{"id":1510,"date":"2023-12-06T21:26:18","date_gmt":"2023-12-06T21:26:18","guid":{"rendered":"https:\/\/books.gw-project.org\/structural-geology-applied-to-fractured-aquifer-characterization\/?post_type=part&p=1510"},"modified":"2023-12-11T16:29:15","modified_gmt":"2023-12-11T16:29:15","slug":"notations","status":"publish","type":"part","link":"https:\/\/books.gw-project.org\/structural-geology-applied-to-fractured-aquifer-characterization\/part\/notations\/","title":{"raw":"Notations","rendered":"Notations"},"content":{"raw":"\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
\r\n

1\/v<\/em><\/p>\r\n<\/td>\r\n

\r\n

Poisson's number (m) the inverse of Poisson\u2019s ratio [M0<\/span><\/sub>L0<\/span><\/sub>T0<\/span><\/sub>, dimensionless]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

C<\/em><\/p>\r\n<\/td>\r\n

\r\n

cohesion or intrinsic shear strength of material [ML-1<\/sup><\/span>T-2<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u00a0\u00a0 CDZ<\/em><\/p>\r\n<\/td>\r\n

\r\n

composite deformation zone<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

C<\/em>f<\/span><\/sub><\/p>\r\n<\/td>\r\n

\r\n

cohesion or intrinsic shear strength along-foliation feature [ML-1<\/sup><\/span>T-2<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u00a0\u00a0 DDZ<\/em><\/p>\r\n<\/td>\r\n

\r\n

distributed deformation zone<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

E<\/em><\/p>\r\n<\/td>\r\n

\r\n

Young's modulus [ML-1<\/sup><\/span>T-2<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

e<\/em><\/p>\r\n<\/td>\r\n

\r\n

fracture aperture [L]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

e<\/em>v<\/span><\/sub><\/p>\r\n<\/td>\r\n

\r\n

vertical compression [LL-1<\/sup><\/span>, dimensionless]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u00a0\u00a0 FPF<\/em><\/p>\r\n<\/td>\r\n

\r\n

foliation parallel fracture<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

g<\/em><\/p>\r\n<\/td>\r\n

\r\n

gravitational acceleration [LT\u22122<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

h<\/em><\/p>\r\n<\/td>\r\n

\r\n

depth [L]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u00a0\u00a0 ISF<\/em><\/p>\r\n<\/td>\r\n

\r\n

intermediate to high dip fracture<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

K<\/em><\/p>\r\n<\/td>\r\n

\r\n

hydraulic conductivity [LT-1<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

k<\/em><\/p>\r\n<\/td>\r\n

\r\n

permeability [L2<\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

K<\/em>f<\/span><\/sub><\/p>\r\n<\/td>\r\n

\r\n

fracture hydraulic conductivity [LT\u22122<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u00a0\u00a0 LDZ<\/em><\/p>\r\n<\/td>\r\n

\r\n

localized deformation zone<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u00a0\u00a0 MPa<\/em><\/p>\r\n<\/td>\r\n

\r\n

megapascal [106 <\/span>Pascals]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

N<\/em><\/p>\r\n<\/td>\r\n

\r\n

number of fractures per unit length [L\u22122<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u03c1<\/em><\/p>\r\n<\/td>\r\n

\r\n

density [ML\u22123<\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

p<\/em><\/p>\r\n<\/td>\r\n

\r\n

fluid pressure [ML-1<\/sup><\/span>T-2<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

R<\/em>1<\/span><\/sub><\/p>\r\n<\/td>\r\n

\r\n

Riedel shear [same sense of movement]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

R<\/em>2<\/span><\/sub><\/p>\r\n<\/td>\r\n

\r\n

Riedel shear [opposite sense of movement]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

SFF<\/em><\/p>\r\n<\/td>\r\n

\r\n

single fracture fault<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u00a0\u00a0 SHF<\/em><\/p>\r\n<\/td>\r\n

\r\n

subhorizontal fracture<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

SHmax<\/span><\/sub><\/em>,<\/p>\r\n<\/td>\r\n

\r\n

maximum horizontal stress [ML-1<\/sup><\/span>T-2<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

SVF<\/em><\/p>\r\n<\/td>\r\n

\r\n

subvertical fractures<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

S<\/em>z<\/span><\/sub><\/p>\r\n<\/td>\r\n

\r\n

vertical stress [ML-1<\/sup><\/span>T-2<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

T<\/em><\/p>\r\n<\/td>\r\n

\r\n

definition depends on context, fluid flow - transmissivity [L2<\/span>T-1<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

T<\/em><\/p>\r\n<\/td>\r\n

\r\n

definition depends on context, material property - tensile strength [ML-1<\/sup><\/span>T-2<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

t<\/em>f<\/span><\/sub><\/p>\r\n<\/td>\r\n

\r\n

intrinsic transmissivity [L3<\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

