CN114462185B - Method for estimating five-dimensional evolution of space form of surface subsider caused by tunnel construction - Google Patents

Method for estimating five-dimensional evolution of space form of surface subsider caused by tunnel construction Download PDF

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CN114462185B
CN114462185B CN202111438409.8A CN202111438409A CN114462185B CN 114462185 B CN114462185 B CN 114462185B CN 202111438409 A CN202111438409 A CN 202111438409A CN 114462185 B CN114462185 B CN 114462185B
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彭斌
张鹏辉
罗伟庭
于英年
姚欣鹏
于广明
谭芝文
岳强
杜佳明
张立
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Abstract

The invention discloses a method for estimating five-dimensional evolution of space form of a surface subsider caused by tunnel construction, which comprises the following steps of firstly judging the application condition of a Peck formula in a region to be researched; obtaining the area A of a shield cutter head, the volume loss rate eta caused by each longitudinal ring excavation of the tunnel and the stratum loss rate V of the transverse unit length of the tunnel i Data; and then correcting the traditional Peck formula to obtain the Peck formula in the five-dimensional space, and combining the data to obtain the dynamic change rule of the earth surface along with time and shield propulsion. According to the scheme, the five-dimensional space effect of the surface subsidence is used as a rule, a time factor and a step factor are introduced on the basis of the three-dimensional surface subsidence tank, and a Peck formula in the five-dimensional space is established, so that the dynamic development rule of the surface subsidence tank along with construction disturbance and the time process can be more accurately described in the five-dimensional space, the defects of the surface subsidence in the aspect of researching the dynamic change rule are overcome, the surface subsidence prediction is more refined, and the result is more accurate.

Description

Method for estimating five-dimensional evolution of space form of surface subsider caused by tunnel construction
Technical Field
The invention belongs to the field of shield tunnel construction risk control, and particularly relates to a method for estimating five-dimensional evolution of a surface subsider space form caused by tunnel construction.
Background
With the rapid development of economy in China and the continuous expansion of urban scale, the number of constructed subways in cities is gradually increased, and the problem of ground surface settlement disasters caused by the construction of subways is increasingly prominent, so that the dislocation and the damage of urban life lines such as underground pipelines and the like can be caused, ground buildings can be seriously damaged, the problems become hot problems concerned by the whole society, and the occurrence mechanism and the effective control of the problems also become difficult problems of scientific research in the related fields of the whole world.
The Peck provides a rule that the curve of the earth surface settling tank approximately follows normal distribution on the basis of a large amount of actually measured data, and the Peck formula is used for expressing the rule
Figure GDA0003833915660000011
In the case of prediction using the formula, the K value and V are generally obtained from the data of the conventional engineering l Value and then substituted into the processed formula
Figure GDA0003833915660000012
And predicting the final shape of the surface settling tank.
The following problems exist with respect to the conventional Peck formula for predicting surface subsidence:
(1) The final form of the surface subsider after the settlement is finished can only be considered, the evolution process of the surface subsider in the construction process cannot be considered, the damage of the building on the ground is not only determined by the final differential settlement difference due to the factors such as the long-term rigidity of concrete, the creep of concrete and the like, and the damage of the building caused by the development process of the differential settlement is also crucial;
(2) The traditional Peck formula is only an empirical formula in statistical significance, lacks physical mechanical significance, and does not express the mechanical mechanism of surface subsidence caused by soil layer disturbance caused by shield excavation;
(3) The development of the earth surface moving process in the shield propelling process cannot be considered, and the dynamic moving rule and mechanism of the earth surface are not described.
Disclosure of Invention
The invention provides a method for estimating five-dimensional evolution of space form of an earth surface subsidence tank caused by tunnel construction aiming at the defect that the traditional Peck formula cannot predict earth surface subsidence in a construction stage, and realizes the estimation of the earth surface subsidence under the combined action of time-containing factors and shield step length factors.
