4

6

8

10

12

14

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Load ratio

Displacement

Non convergence

Case study 4 - Tunnels in a blocky rockmass


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Fractures can be introduced in the model by stochastic distribution laws or in a deterministic way.

Gravity load can be applied step by step to determine the safety factor of the slope.

Horizontal and vertical accelerations can be applied in order to analyze the stability against seismic loads.

Rock slope with two types of fractures

Finite Element mesh created by DISCRAC® and GID

Displacement under prescribed load

Shear stress on fractures

Analysis and stabilization of natural rock slopes, rock cuttings and open pit mines

II. Rock slope stability

Main activities: Consulting services – SLOPE STABILITY

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Slope stability under seismic load

Application of gravity forces to define the initial state of stress

Rock cut in a blocky rockmass

Displacement of the point A versus seismic load ratio. The calculations can not go beyond 0.7 g horizontal acceleration and diverge at this stage.

Addition of 1 g horizontal acceleration to represent seismic load

00.20.40.60.8

11.21.41.61.8

2

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Load ratio

Displacement

The displacement field at 0.7g horizontal acceleration reveals an instable block (blue in the figure)

A

(A)


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Slope design optimization

Design modification Modified model in DISROC

Meshing facilities of DISROC for fractured rocks allow easy optimization of rock cutting design.If the projected slope reveals instable, it is easy to change quickly the design in DISROC® and analyze the modified project.

Initial slope design revealed to be instable


• Cross section of an Earth Dam lying on a rock mass foundation with two sets of discontinuities (DISROC)

• Rock foundation along with the dam and the dam-foundation interaction are analyzed in a unique model enclosing all the fractures’ sets

III. Dams

Main activities: Consulting services – DAMS

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Homogenization in DISROC : Fracturing model data acquisitionI) For each family of fractures, the fractures’ orientation, length, spacing and mechanical parameters are specified.

II) Fractures sets are generated stochastically according to specified parameters.

III) A conform Finite Element mesh is created by Discrac® + GID.

Main activities: Consulting services - HOMOGENEIZATION

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Homogenization in DISROC : Load application on the REV

Uy displacement under uniaxial compression syy

Ux displacement under shear stress sxy

V) The average stresses and strains in the REV, taking into account the fractures opening, are computed for each loading case and the homogenized elastic properties of the fractured rock mass are determined from the average values.

IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are applied on the REV’s contour.

12.1 1.6 2.3 2.6

1.6 14.2 3.5 2.8

2.3 3.5 18.4 1.2

2.6 2.8 1.2 5.3

ij

xx yy zz xy

C

Anisotropic elastic coefficientsfor the homogenized behavior


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Homogenization : Anisotropic stiffness and compliance tensor calculation

The stiffness and compliance tensors lines are computed automatically by imposing boundary conditions corresponding to macroscopic strain or stress in different directions.

1

2

3

4

5

6

7

8

11 12 13 1611 11

22 23 2622 22

33 3633 33

6612 122

c c c c

c c c

c c

c

11 12 13 1611 11

22 23 2622 22

33 3633 33

6612 122

s s s s

s s s

s s

s

1111

2122

3

12

13

13 16

22 23 26

32 33 36

62 6

3

611 3 62 6

1

0

0

0

c c c

c c c

c c

c

c

cc

c

c c

c


34

Homogenization : Anisotropic stiffness and compliance tensor calculation

1111

2122

3

12

13

13 16

22 23 26

32 33 36

62 6

3

611 3 62 6

1

0

0

0

c c c

c c c

c c

c

c

cc

c

c c

c

The homogenized stiffness and compliance tensors lines are given as a direct result of calculation.

0.347 1 0.495 2 0.353 16 0.

. . .

.

128

. .

.

0

.

. .

.

.

ijC

E E E E


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Example : sedimentary bedded rock

11 12 13 33 441 1 1 1 1

, , ,n t

s s s s sE E E k D G k D

r11 12 13 16

r12 22 23 26

r r r r13 23 33 36

r16 26 36 66

s s s s

s s s s

s s s s

s s s s

1 1 1e

nE k DE

E = 10 GPa, n = 0.25, Kn= 10 GPa.m, Kt= 2.5 GPa.m, D = 1m

Goodman formula:


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IV. Fractured rock mass replaced by a continuous effective Material

Case study 1- Sedimentary Rock mass : Kousba – North Lebanon

• Accurate calculation of the Homogenized large scale mechanical properties of rock masses: Equivalent anisotropic mechanical properties: E(MPa), n, C (MPa) and f ().• This method replaces the inaccurate empirical classification systems like RMR and Q used by

engineers.


Equivalent elastic modulus in different

directions determined by homogenization

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Case study 2 - Granitic rock mass : De la Vienne, France


Far-field fractures act only by their global effects, and only in elastic phase.

A preliminary homogenization allows replacing the fractured rock mass with a continuous media with effective properties. Great discontinuities like faults can be introduced in the final model as individual lines.

Fractures replaced by a continuous effective material

Combination of fractures modeled individually (near-field) and replaced by an effective material (far-field).

Fractures and faults modeled individually as discontinuities

?


Case study 3 – General case

39

Rockmass with general configuration of fracturesThe effective elastic coefficients Cij are directly calculated by DISROC Homogenization module, and can be introduced as material parameters for modeling the rock mass by its effective properties.

ij

xx yy zz xy

C

0.1 -0.25 -0.25 0

. 0.2 -0.25 0

. . 0.1 0

. . . 0.325

?


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V. Masonry structures

Stability assessment for retrofitting purposesCase study 1 – Bridges

Main activities: Consulting services – MASONRY STRUCTURES

Pont de Nahr el Kalb-Liban

Ouverture et décollementdes joints en traction

Déformée du pont sous charge concentrée

Cartographie de la contrainte verticale

Concentration des contraintes au voisinage des fractures

Evolution de l’état d’endommagement dans le pont

1

2

3

2

Force (T)

Déplacement (m)

1 3

Evolution de l’état d’endommagement dans le pont

1

2

3

2

Force (T)

Déplacement (m)

1 3

Evolution of the damage state in the bridgeOpening of the active fractures

Vertical stress maps

Concentration of stress near the fractures zone

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Case study 2 – Bridge: Retrofitting, with iron bolts, of a masonry bridge suffering from the development of an active fracture due to foundation settlement


Geometry of the masonry bridge Finite elements mesh

Deformed shape: Total displacement : Bolts crossing active fractures

Vertical stress Horizontal stress

42

Case study 3 – Temple: Assessment of the temple’s stability for retrofitting purposes


Yanouh Roman temple, Lebanon

Mesh generation in presence of fractures and Stress maps

43

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http://www.mecharock.com/

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