El modelo de juntas difusas (Plaxis: Jointed Rock) (FLAC: Ubiquitous Joint)
Iñaki García Mendive SRK Consulting (Argentina)
latam.srk.com
[email protected]
El modelo jointed-rock en Plaxis Verification of MC model with 1, 2 or 3 planes:
El modelo de juntas difusas
(see Verification_014_(Mohr-Coulomb,_Ubiquitous_Joints).pdf) Parameters: E= Poisson's ratio Cohesion Friction angle Dilation angle
20 000 kPa 0.3 100 kPa 35° 35°
G = 7692
Características • Direcciones de discontinuidades: plasticidad perfecta • Otras direcciones: elástico – lineal anisotrópica Parámetros • Rigidez (ortotrópica) de roca intacta • Orientación de discontinuidades • Resistencia friccional (hasta tres familias de discontinuidades) Planes
Cohesion Friction Dilation
First angle Second angle Third angle
40 kPa 30° 30°
varies ( 0°.. 90°) = first - 90° =first +45°
Figure 14-5: Variation of uniaxial compressive strength for three sets of joints
2
(From: Verification_014_(Mohr-Coulomb,_Ubiquitous_Joints).pdf) Apart from the 'resolution' of angles, the results of the image below agree quite well with the image above.
8
1
Modelling Rock in Plaxis
El modelo de juntas difusas
Anisotropía elástica: ortotropía inducida por estratificación
3
Jointed-Rock model Cinco parámetros elásticos, deben rock formation cumplir con 𝐸" < 𝐸$ → 1 − 𝜈$ 𝐸" ≥ 2𝜈""𝐸$ E1 E2
stratification
major joint direction
1⁄𝐸$ −𝜈"⁄𝐸" −𝜈$⁄𝐸$ 𝐂= 0 0 0
−𝜈"⁄𝐸" 1⁄𝐸" −𝜈"⁄𝐸" 0 0 0
−𝜈$⁄𝐸$ −𝜈"⁄𝐸" 1⁄𝐸$ 0 0 0
• •
•
Anisotropic elastic be intact rock Maximum of 3 planes – shear failure acco Mohr-Coulomb – Tension cut-off Plane 1 is assumed to stratification direction
0 0 0 0 0 0 0 0 0 • Intact rock : 𝐺" 0of 3 planes with 0 • 1⁄ Maximum – shear failure according 0 1⁄𝐺" 0 to Mohr-Coulomb – Tension cut-off 0 0 2 1 + 𝜈 ⁄𝐸$ Parameters:
E1, ν1 ,E2, ν2, G
ci, φi,ψi for i=1 σt,i for i=1,2,3
(Plaxis UM)
El modelo de juntas difusas
Elasticidad ortotrópica restringida
Tres parámetros elásticos: calibración Jointed más Rocksimple model – orientation of sliding plane
𝐂=
1 𝐸"
1 −𝜈 −𝛼 𝜈 0 0 0
−𝜈 1 −𝛼 𝜈 0 0 0
−𝛼 𝜈 −𝛼 𝜈 1 0 0 0
0 0 declination 0 0 0 0 N y t 2𝛼 1 + 𝜈 0 0 2𝛼 1 +𝜈 α2 s* 0 0
0 0 0 z 0 0 2 1+𝜈
α1 s
𝛼= 4
𝐸"⁄𝐸$
sliding plane
x
(Graham & Houlsby 1983)
Direction of sliding plane defined • Dip angle (α1) • Dip direction (α2) • Declination
t = horizontal direction of sliding s = falling direction of sliding plan s* = horizontal component of s
α1 = angle between s* and s, meas s* to s looking into the direct α2 = angle between North (N) and clockwise from N to s* lookin Declination = angle between Nort
NOTE: when creating input this is ba z-plane with highest z-coordi origin
2
El modelo de juntas difusas
Comportamiento numérico: talud uniforme 𝛼$ = 30°
Geometría • ℎ = 26𝑚 • 𝛽 = 51º Materiales • 𝛾 = 20 𝑘𝑁⁄𝑚> • Elasticidad isotrópica • 𝑐 = 100𝑘𝑃𝑎 • 𝜙 = 20º • 𝜓 = 0º
𝛼$ = 10° 𝛼" = 50°
5
El modelo de juntas difusas
El modelo ISO Jointed Rock
El model Jointed Rock se ha extendido para incorporar plasticidad Mohr-Coulomb en direcciones distintas a las de las discontinuidades Plastic points after safety analysis (Phase 4)
Plastic points after safety analysis (Phase 4)
Plastic points after safety analysis (Phase 5)
Plastic points after safety analysis (Phase 6)
Conclusions The Iso-JRMC model has been implemented as a user-defined soil model and seems to work correctly in 2D and 3D; both in normal calculations as well as in safety factor calculations. The (Bonnier model has been verified and applied on simple practical2015) applications.
6
References Azami A., Yacoub T. & Curran J. (2012) “Effects of Strength Anisotropy on the Stability of Slopes”, GeoManitoba 2012 - Canadian Geotechnical Society, Winnepeg, Manitoba, Canada, Sept. 30 - October 3, 2012
14
http://www.rocscience.com/help/RS3beta/webhelp/pdf_files/verification/Verification_014_%28M ohr-Coulomb,_Ubiquitous_Joints%29.pdf
Plastic points after safety analysis (Phase 5)
3
El modelo de juntas difusas
Ventajas y desventajas del modelo jointed-rock
7
Ventajas • Permite una representación realista del comportamiento de macizos rocosos anisotrópicos • Reproduce la anisotropía elástica y plástica Desventajas • No simula la falla de roca intacta (mejorado con el modelo ISO Jointed Rock Mohr Coulomb) • En 2D, las discontinuidades tienen que ser perpendiculares al plano del modelo • Hay “infinitas” discontinuidades: los mecanismos de falla siempre involucran todo el talud
(Bonnier 2015)
4