The invention is realized by adopting the following technical scheme: a method for estimating the five-dimensional evolution of the space form of an earth surface settling tank caused by tunnel construction comprises the following steps:
step A, judging the application condition of a Peck formula of a region to be researched:
collecting historical settlement data of monitoring points of a region to be researched, carrying out deformation and least square analysis on a traditional Peck formula, constructing a regression equation and obtaining a linear correlation coefficient R of the regression equation; if the earth surface settlement is suitable to be predicted by using a Peck formula, carrying out the next operation;
step B, obtaining the area A of the shield cutter head, the volume loss rate eta caused by each longitudinal ring excavation of the tunnel and the stratum loss rate V of the transverse unit length of the tunnel i Data;
and C, correcting the traditional Peck formula to obtain the Peck formula in the five-dimensional space so as to achieve the effect of accurately predicting the influence of time and step length on the surface subsidence:
Figure GDA0003833915660000021
wherein: v i The soil stratum loss per unit length; s max The maximum subsidence value of the earth surface; i is the width of the surface settling tank; eta is volume loss rate; s is the surface sedimentation value; s is the excavated length of the tunnel; x is the vertical distance, namely the transverse distance, of the ground point data tunnel center line; y is the origin of the surface point data (figure)Point o) along the tunnel run distance, i.e. the longitudinal distance; c is a proportionality coefficient, related to rock stratum properties and the buried depth of the shield tunneling machine, and t represents time; a is the cutter head area of the shield machine; l is the step length; tau represents the time of unit excavation;
and D, substituting the data obtained in the step B into a five-dimensional space Peck formula to obtain the dynamic change rule of the earth surface along with time and shield propulsion.
Further, in the step C, a specific manner of correcting the Peck formula is as follows:
(1) Note S ∞ And (3) constructing the final settlement amount of the earth surface for the shield tunnel:
introduce the assumption 1: the subsidence rate at a surface point is proportional to the difference between the final subsidence at that point and the instantaneous subsidence at that point, i.e.:
Figure GDA0003833915660000022
when a boundary condition t =0 is introduced, S (t) =0, and S (t) = S is solved ∞ (1-e -ct )；
(2) Introduce hypothesis 2: the traditional Peck formula yields the final settlement of the earth's surface, i.e.:
Figure GDA0003833915660000023
further obtaining:
Figure GDA0003833915660000024
(3) And (3) verification: when t =0, S (x, 0) =0, which satisfies the practical situation;
when t → ∞ is reached,
Figure GDA0003833915660000025
the practical situation is met;
(4) When t = τ is assumed, a rock with width dy and area w (y) is suddenly mined at S, and the rock subsidence dS caused by the micro mining is assumed as follows:
Figure GDA0003833915660000031
when the mining width reaches L,
Figure GDA0003833915660000032
determining the area of the micro rock excavated in the propelling process:
Figure GDA0003833915660000033
wherein, A is shield structure machine cutter head area, and D is shield structure machine cutter head diameter, then has:
Figure GDA0003833915660000034
and further, a Peck formula in a five-dimensional space is obtained and is designed into a piecewise function along the x axis and the y axis.
Further, in the step a, the determination method is as follows:
1) Collecting historical settlement data of monitoring points of an area to be researched, wherein the settlement data comprises the distance X from the monitoring points to the center line of the tunnel i Monitoring point settlement value S (x);
2) The conventional Peck formula is deformed and least squares analyzed:
Figure GDA0003833915660000035
mixing lnS (x) and
Figure GDA0003833915660000036
set as regression variable for analysis, set lnS max For the constant term after regression, let
Figure GDA0003833915660000037
Linear coefficient after regression;
3) Obtaining a regression equation:
Figure GDA0003833915660000038
Figure GDA0003833915660000039
Figure GDA00038339156600000310
and the historical settlement data lnS (X) collected in the step 1) is collected i ) And the distance X of the monitoring point according to the central line of the tunnel i Substituting into regression equation to calculate S xx 、S xy 、S yy ；
4) Order:
Figure GDA00038339156600000311
Figure GDA00038339156600000312
substituting regression equation data and the monitoring point data in the step 1) to calculate
Figure GDA00038339156600000313
5) By calculated S xx 、S xy 、S yy The result is substituted into the following formula: (ii) a
Figure GDA0003833915660000041
Wherein, R is a linear correlation coefficient of the linear regression equation.
