Line of intersection of two planes stereonet pdf

No other part of the spherical triangle represents a line of steeper dip than. Mark the outer circle at the closest end of the ns or ew line. If we repeat this operation for all the points of intersection of the plane with the hemisphere then a curved line, a great circle trace, is formed on the streonet. If the line l is a finite segment from p 0 to p 1, then one just has to check that to verify that there is an intersection between the segment and the plane. The trend and plunge of this line can be read directly off the stereonet. Find both the vector equation and the parametric equation of the line containing the points p 1,2. Draw a great circle projection for each plane 1 there will be one unit point of intersection between the two great circles b. Finding the line of intersection of two planes is simple. Any system of equations in which some variables are each dependent on one or more of the other remaining variables. B a line can be defined in threedimensional space by its angle with three orthogonal axes. The idea is similar in its goal to representing the threedimensional surface of the earth in two dimensions on a topographic map.

The stereographic projection relates to the plane inversion in a simple way. Plot the planes collected from the fold and the corresponding poles. To record the dip of a plane all that is needed are two numbers. A geological structures are represented by one or more lines or planes. Map patterns and finding the strike and dip from a mapped. Let p and q be two points on the sphere with projections p. In general, two planes are coincident if the equation of one can be. In the above diagram two planes are plotted, one red, one blue. Since the line is common to both planes, its direction vector can be used as a direction vector in each plane. Intersections are used in kinematic analysis for wedge sliding and direct toppling failure modes, and can also be contoured like pole or dip vectors.

May 27, 2005 how do i find the line of intersection of two planes. Besides, the intersection of two planes will not a point, but nothing, a line or a plane. A wedge failure may occur when the line of intersection of two discontinuities, forming the wedgeshaped block, plunges in the same direction as the slope face and the plunge angle is less than the slope angle but greater than the friction angle along the planes of failure hoek and bray, 1981 figure 1. The intersection of two planes university of waterloo. The pole to a plane is a line that is perpendicular to the plane. Lecture 1s finding the line of intersection of two planes page 55 now suppose we were looking at two planes p. To write the equation of a line of intersection of two planes we still need any point of that line. This is a curved line inside a circle that represents the line of intersection of a plane and the inside of a lower hemisphere, like the inside of a bowl.

Two nonparallel planes i, ii meet in a line l not parallel to plane iii. The intersection line between two planes passes throught the points 1,0,2 and 1,2,3 we also know that the point 2,4,5is located on the plane,find the equation of the given plan and the equation of another plane with a tilted by 60 degree to the given plane and has the same intersection line given for the first plane. Parametric equations for the intersection of planes. Rotate the tracing paper so that the point of intersection lies on the ns or ew line of the net. Where p is the point of intersection, t can go from inf, inf, and d is the direction vector that is the cross product of the normals of the two original planes. The angle of dip is an angle between 0 for horizontal planes and 90 for vertical planes. So, is there some other way to solve this, or am i missing something. Equation for the line of intersection between two planes. In three dimensions which we are implicitly working with here, what is the intersection of two planes. I can see that both planes will have points for which x 0. The parametric equation of the line is simple to obtain once the vector equation is known. Line these two points up with a greatcircle and draw in the axial plane.

The point where the two great circles intersect defines the line contained by both planes. The intersection of the great circles defines the fold axis. Two planes are coincident when they are the same plane. Understanding that the axial hinge is the point of maximum curvature or bending in a fold, it is going to be located at the intersection of the two limbs or great circles in this case. Plane dip and strike, lineation plunge and trend, structural. Equal angle stereonet pdf equal area stereonet with small circles showing consistent size. If a plane projects onto the stereonet as a great circle, then a line or lineation on the plane will plot as a point on the same great circle. The intersection of the two planes is the line x 2t 16, y t this system of equations was dependent on one of the variables we chose z in our solution. Stereonet clip 6 intersection of two planes duration. A wedge failure may occur when the line of intersection of two discontinuities, forming the wedgeshaped block, plunges in the same direction as the slope face and the plunge angle is less than the slope angle but greater than the friction angle along the planes of failure. Contents school of earth and environment 14 lineations due to intersection of two planes where two planes intersect a lineation is created on one plane where the other plane cuts through it. Important tips for practice problem for question 1,direction number of required line is given by1,2,1,since two parallel lines has same direction numbers. For question 2,see solved example 5 for question 3, see solved example 4 for question 4,put the value of x,y,z in the equation of plane.

