PERMFILE135086

• Permit No: C1981038
• IBM Index Class Name: Permit File
• Doc Date: 12/11/2001
• Doc Name: Geotechnical Review
• Section_Exhibit Name: Volume 6 PHASE I STABILITY ANALYSES Appendix
• Media Type: D
• Archive: No

SPHERICAL PROJECTION

SPHERICAL PROJELTION ]S A SIMPLE AND USEFUL TOOL FOR THE PRESENTATION
AND ANALYSIS OF DATA ON THE ORIENTATION OF Ih1PORTANT PLANES OF MECHANICAL
DISCONTINUITIES SUCH AS JOINTS, BEDDING PLANES, FAULTS, ETL., THAT ARE
USUALLY PRESENT IN ROCK MASSES.
THE TECHNIQUE USES A REFERENCE HEMISPHERE TO REPRESENT THE ORIENTATION
OF ANY PLANE OR LINE. THE INTERCEPT OF THE LINE OR PLANE WITH THE REFER-
ENCE HEMISPHERE IS PROJECTED ONTO A HORIZONTAL PLANE, WHERE LINES PROJECT
AS POINTS AND PLAtJES PROJECT AS LINES, AS SHOWN IN FIGURE 1. THIS PRO-
JECTION COt4PLETELY AND UNIQUELY DEFINES THE ORIENTATION OF A PLANE OR OF
A LINE.
A PLANE LAN BE REPRESENTED EITHER BY ITS GREAT CIRCLE, OR, MORE
COMMONLY, BY ITS POLE. A POLE REPRESENTS THE INTERSECTION OF THE NORMAL
TO THE PLANE WITH THE REFERENCE HEMISPHERE.
THE DISTRIBUTION OF PLANE ORIENTATIONS CAN BE ANALYZED STATISTICALLY
ON AN EQUAL AREA PROJECTION, FOR WHICH A UtJIT OF AREA ANYWHERE ON THE
PROJECTION REPRESENTS THE SAME FRACTION OF THE TOTAL AREA OF THE REFER-
ENCE HEMISPHERE. THE NUMBER OF PLANE POLES FALLING WITHIN A COUNTING
CIRCLE OF AREA 1 PERCENT THAT OF THE NET IS DETERt4INED AT POINTS OVER THE
NET, AND THESE VALUES ARE CONTOURED.
u

PLOTS OF BOTH ItJDIVIDUAL POINTS AND CONTOUR DIAGRAM ARE PRODUCED
AUTOMATICALLY BY A COMPUTER PROGRAM. FURTHER ANALYSIS CAN GIVE THE
PROBABILITY DISTRIBUTION OF EACH CONTOUR CLUSTER APPEARIIJG ON THE NET,
AS WELL AS THE DISPERSION OR RANDOt4NESS OF THE ENTIRE PLANE SYSTEMS.
LONER HEMISPHERE
EOWL AREA PROJECTION
TOA HORIZONTAL N
PLANE plan,
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GEO-HYDRO CONSULTING,INC.
RE PR ESE NTAT1pN OF A
PLANE ON A NET
PLATE 3A
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