CN112347620A - Method for predicting damage time of rock-soil disaster body in real time by using three characteristic points - Google Patents

Method for predicting damage time of rock-soil disaster body in real time by using three characteristic points Download PDF

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CN112347620A
CN112347620A CN202011147272.6A CN202011147272A CN112347620A CN 112347620 A CN112347620 A CN 112347620A CN 202011147272 A CN202011147272 A CN 202011147272A CN 112347620 A CN112347620 A CN 112347620A
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郝圣旺
王立伟
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Abstract

The invention provides a method for predicting the damage time of a rock and soil disaster body in real time by three characteristic points, which comprises the following steps: s1: obtaining a rate time curve of the monitored quantity; s2: defining three characteristic points A, B, C on the speed time curve, and setting the speed relation of the three points; s3: optionally selecting two points on the speed time curve as characteristic points A, C, and determining the position of the characteristic point B according to the speed relation; s4: determining the relationship between the destruction time and the three points according to the three-point rate relationship and the power law singularity precursor expression: s5: determining a destruction time tf(ii) a S6: repeating the steps S3-S5 for the destruction time tfUpdating and correcting to obtain final destruction time tf*. The prediction process of the invention is irrelevant to the power exponent, and the damage time can be predicted under the condition of unknown critical power exponent.

Description

Method for predicting damage time of rock-soil disaster body in real time by using three characteristic points
Technical Field
The invention relates to the technical field of geological disaster prediction, in particular to a method for predicting damage time of a rock and soil disaster body in real time by using three characteristic points.
Background
The accurate prediction of the damage time of the disaster body is the basis and the precondition of the evaluation, prevention and prediction early warning of the geological disaster. The key to the difficulty in predicting the time of failure lies in the uncertainty of catastrophic failure. An important approach to dealing with such problems is to find precursors to catastrophic failure. The field monitoring of disasters of different scales such as earthquake, volcanic eruption, landslide, collapse and the like and laboratory experiment observation data show that the response quantities such as deformation, acoustic emission and the like can show a critical power law singularity acceleration trend when approaching the catastrophe damage moment, and are effective damage precursors, and the effectiveness of predicting the damage time of the precursors is verified by a large number of laboratory and field measurement results. However, these predictions are mainly a posteriori, that is, predictions made with knowledge of the power law singularity index.
The power law singularity precursor expression is: k (t)f-t)-β；
Where v is the rate of the monitored quantity (e.g., deformation, acoustic emission), tfRepresenting the destruction time, k is a parameter, and β is the power law singularity index. From the above formula, one can obtain:
v-1/β＝k-1/β(tf-t)
however, at the destruction time tfWhen unknown, namely before destruction, the value of the power exponent beta is unknown, and the specific value of the power law singularity exponent can be determined only after the destruction occurs. Therefore, the unknown power exponent is a key difficulty in predicting the destruction time based on the power law singularity precursor.
Disclosure of Invention
According to the technical problems, the method is provided for predicting the damage time in real time based on the geometric drawing of the rate-time evolution curve under the condition of unknown power law singularity index, and updating and correcting the prediction result based on the newly added data.