TFZ<\/em><\/p>\r\n<\/td>\r\n

\r\n

throughgoing fracture zone<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

v<\/em><\/p>\r\n<\/td>\r\n

\r\n

Poisson's ratio [M0<\/span>L0<\/span>T0<\/span>, dimensionless]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

v<\/em><\/p>\r\n<\/td>\r\n

\r\n

Darcy flux [L2<\/span>T\u22122<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

z<\/em><\/p>\r\n<\/td>\r\n

\r\n

depth [L]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u0394h<\/sub><\/p>\r\n<\/td>\r\n

\r\n

hydraulic head gradient [LL-1<\/sup><\/span>, dimensionless]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u03bc<\/em><\/p>\r\n<\/td>\r\n

\r\n

dynamic viscosity [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u03c6<\/em><\/p>\r\n<\/td>\r\n

\r\n

friction angle [\u00b0]<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u03c3<\/em>1<\/span><\/sub><\/p>\r\n<\/td>\r\n

\r\n

maximum principal stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u03c3<\/em>2<\/span><\/sub><\/p>\r\n<\/td>\r\n

\r\n

intermediate principal stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u03c3<\/em>3<\/span><\/sub><\/p>\r\n<\/td>\r\n

\r\n

minimum principal stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u03c3<\/em>h<\/span><\/sub><\/p>\r\n<\/td>\r\n

\r\n

horizontal stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u03c3h<\/span><\/sub>\u00b0<\/p>\r\n<\/td>\r\n

\r\n

initial horizontal stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u03c3<\/em>h<\/sub> dol<\/sub><\/span><\/p>\r\n<\/td>\r\n

\r\n

dolostone horizontal stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u03c3<\/em>h mud<\/span><\/sub><\/p>\r\n<\/td>\r\n

\r\n

mudstone horizontal stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u03c3<\/em>n<\/span><\/sub><\/p>\r\n<\/td>\r\n

\r\n

normal stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u03c3<\/em>v<\/span><\/sub><\/p>\r\n<\/td>\r\n

\r\n

vertical stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u03c3<\/em>v<\/span><\/sub>\u00b0<\/p>\r\n<\/td>\r\n

\r\n

Initial vertical stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u03c4<\/em><\/p>\r\n<\/td>\r\n

\r\n

shear stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u03b8<\/em><\/p>\r\n<\/td>\r\n

\r\n

angle between shear fracture and \u03c3<\/span><\/em>1 <\/span><\/sub>[\u00b0]<\/span><\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n ","rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\n

1\/v<\/em><\/p>\n<\/td>\n

\n

Poisson’s number (m) the inverse of Poisson\u2019s ratio [M0<\/span><\/sub>L0<\/span><\/sub>T0<\/span><\/sub>, dimensionless]<\/p>\n<\/td>\n<\/tr>\n

\n

C<\/em><\/p>\n<\/td>\n

\n

cohesion or intrinsic shear strength of material [ML-1<\/sup><\/span>T-2<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

\u00a0\u00a0 CDZ<\/em><\/p>\n<\/td>\n

\n

composite deformation zone<\/p>\n<\/td>\n<\/tr>\n

\n

C<\/em>f<\/span><\/sub><\/p>\n<\/td>\n

\n

cohesion or intrinsic shear strength along-foliation feature [ML-1<\/sup><\/span>T-2<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

\u00a0\u00a0 DDZ<\/em><\/p>\n<\/td>\n

\n

distributed deformation zone<\/p>\n<\/td>\n<\/tr>\n

\n

E<\/em><\/p>\n<\/td>\n

\n

Young’s modulus [ML-1<\/sup><\/span>T-2<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

e<\/em><\/p>\n<\/td>\n

\n

fracture aperture [L]<\/p>\n<\/td>\n<\/tr>\n

\n

e<\/em>v<\/span><\/sub><\/p>\n<\/td>\n

\n

vertical compression [LL-1<\/sup><\/span>, dimensionless]<\/p>\n<\/td>\n<\/tr>\n

\n

\u00a0\u00a0 FPF<\/em><\/p>\n<\/td>\n

\n

foliation parallel fracture<\/p>\n<\/td>\n<\/tr>\n

\n

g<\/em><\/p>\n<\/td>\n

\n

gravitational acceleration [LT\u22122<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

h<\/em><\/p>\n<\/td>\n

\n

depth [L]<\/p>\n<\/td>\n<\/tr>\n

\n

\u00a0\u00a0 ISF<\/em><\/p>\n<\/td>\n

\n

intermediate to high dip fracture<\/p>\n<\/td>\n<\/tr>\n

\n

K<\/em><\/p>\n<\/td>\n

\n

hydraulic conductivity [LT-1<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

k<\/em><\/p>\n<\/td>\n

\n

permeability [L2<\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

K<\/em>f<\/span><\/sub><\/p>\n<\/td>\n

\n

fracture hydraulic conductivity [LT\u22122<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