Further, in the step a, if | R | <0.3, it is determined that the subsidence of the area is not suitable to be predicted by using the Peck formula; if R is greater than 0.8, the area is judged to be suitable for predicting the surface subsidence by using a Peck formula.
Further, in the step B, the data is obtained as follows:
4) Determining an accurate value in a project file of a construction unit by using the cutter head area A of the shield machine;
5) According to step A
Figure GDA0003833915660000042
Values, wherein:
Figure GDA0003833915660000043
based on the obtained data, the stratum loss rate V of unit length is obtained i ；
6) Calculating the volume loss rate eta caused by excavation of each longitudinal ring of the tunnel:
Figure GDA0003833915660000044
and summarizing the volume loss rate eta of a plurality of groups of different propulsion ring numbers, and taking the average value of the volume loss rate eta.
Compared with the prior art, the invention has the advantages and positive effects that:
according to the scheme, the five-dimensional space effect of the surface subsidence is used as an outline, a traditional Peck formula is corrected, a time factor and a step factor are introduced, and the Peck formula in the five-dimensional space is established, so that the dynamic development rule of the surface subsidence tank along with construction disturbance and the time process can be more accurately described in the five-dimensional space, a more effective and reliable theoretical basis is provided for the prediction of the surface subsidence, the defects of the surface subsidence in the aspect of researching the dynamic change rule are overcome, the prediction of the surface subsidence is more refined, and the result is more accurate.
Drawings
FIG. 1 is a schematic illustration of rock subsidence caused by micro-mining in accordance with an embodiment of the present invention;
FIG. 2 is a schematic diagram of a shield tunneling machine causing rock subsidence according to an embodiment of the present invention;
fig. 3 is a flow chart of estimating surface subsidence based on the five-dimensional space Peck formula according to the embodiment of the present invention.
Detailed Description
In order to make the above objects, features and advantages of the present invention more clearly understood, the present invention will be further described with reference to the accompanying drawings and examples. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those described herein, and thus, the present invention is not limited to the specific embodiments disclosed below.
Aiming at the problem of surface subsidence caused by shield tunnel construction, the five-dimensional dynamic process of generation and development of the problem is researched, the inventor of the scheme provides a surface subsidence evolution idea based on a five-dimensional space and analyzes the complexity of surface subsidence distribution and the development process: with the continuous tunneling of the shield tunnel, the ground surface settlement is not only distributed in three dimensions of X, Y and Z, but also continuously evolves along with two dimensions of the tunneling step length (L) and the tunneling time (T) of the shield tunnel. Therefore, it is defined as a "five-dimensional" space effect in which shield tunnel construction causes surface subsidence. Therefore, the method takes the five-dimensional space effect of the surface subsidence as a rule, corrects the traditional Peck formula, introduces time factors and step factors, and establishes the Peck formula in the five-dimensional space, so that the dynamic development rule of the surface subsidence tank along with the construction disturbance and the time process can be more accurately described in the five-dimensional space.