The technical means adopted by the invention are as follows:
a method for predicting the damage time of a rock and soil disaster body in real time by three characteristic points comprises the following steps:
s1: obtaining a rate-time curve of the evolution of the monitoring quantity development rate along with time based on field monitoring and experimental observation data; calculating the evolution rate of monitoring quantities such as disaster body deformation and acoustic emission signals according to field monitoring and experimental observation data, making a rate-time curve of the evolution rate of each monitoring quantity along with time, and determining an accelerated development period based on the rate-time evolution curve;
s2: three feature points A, B, C on the rate-time curve are defined, and the rate relationship between feature points A, B, C is set as:
Figure BDA0002740059620000021
vB、vA、vCthe velocities at characteristic points A, B, C in the velocity curves, respectively;
s3: two optional points on the speed time curve are used as characteristic points A, C, and the position of the characteristic point B is determined according to the speed relation between the characteristic points A, B, C;
s4: determining the relationship between the destruction time and the time of three characteristic points A, B, C according to the speed relationship between the characteristic points A, B, C and the power law singularity precursor expression:
Figure BDA0002740059620000022
tfto break time, tA、tB、tCTime corresponding to the characteristic point A, B, C in the rate curve;
s5: determining the destruction time t according to the relationship between the destruction time and the time of the three characteristic points A, B, Cf；
S6: repeating the steps S3-S5 for the destruction time tfUpdating and correcting to obtain final destruction time tf*。
Further, in step S4, the power law singularity precursor expression is:
v＝k(tf-t)-β (3)
wherein v is the rate of the monitoring quantity, k is a parameter, and beta is a power law singularity index;
taking logarithm of two sides of the formula (3) to obtain:
logv＝logk-βlog(tf-t) (4)
i.e., the relationship of the rate, time and destruction time of the feature point A, B, C is:
logvA＝logk-βlog(tf-tA) (5)
logvB＝logk-βlog(tf-tB) (6)
logvC＝logk-βlog(tf-tC) (7)
subtracting the formula (4) from the formula (3), and subtracting the formula (5) from the formula (4) to obtain:
Figure BDA0002740059620000031
Figure BDA0002740059620000032
obtained according to formula (1), formula (8) and formula (9)
Figure BDA0002740059620000033
The destruction time can be obtained from equation (10):
Figure BDA0002740059620000034
subtracting t from both sides of the above formulaAAfter that, it is possible to obtain:
Figure BDA0002740059620000035
。
determining the position of the characteristic point B by using a geometric drawing method I according to the speed relation among the characteristic points A, B, C in the step S3;
the geometric mapping method I is as follows: on the speed time curve, two characteristic points A, C are arbitrarily selected, the passing point A is taken as the perpendicular line of the t axis, and the perpendicular foot is taken as the point tAPerpendicular to the v-axis, with the foot "vA(ii) a The passing point C is taken as a vertical line of the t axis and the foot isPoint tCPerpendicular to the v-axis, with the foot "vC；
At the point tCAs the center of circle, line segment CtcIs a radius making arc intersecting the t-axis at point R;
the parallel line passing through point A and serving as the t axis and the line segment CtcIntersect at point M;
at the point tCCentered on line segment MtCMaking an arc with a radius, intersecting the t-axis at a point S, the length of the segment RS being:
RS＝vC+vA (13)
using the line segment RS as the diameter to make the arc and the line segment CtcIntersect at point N;
obtaining:
Ntc 2＝Stc×Rtc (14)
combining formula (1) to obtain a line segment NtC＝vB；
And (4) taking a parallel line of the t axis as the passing point N, and taking the intersection point of the parallel line and the speed curve as the point B.
Determining the destruction time by using a geometric drawing method II according to the relationship between the destruction time and the time of the three characteristic points A, B, C in the step S5;
the geometric drawing method II is as follows:
the vertical line of the t axis is made through the point B, and the vertical foot is tB；
Respectively making line segments tAtBAnd tAtCMidpoint P, Q;
at the point tBAs the center of circle, with tBP is a radius as an arc, which is related to the line segment BtBCross over at H point, with tBQ is a radius forming an arc with line segment BtBCrossing at the E point;
parallel to the t-axis through the H-point, andAthe extension line of E is crossed with the point F;
the vertical line of the t axis is made through the point F, and the vertical foot is the destruction time t according to the formula (2)f。
Compared with the prior art, the invention has the following advantages:
the prediction process of the method is irrelevant to the power exponent, and the damage time can be predicted under the condition of unknown critical power exponent;
the method is realized by geometric drawing, has clear concept and simple operation, and can be programmed and operated;
the method can directly predict the damage time in real time according to the rate time evolution curve, and update and correct the prediction result in real time along with the increase of data.
