Mecha Rock International Consultants www mecharock com Mecha

Mecha. Rock International Consultants www. mecharock. com

Mecha. Rock International Consultants • About us • Main activities Software DISROC® Consulting services

About us Mecha. Rock 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

Mecha. Rock International Consultants • About us • Main activities Software DISROC® Consulting services

Main activities: Software development : DISROC ® 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 as given by the following figures: 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, softwares based on Finite Difference or Distinct Element methods seems to be needed, even if these methods and software less efficient or less pleasant to use (calculation time, geometry, outputs…). Necessity of a suitable FE software for rock masses design => DISROC® 5

Main activities: Software development : DISROC ® Joint Elements for fractures in Finite Element Method Zero thickness Joint Element was proposed by (Goodman 1976) for modeling discontinuities in the Finite Element Method. Fracture 3 4 1 2 Joint Element (Goodman 1976) With appropriate parameters, joint elements can reproduce the behavior of fractures, rockjoints, interfaces and contact surfaces. Rockjoint, Masonry mortar However, their use in presence of a great number of discontinuities or fractures poses the difficulty of Conform Finite Element mesh creation. Contact interface 6

Main activities: Software development : DISROC ® 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 e Joint : K n , Kt, c, s e 7

Main activities: Software development : DISROC® Architecture Win. Disroc Fracture generation Parameters GID is a powerful pre and post processor developed by Cimne: www. gidhome. com Disroc. FP generates fractured rock mass DISROC ® GID Geometry Boundary conditions Mesh input file DISROC® Discrac allows joint elements creation DISROC® is the calculation module output file GID Post Process 8

Main activities: Software development : DISROC ® 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 9 curves, etc.

Main activities: Software development : DISROC ® Modelling fractured rocks with DISROC® With DISROC® it becomes easy to model geotechnical projects like dams, tunnels, bridges and rock cuttings in fractured rocks. Tunnel in fractured rock Rock Slope Stability 10

Main activities: Software development : DISROC ® 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). Homogenization of fractured rock properties Bolting fractured rock 11

Main activities: Software development : DISROC ® Modeling bolts and anchors in DISROC® Complete models for bolts, anchors and bars are available in Disroc with full integration of the grout behavior by an elastic-plastic interface model. 41110 : Elastic-plastic bolt + elastic-plastic bolt/roc contact Nb = 8 Param 1 = E (bolt elastic modulus) Param 2 = Kt (bolt/rock contact shear stifness ) Param 3 = Kn (bolt/rock contact normal stifness ) Param 4 = Knt = Ktn (bolt/rock contact ns stifness ) Param 5 = Ys (bolt elastic limit) Param 6 = c (bolt/rock contact cohesion) Param 7 = (bolt/rock contact friction angle) Param 8 = s 0 (bolt pres-stress) 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. 12

Main activities: Software development : DISROC ® Representing bolt stresses in DISROC® q Pull out test on a bolt crossing a fracture F SL SL (MN) 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. q Deformation at the roof of a bolted tunnel SL (MN) SL Weight FEM mesh for the rock, Bolt and fracture Axial force SL in the bolt represented in two different ways. 13 SL passes by a maximum when crossing the fracture.

Main activities: Software development : DISROC ® 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 Joint : K n , K t , C , • Rockbolts and cables - Elastic and plastic limit for steel rod, - Elastic stiffness, cohesion and friction angle for rock–grout interface 14

Main activities: Software development : DISROC ® Displaying results in DISROC® 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 Stress vectors on rock joints Normal stress on rock joints 15

Mecha. Rock International Consultants • About us • Main activities Software DISROC® Consulting services

Consulting services Tunnels Slope stablity Dams Homogeneization Masonry structures

Main activities: Consulting services - TUNNELS I. Tunnels design Case study 1 - Tunnels : Example of a project in fractured formation with rock cutting 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®. 18

Main activities: Consulting services - TUNNELS 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) (a) (c) (b) 19

Main activities: Consulting services - TUNNELS

Main activities: Consulting services - TUNNELS Case study 2 - Tunnels : Example of a project in fractured formation with rock cutting 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 (Fracture 1). Two faults are present in the formation (Fracture 2). Modeling passes through the following stages. I) The fractures are generated stochastically (Fracture 1)and faults are placed in the model with their known position (Fracture 2). road II) Other lines defining the soil profile, the tunnel contour, the cutting contour and the 21 rock bolts are introduced in the model.