Map patterns and finding the strike and dip from a. Line of intersection of two planes middle right, above, shows how to find the angle between the two planes in the previous example. Two planes are either parallel or they intersect in a line. The intersection of two planes forms a line in 3dimensional space which plots as a point on the stereonet. The stereonet grid is divided into two degree segments with a thicker ten degree lines figure 4. Lecture 1s finding the line of intersection of two planes. Jul 30, 2015 jr plots two planes and finds the orientation of their intersection line. The plunge of a pole and the dip of a plane sum to 90. The line of intersection between the plane and the sphere will then represent a circle, and this circle is formally known as a.

The floor and a wall of a room are intersecting planes, and where the floor meets the wall is the line of intersection of the two planes. I would appreciate it if someone could guide me or show me some way to do it. The procedures here are slightly simplified because we assume that planes are specified by right hand rule, our preferred convention. We can use the intersection point of the line of intersection of two planes with any. We saw earlier that two planes were parallel or the same if and.

Crains petrophysical handbook structural analysis stereonets. I have an idea, but both of the planes have a 2z ie. Rotate tracing paper so point of intersection lies on eastwest line of stereonet 1 make tick mark on primitive circle showing direction of. To create the rst plane, construct a vector from the known. To find the direction, you determine the cross product of the two normals of the two planes since the line must be perpendicular to both normals. Jul 25, 2017 how to use a paper stereonet to find the line of intersection between two planes. Apply construction 62 twice for two different cutting planes to find two intersection points, x and y. Measure the plunge of the line of intersection and add an arrow pointing in the. They are used for analysis of various field data such as bedding attitudes, planes, hinge lines and numerous other structures. I create online courses to help you rock your math class. So this cross product will give a direction vector for the line of intersection. Find the parametric equations for the line of intersection of the planes. Intersection of two planes in 3d, two planes will intersect in a line.

The line of intersection of two planes, projection of a line. Since any two planar surfaces intersect in a line, most rocks folded with concomitant development of an axial plane foliation display the between bedding and the axial plane. Rakes the stereonet program supports rakes through the input of a plane and an orientation rake in that plane. The three structural discontinuity sets, represented by the great circles plotted in figure 1. Strikes and azimuths bearings are read around the primitive of the stereonet, dips and plunges are read along the equator. If two planes intersect each other, the intersection will always be a line. I havent really worked with mathematica that much, and therefore i dont know how i should get these answers, and also plot the intersection of these two planes. Stereonets are commonly reported to be the leastintuitive part of structural geology. In 3d, two planes p 1 and p 2 are either parallel or they intersect in a single straight line l. Although some planes lines of intersection may be dipping at angles greater than the friction angle, sliding is not. Within a dipping plane the line at right angles to the strike line is the line with the steepest plunge. Rotate the tracing paper until the intersection of the two planes lies on the eastwest diameter of the stereonet. If planes are parallel, their coefficients of coordinates x, y and z are proportional, that is. Lecture 1s finding the line of intersection of two planes page 55 now suppose we were looking at two planes p 1 and p 2, with normal vectors n 1 and n 2.