Based on the reason, the method can be widely popularized in the fields of geological disaster prediction and the like.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
Fig. 1 is a flowchart of a method for predicting the damage time of a geotechnical disaster body in real time by using three characteristic points in an embodiment of the invention.
FIG. 2 is a schematic diagram of a geometric mapping method I according to an embodiment of the present invention.
FIG. 3 is a schematic diagram of a geometric drawing method II according to an embodiment of the present invention.
Detailed Description
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict. The present invention will be described in detail below with reference to the embodiments with reference to the attached drawings.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The relative arrangement of the components and steps, the numerical expressions and numerical values set forth in these embodiments do not limit the scope of the present invention unless specifically stated otherwise. Meanwhile, it should be understood that the sizes of the respective portions shown in the drawings are not drawn in an actual proportional relationship for the convenience of description. Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail but are intended to be part of the specification where appropriate. Any specific values in all examples shown and discussed herein are to be construed as exemplary only and not as limiting. Thus, other examples of the exemplary embodiments may have different values. It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, further discussion thereof is not required in subsequent figures.
In the description of the present invention, it is to be understood that the orientation or positional relationship indicated by the directional terms such as "front, rear, upper, lower, left, right", "lateral, vertical, horizontal" and "top, bottom", etc., are generally based on the orientation or positional relationship shown in the drawings, and are used for convenience of description and simplicity of description only, and in the absence of any contrary indication, these directional terms are not intended to indicate and imply that the device or element so referred to must have a particular orientation or be constructed and operated in a particular orientation, and therefore should not be considered as limiting the scope of the present invention: the terms "inner and outer" refer to the inner and outer relative to the profile of the respective component itself.
Spatially relative terms, such as "above … …," "above … …," "above … …," "above," and the like, may be used herein for ease of description to describe one device or feature's spatial relationship to another device or feature as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if a device in the figures is turned over, devices described as "above" or "on" other devices or configurations would then be oriented "below" or "under" the other devices or configurations. Thus, the exemplary term "above … …" can include both an orientation of "above … …" and "below … …". The device may be otherwise variously oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
It should be noted that the terms "first", "second", and the like are used to define the components, and are only used for convenience of distinguishing the corresponding components, and the terms have no special meanings unless otherwise stated, and therefore, the scope of the present invention should not be construed as being limited.
As shown in FIGS. 1 to 3, a method for predicting the damage time of a geotechnical disaster body in real time by using three characteristic points comprises the following steps:
s1: obtaining a rate-time curve of the evolution of the monitoring quantity development rate along with time based on field monitoring and experimental observation data;
s2: three feature points A, B, C on the rate-time curve are defined, and the rate relationship between feature points A, B, C is set as:
Figure BDA0002740059620000071
vB、vA、vCthe velocities at characteristic points A, B, C in the velocity curves, respectively;