Main activities: Consulting services - TUNNELS Tunnels : Modeling stages III) 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 1 a, 1 b, 2 a, 2 b are identical to Limestone 1 and Limestone 2 and are introduced for determination of the initial in situ stresses before tunnel excavation and rock cutting. 22

Main activities: Consulting services - TUNNELS IV) The next steps are achieved like in classical Finite Element codes: prescribing loads and boundary conditions, modeling excavation stages, displaying results… In situ stress (syy) before excavation Vertical stress (syy) after tunnel excavation SL 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 23

Main activities: Consulting services - TUNNELS Vertical stress (syy) after rock cutting Vertical displacement details showing fractures opening Vertical displacement showing uplift after rock cutting Bolts stresses change when crossing fractures 24 and attain a maximum value of 2 T.

Main activities: Consulting services - TUNNELS Case study 3 - Tunnels A double line tunnel in a sedimentary rock mass

Main activities: Consulting services - TUNNELS Case study 4 - Tunnels in a blocky rockmass Tunnels Non convergence Displacement at the roof of the tunnel versus the excavation ratio Tunnel in a blocky rockmass 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

Main activities: Consulting services – SLOPE STABILITY II. Rock slope stability Analysis and stabilization of natural rock slopes, rock cuttings and open pit mines q q q 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. Finite Element mesh created by DISCRAC® and GID Shear stress on fractures Rock slope with two types of fractures Displacement under prescribed load 27

Main activities: Consulting services – SLOPE STABILITY Slope stability under seismic load A Rock cut in a blocky rockmass Application of gravity forces to define the initial state of stress Addition of 1 g horizontal acceleration to represent seismic load (A) 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. The displacement field at 0. 7 g horizontal acceleration reveals an instable block (blue 28 in the figure)

Main activities: Consulting services – SLOPE STABILITY Slope design optimization 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 Design modification Modified model in DISROC 29

Main activities: Consulting services – DAMS III. Dams • 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

Main activities: Consulting services - HOMOGENEIZATION Homogenization in DISROC : Fracturing model data acquisition I) 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. 31

Main activities: Consulting services - HOMOGENEIZATION Homogenization in DISROC : Load application on the REV IV) 3 different basic loads; uniaxial compression in x and y directions and pure xy shear, are applied on the REV’s contour. 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. Anisotropic elastic coefficients for the homogenized behavior 32

Main activities: Consulting services - HOMOGENEIZATION 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. 33

Main activities: Consulting services - HOMOGENEIZATION Homogenization : Anisotropic stiffness and compliance tensor calculation The homogenized stiffness and compliance tensors lines are given as a direct result of calculation. 34

Main activities: Consulting services - HOMOGENEIZATION Example : sedimentary bedded rock Goodman formula: E = 10 GPa, n = 0. 25, Kn= 10 GPa. m, Kt= 2. 5 GPa. m, D = 1 m 35

Main activities: Consulting services - HOMOGENEIZATION IV. Fractured rock mass replaced by a continuous effective Material • • 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. Case study 1 - Sedimentary Rock mass : Kousba – North Lebanon 36 in different Equivalent elastic modulus directions determined by homogenization

Main activities: Consulting services - HOMOGENEIZATION Case study 2 - Granitic rock mass : De la Vienne, France 37

Main activities: Consulting services - HOMOGENEIZATION Case study 3 – General case 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 and faults modeled individually as discontinuities Far-field fractures act only by their global effects, and only in elastic phase. Combination of fractures modeled individually (nearfield) and replaced by an effective material (far-field). Fractures replaced by a continuous effective material

Main activities: Consulting services - HOMOGENEIZATION Rockmass with general configuration of fractures The 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. ? 39

Main activities: Consulting services – MASONRY STRUCTURES V. Masonry structures Case study 1 – Bridges Stability assessment for retrofitting purposes Evolution of the damage state in the bridge Opening of the active fractures Vertical stress maps Concentration of stress near the fractures zone 40

Main activities: Consulting services – MASONRY STRUCTURES 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 41

Main activities: Consulting services – MASONRY STRUCTURES 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 42

For more information: Mecha. Rock International Consultants www. mecharock. com 43