How to use a paper stereonet to find the line of intersection between two planes. Find an equation of the plane passes through a point and has. Lineations due to intersection of two planes where two planes intersect a lineation is created on one plane where the other plane cuts through it. Stereographic projection the basics geological digressions. Spherical projections with osxstereonet sciencedirect. Flatlying bedding contacts cropping out on sloped topography. As long as the planes are not parallel, they should intersect in a line. A vertical plane will produce a straight line that passes through the. A great circle is the line of intersection with the surface of a sphere of a plane that passes through the center of the sphere. Find the intersection of the line through the points 1, 3, 0 and 1, 2, 4 with the plane through the points 0, 0, 0, 1, 1, 0 and 0, 1, 1. Strike dip 030 30 057 33 043 33 078 40 092 53 100 59 107 70 011 32 335 43 325 55 315 63 311 73 2. Stereographic projection is about representing planar and linear features in a two dimensional diagram. The orientation of a plane is represented by imagining the plane to pass through the centre of a sphere fig.

For a positive ray, there is an intersection with the plane when. In order to explicitly find it, you need a point on the line and the direction of it. We need to find the vector equation of the line of. Similar to planar failures, seve ral conditions relating to the line of intersection must be met for wedge failure to be kinematically admissible.

When planes intersect, the place where they cross forms a line. When two planes intersect they define a line, which is common to both planes. Intersecting planes when two planes intersect they define a line, which is common to both planes. The trend of the pole is opposite the direction a plane dips. We collected a bunch of planar data from the limbs of a fold. A plane can be represented by its normal, which itself is a line.

Garvinintersections of two planes slide 714 intersections of lines and planes intersections of two planes example represent the line r 3. The stereonet itself shows the projection of great circles and small circles. Figure 10 shows a beddingcleavage lineation where cleavage cuts bedding and a joint cleavage lineation where cleavage cuts the joint surface. Determining the orientation of a line of intersection between two planes a. For the second menu, entries are added to a planes dataset plotted as great circles.

The line is contained in the plane in nite intersections the line is parallel to the plane no intersections the line intersects the plane one point of intersection intersections of lines and planes. Lecture notes mineralogy stereographic projections. Plane dip and strike, lineation plunge and trend, structural measurment conventions, the brunton compass, field book, and njgs fms. The subject of linear algebra includes the solution of linear equations. However, not all lines of maximum dip on a stereonet projection will be candidates for the sliding direction. Structural geology laboratory university of south alabama. A small circle marks the path in space of a point on the surface of a sphere that is rotating about an axis. Count in from the outer circumference to find the plunge. These threedimensional features are commonly represented on a twodimensional projection called a stereonet. Given two planes in two adjacent views, where the planes are defined by. Def, find the intersection line by the twoview method. The trace of bedding on an intersecting foliation plane commonly appears as. The line of intersection of two planes, projection of a. The orientation is converted automatically to a line with a trend and plunge, but still remains veiwable as a rake.

Since the intersection of two planes forms a line, we will plot the hinge as a dot on the stereonet. Finding the trend and plunge of the intersection of two planes. Grtu4stereonet civl2002 engineering geology and rock. We saw earlier that two planes were parallel or the same if and only if their normal vectors were scalar multiples of each other. Focal mechanism solutions utilize stereonet representations of fault plane orientations. B geologic methods for describing lines and planes c attitude symbols for geologic maps d reference frames ii definitions of points, lines, and planes a point 1 defined by one set of coordinates an ordered triple in 3d 2 defined by distance and direction from a reference point 3 intersection of two lines 4 intersection of three planes b line.

The line of intersection between the red and blue planes looks like this. Orientations of lines and planes in space a definitions of. Plotting the orientation of a line the simplest geometric information one can display on a stereonet is the orientation of a vertical line. Gr tu4stereonet civl2002 engineering geology and rock. Once it is found, rotate the tracing paper until the intersection is aligned with either the northsouth or eastwest vertical great circle fig. Once you have a point of intersection common to the 2 planes, the line just goes. He calls multiple parks in the area that offer rock climbing and collects data on the height of the rock formations and the average time it takes people to reach the top and come back down. To illustrate, we will find the true dip and strike of a plane for which we have measured two apparent dips. Mar 20, 2019 the green represents the planes orientation when north is rotated back to its standard topofthe stereonet position.