s3: two optional points on the speed time curve are used as characteristic points A, C, and the position of the characteristic point B is determined according to the speed relation between the characteristic points A, B, C;
s4: determining the relationship between the destruction time and the time of three characteristic points A, B, C according to the speed relationship between the characteristic points A, B, C and the power law singularity precursor expression:
Figure BDA0002740059620000081
tfto break time, tA、tB、tCTime corresponding to the characteristic point A, B, C in the rate curve;
s5: determining the destruction time t according to the relationship between the destruction time and the time of the three characteristic points A, B, Cf；
S6: repeating the steps S3-S5 for the destruction time tfUpdating and correcting to obtain final destruction time tf*。
In step S4, the power law singular precursor expression is:
v＝k(tf-t)-β (3)
wherein v is the rate of the monitoring quantity, k is a parameter, and beta is a power law singularity index;
taking logarithm of two sides of the formula (3) to obtain:
logv＝logk-βlog(tf-t) (4)
i.e., the relationship of the rate, time and destruction time of the feature point A, B, C is:
logvA＝logk-βlog(tf-tA) (5)
logvB＝logk-βlog(tf-tB) (6)
logvC＝logk-βlog(tf-tC) (7)
subtracting the formula (4) from the formula (3), and subtracting the formula (5) from the formula (4) to obtain:
Figure BDA0002740059620000082
Figure BDA0002740059620000083
obtained according to formula (1), formula (8) and formula (9)
Figure BDA0002740059620000091
The destruction time can be obtained from equation (10):
Figure BDA0002740059620000092
subtracting t from both sides of the above formulaAAfter that, it is possible to obtain:
Figure BDA0002740059620000093
determining the position of the characteristic point B by using a geometric drawing method I according to the speed relation among the characteristic points A, B, C in the step S3;
the geometric mapping method I is as follows: on the speed time curve, two characteristic points A, C are arbitrarily selected, the passing point A is taken as the perpendicular line of the t axis, and the perpendicular foot is taken as the point tAPerpendicular to the v-axis, with the foot "vA(ii) a The passing point C is taken as a vertical line of the t axis, and the falling foot is taken as a point tCPerpendicular to the v-axis, with the foot "vC；
At the point tCAs the center of circle, line segment CtcAn arc 1 with a radius intersecting the t-axis at a point R;
the parallel line passing through point A and serving as the t axis and the line segment CtcIntersect at point M;
at the point tCCentered on line segment MtCIs a circular arc 2 with a radius, which intersects the t-axis at a point S,the length of the line segment RS is:
RS＝vC+vA (13)
using the line segment RS as the diameter to make the arc 3 and the line segment CtcIntersect at point N;
because of & lt SNct+∠SNct＝∠ScNt+∠cRN; so NSct＝∠RcN, in combination with
Figure BDA0002740059620000101
And
Figure BDA0002740059620000102
obtaining:
Ntc 2＝Stc×Rtc (14)
combining formula (1) to obtain a line segment NtC＝vB；
And (4) taking a parallel line of the t axis as the passing point N, and taking the intersection point of the parallel line and the speed curve as the point B.
Determining the destruction time by using a geometric drawing method II according to the relationship between the destruction time and the time of the three characteristic points A, B, C in the step S5;
the geometric drawing method II is as follows:
the vertical line of the t axis is made through the point B, and the vertical foot is tB；
Respectively making line segments tAtBAnd tAtCMidpoint P, Q;
at the point tBAs the center of circle, with tBP is a radius as arc 4, which is connected with line segment BtBCross over at H point, with tBQ is a radius as arc 5, which is associated with line segment BtBCrossing at the E point;
parallel to the t-axis through the H-point, andAthe extension line of E is crossed with the point F;
making a vertical line of the t axis through the point F, and obtaining the damage time tf。
As can be seen from the formula (2),
Figure BDA0002740059620000103
also, Δ Ft in the figureAtfAnd Δ EtAtBIs similar to a triangle, satisfies
Figure BDA0002740059620000104
In accordance with equation (2).
