CPC G01B 11/303 (2013.01) [G01N 33/24 (2013.01)] | 4 Claims |
1. A method for determining a reasonable sampling interval with three-dimensional (3D) laser scanning, comprising the following steps:
step S1, collecting rock joint samples;
step S2, acquiring point cloud data of the rock joint samples with 3D laser scanning;
step S3, preprocessing the acquired point cloud data to obtain preprocessed data;
step S4, conducting indoor mechanical tests on the rock joint samples to determine rock mechanics parameters;
step S5, calculating, with the preprocessed data, joint roughness coefficients (JRCs) under different intervals obtained from statistical roughness parameters;
step S6, fitting different relational curves according to a scatter plot between the different intervals and the JRCs to obtain a fitting equation;
step S7, reversely calculating a JRC of each of the rock joint samples with the rock mechanics parameters to obtain a reversely calculated JRC;
step S8, substituting the reversely calculated JRC in the step S7 into the fitting equation obtained in the step S6 to determine a reasonable sampling interval for roughness evaluation;
wherein the rock mechanics parameters comprise a normal stress σ, a peak shear strength τp, a basic frictional angle φb, and a joint compressive strength (JCS);
wherein the step S5 specifically comprises:
step S51, evaluating roughness of any two-dimensional (2D) profile of the rock joint samples with a roughness parameter SDi, wherein an interval between selected 2D profiles is the same as a sampling interval of a point cloud for the rock joint samples, and the roughness parameter is calculated by:
![]() wherein zj+1 and zj are respectively a Z-coordinate of a (j+1)th point and a Z-coordinate of a jth point in a given 2D profile, yj+1 and yj are respectively a Y-coordinate of the (j+1)th point and a Y-coordinate of the jth point, N is a total number of points in the any 2D profile of the rock joint samples, L is a profile length, and iave is an average dip angle;
step S52, calculating a JRC2D of a single 2D profile according to the roughness parameter SDi;
step S53, averaging JRCs of all 2D profiles of a given rock joint sample to determine a JRC3D of a rock joint surface:
![]() wherein, M is a total number of the 2D profiles of the given rock joint sample, and i is an ith 2D profile;
step S54, drawing the scatter plot between sampling intervals and the JRCs;
wherein the step S6 specifically comprises:
step S61, constructing the relational curves between the sampling intervals and the JRCs, comprising a first exponential type, a second exponential type and a Logistic type;
step S62, observing each of the relational curves, proceeding with a step S63 when the relational curve is the first exponential type, proceeding with a step S64 when the relational curve is the second exponential type, and proceeding with a step S65 when the relational curve is the Logistic type;
step S63, defining the fitting equation as y=A1×e−x/t1+y0 or a second-order form y=A1×e(−x/t1)+A2×e(−x/t2)+y0, wherein, A1 is an attenuation coefficient, and controls a rate and a direction in attenuation or growth, t1 is a time scale in the attenuation or the growth and is a constant term, y0 is an offset and a constant term, and determines a position of a curve below or above an x-axis;
step S64, performing fitting by:
![]() wherein, the two stages of the equation are growth and attenuation, respectively, and y0, Ad, Ag, tg, xc, and td are undetermined coefficients;
step S65, performing fitting by:
![]() wherein, A1 is an upper limit of a Logistic function, A2 is a lower limit of the Logistic function, p is a shape parameter, and x0 is a midpoint parameter of the Logistic function;
wherein the reversely calculated JRC in the step S7 is specifically given by:
![]() wherein, τ is the peak shear strength of the rock joint sample obtained in the tests.
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