\u00a0\u00a0 LDZ<\/em><\/p>\n<\/td>\n

\n

localized deformation zone<\/p>\n<\/td>\n<\/tr>\n

\n

\u00a0\u00a0 MPa<\/em><\/p>\n<\/td>\n

\n

megapascal [106 <\/span>Pascals]<\/p>\n<\/td>\n<\/tr>\n

\n

N<\/em><\/p>\n<\/td>\n

\n

number of fractures per unit length [L\u22122<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

\u03c1<\/em><\/p>\n<\/td>\n

\n

density [ML\u22123<\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

p<\/em><\/p>\n<\/td>\n

\n

fluid pressure [ML-1<\/sup><\/span>T-2<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

R<\/em>1<\/span><\/sub><\/p>\n<\/td>\n

\n

Riedel shear [same sense of movement]<\/p>\n<\/td>\n<\/tr>\n

\n

R<\/em>2<\/span><\/sub><\/p>\n<\/td>\n

\n

Riedel shear [opposite sense of movement]<\/p>\n<\/td>\n<\/tr>\n

\n

SFF<\/em><\/p>\n<\/td>\n

\n

single fracture fault<\/p>\n<\/td>\n<\/tr>\n

\n

\u00a0\u00a0 SHF<\/em><\/p>\n<\/td>\n

\n

subhorizontal fracture<\/p>\n<\/td>\n<\/tr>\n

\n

SHmax<\/span><\/sub><\/em>,<\/p>\n<\/td>\n

\n

maximum horizontal stress [ML-1<\/sup><\/span>T-2<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

SVF<\/em><\/p>\n<\/td>\n

\n

subvertical fractures<\/p>\n<\/td>\n<\/tr>\n

\n

S<\/em>z<\/span><\/sub><\/p>\n<\/td>\n

\n

vertical stress [ML-1<\/sup><\/span>T-2<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

T<\/em><\/p>\n<\/td>\n

\n

definition depends on context, fluid flow – transmissivity [L2<\/span>T-1<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

T<\/em><\/p>\n<\/td>\n

\n

definition depends on context, material property – tensile strength [ML-1<\/sup><\/span>T-2<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

t<\/em>f<\/span><\/sub><\/p>\n<\/td>\n

\n

intrinsic transmissivity [L3<\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

TFZ<\/em><\/p>\n<\/td>\n

\n

throughgoing fracture zone<\/p>\n<\/td>\n<\/tr>\n

\n

v<\/em><\/p>\n<\/td>\n

\n

Poisson’s ratio [M0<\/span>L0<\/span>T0<\/span>, dimensionless]<\/p>\n<\/td>\n<\/tr>\n

\n

v<\/em><\/p>\n<\/td>\n

\n

Darcy flux [L2<\/span>T\u22122<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

z<\/em><\/p>\n<\/td>\n

\n

depth [L]<\/p>\n<\/td>\n<\/tr>\n

\n

\u0394h<\/sub><\/p>\n<\/td>\n

\n

hydraulic head gradient [LL-1<\/sup><\/span>, dimensionless]<\/p>\n<\/td>\n<\/tr>\n

\n

\u03bc<\/em><\/p>\n<\/td>\n

\n

dynamic viscosity [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

\u03c6<\/em><\/p>\n<\/td>\n

\n

friction angle [\u00b0]<\/span><\/p>\n<\/td>\n<\/tr>\n

\n

\u03c3<\/em>1<\/span><\/sub><\/p>\n<\/td>\n

\n

maximum principal stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

\u03c3<\/em>2<\/span><\/sub><\/p>\n<\/td>\n

\n

intermediate principal stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

\u03c3<\/em>3<\/span><\/sub><\/p>\n<\/td>\n

\n

minimum principal stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

\u03c3<\/em>h<\/span><\/sub><\/p>\n<\/td>\n

\n

horizontal stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

\u03c3h<\/span><\/sub>\u00b0<\/p>\n<\/td>\n

\n

initial horizontal stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

\u03c3<\/em>h<\/sub> dol<\/sub><\/span><\/p>\n<\/td>\n

\n

dolostone horizontal stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

\u03c3<\/em>h mud<\/span><\/sub><\/p>\n<\/td>\n

\n

mudstone horizontal stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

\u03c3<\/em>n<\/span><\/sub><\/p>\n<\/td>\n

\n

normal stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

\u03c3<\/em>v<\/span><\/sub><\/p>\n<\/td>\n

\n

vertical stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

\u03c3<\/em>v<\/span><\/sub>\u00b0<\/p>\n<\/td>\n

\n

Initial vertical stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

\u03c4<\/em><\/p>\n<\/td>\n

\n

shear stress [ML\u22122<\/sup><\/span>T\u22122<\/sup><\/span>]<\/p>\n<\/td>\n<\/tr>\n

\n

\u03b8<\/em><\/p>\n<\/td>\n

\n

angle between shear fracture and \u03c3<\/span><\/em>1 <\/span><\/sub>[\u00b0]<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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