With the increase of the sampling data, the point A, C can be continuously slid, the characteristic point B is determined according to the geometric drawing method, and then the predicted value of the damage time is updated and corrected according to the geometric drawing.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (4)

1. A method for predicting the damage time of a rock and soil disaster body in real time by three characteristic points is characterized by comprising the following steps:
s1: obtaining a rate-time curve of the evolution of the monitoring quantity development rate along with time based on field monitoring and experimental observation data;
s2: three feature points A, B, C on the rate-time curve are defined, and the rate relationship between feature points A, B, C is set as:
Figure FDA0002740059610000011
vB、vA、vCthe velocities at characteristic points A, B, C in the velocity curves, respectively;
s3: two optional points on the speed time curve are used as characteristic points A, C, and the position of the characteristic point B is determined according to the speed relation between the characteristic points A, B, C;
s4: determining the relationship between the destruction time and the time of three characteristic points A, B, C according to the speed relationship between the characteristic points A, B, C and the power law singularity precursor expression:
Figure FDA0002740059610000012
tfto break time, tA、tB、tCTime corresponding to the characteristic point A, B, C in the rate curve;
s5: determining the destruction time t according to the relationship between the destruction time and the time of the three characteristic points A, B, Cf；
S6: repeating the steps S3-S5 for the destruction time tfUpdating and correcting to obtain final destruction time tf*。
2. The method for predicting the damage time of the geotechnical disaster body in real time by using the three characteristic points as claimed in claim 1, wherein:
in step S4, the power law singular precursor expression is:
v＝k(tf-t)-β (3)
wherein v is the rate of the monitoring quantity, k is a parameter, and beta is a power law singularity index;
taking logarithm of two sides of the formula (3) to obtain:
logv＝logk-βlog(tf-t) (4)
i.e., the relationship of the rate, time and destruction time of the feature point A, B, C is:
logvA＝logk-βlog(tf-tA) (5)
logvB＝logk-βlog(tf-tB) (6)
logvC＝logk-βlog(tf-tC) (7)
subtracting the formula (4) from the formula (3), and subtracting the formula (5) from the formula (4) to obtain:
Figure FDA0002740059610000021
Figure FDA0002740059610000022
obtained according to formula (1), formula (8) and formula (9)
Figure FDA0002740059610000023
The destruction time can be obtained from equation (10):
Figure FDA0002740059610000024
subtracting t from both sides of the above formulaAAfter that, it is possible to obtain:
Figure FDA0002740059610000025
3. the method for predicting the damage time of the geotechnical disaster body in real time by using the three characteristic points as claimed in claim 1 or 2, wherein:
determining the position of the characteristic point B by using a geometric drawing method I according to the speed relation among the characteristic points A, B, C in the step S3;
the geometric mapping method I is as follows: on the speed time curve, two characteristic points A, C are arbitrarily selected, the passing point A is taken as the perpendicular line of the t axis, and the perpendicular foot is taken as the point tAPerpendicular to the v-axis, with the foot "vA(ii) a The passing point C is taken as a vertical line of the t axis, and the falling foot is taken as a point tCPerpendicular to the v-axis, with the foot "vC；
At the point tCAs the center of circle, line segment CtcIs a radius making arc intersecting the t-axis at point R;
the parallel line passing through point A and serving as the t axis and the line segment CtcIntersect at point M;
at the point tCCentered on line segment MtCMaking an arc with a radius, intersecting the t-axis at a point S, the length of the segment RS being:
RS＝vC+vA (13)
using the line segment RS as the diameter to make the arc and the line segment CtcIntersect at point N;
obtaining:
Ntc 2＝Stc×Rtc (14)
combining formula (1) to obtain a line segment NtC＝vB；
And (4) taking a parallel line of the t axis as the passing point N, and taking the intersection point of the parallel line and the speed curve as the point B.
4. The method for predicting the damage time of the geotechnical disaster body in real time by using the three characteristic points as claimed in claim 3, wherein: determining the destruction time by using a geometric drawing method II according to the relationship between the destruction time and the time of the three characteristic points A, B, C in the step S5;
the geometric drawing method II is as follows:
the vertical line of the t axis is made through the point B, and the vertical foot is tB；
Respectively making line segments tAtBAnd tAtCMidpoint P, Q;
at the point tBAs the center of circle, with tBP is a radius as an arc, which is related to the line segment BtBCross over at H point, with tBQ is a radius forming an arc with line segment BtBCrossing at the E point;
parallel to the t-axis through the H-point, andAthe extension line of E is crossed with the point F;
the vertical line of the t axis is made through the point F, and the vertical foot is the destruction time t according to the formula (2)f。
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JIAN XUE ET AL.: "The Changeable Power Law Singularity and its Application to Prediction of Catastrophic Rupture in Uniaxial Compressive Tests of Geomedia", 《JOURNAL OF GEOPHYSICAL RESEARCH: SOLID EARTH》 *
周孙基等: "连续损伤力学基临界奇异指数与破坏时间预测", 《力学学报》 *

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