A method for estimating five-dimensional evolution of space form of an earth surface settling tank caused by tunnel construction comprises the following steps:
step A, judging the application condition of a Peck formula in a region to be researched:
collecting historical settlement data of monitoring points of a region to be researched, carrying out deformation and least square analysis on a traditional Peck formula, constructing a regression equation and obtaining a linear correlation coefficient R of the regression equation; if R <0.3, judging that the sedimentation of the area is not suitable to be predicted by using a Peck formula; if R is more than 0.8, judging that the region is suitable for predicting the surface subsidence by using a Peck formula, and carrying out the next operation;
step B, obtaining the area A of the shield cutter head, the volume loss rate eta caused by each longitudinal ring excavation of the tunnel and the stratum loss rate V of the transverse unit length of the tunnel i Data;
and C, correcting the traditional Peck formula to obtain the Peck formula in the five-dimensional space so as to achieve the effect of accurately predicting the influence of time and step length on the surface subsidence:
Figure GDA0003833915660000051
wherein: v i The soil stratum loss per unit length; s max The maximum subsidence value of the earth surface is obtained; i is the width of the surface settling tank; eta is volume loss rate; the right side S of the equation is the surface sedimentation value; the right side s of the equation is the excavated length of the tunnel; x is the vertical distance, namely the transverse distance, of the ground point data tunnel center line; y is the distance of the ground surface point data calculation origin (point o in the figure) along the tunnel trend, namely the longitudinal distance; c is a proportionality coefficient related to rock stratum properties and the buried depth of the shield tunneling machine, and t represents time; a is the cutter head area of the shield machine; l is the step length; tau represents the time of unit excavation; (ii) a
And D, substituting the data obtained in the step B into a five-dimensional space Peck formula to obtain the dynamic change rule of the earth surface along with time and shield propulsion.
Specifically, in the step a, a specific applicable condition of a Peck formula of the area to be researched is judged, that is, whether the geological condition of the research area meets the requirement of estimation by using the Peck formula is judged, because the Peck formula is a formula in the field of statistical mathematics, the Peck formula is obtained by fitting based on the settlement conditions of a large number of monitoring points in each area, and whether the Peck formula is applicable to one area needs to be further judged; as shown in fig. 3, the determination steps are as follows:
1) Collecting historical settlement data of monitoring points in the area, wherein the settlement data comprises the distance X from the monitoring points to the center line of the tunnel i Monitoring pointA sedimentation value S (x);
2) Performing formal change and least square analysis on the conventional Peck formula
Figure GDA0003833915660000052
Taking logarithm at two ends of the formula to obtain a deformation formula:
Figure GDA0003833915660000061
mixing lnS (x) and
Figure GDA0003833915660000062
set as regression variable for analysis, set lnS max For the constant term after regression, let
Figure GDA0003833915660000063
Is a linear coefficient after regression;
3) By a mathematical method, a regression equation is obtained:
Figure GDA0003833915660000064
Figure GDA0003833915660000065
Figure GDA0003833915660000066
4) Collecting the historical settlement data lnS (X) collected in the step 1) i ) And the distance X of the monitoring point according to the central line of the tunnel i Substituting into regression equation of step 3), calculating S xx 、S xy 、S yy ；
5) Order:
Figure GDA0003833915660000067
Figure GDA0003833915660000068
substituting the regression equation data in the step 4) and the monitoring point data in the step 1) to calculate
Figure GDA0003833915660000069
6) S calculated by the previous step xx 、S xy 、S yy Substituting the result into a linear correlation coefficient R of the linear regression equation;
Figure GDA00038339156600000610
if R is more than 0.8, the earth surface settlement can be predicted by a Peck formula in the region; if R <0.3, judging that the sedimentation of the area is not suitable to be predicted by using a Peck formula; and if the other conditions are moderate correlation, the prediction result can be used for self-judging whether to be used as reference.
The meaning of R is explained here: r describes the degree of linear correlation between two variables. The value of R is between-1 and +1, if R >0, the two variables are positively correlated, namely the larger the value of one variable is, the larger the value of the other variable is; if R <0, it indicates that the two variables are negatively correlated, i.e., the larger the value of one variable, the smaller the value of the other variable. A larger absolute value of R indicates a stronger correlation. If R =0, it indicates that the two variables are not linearly related, if R =1 or-1 indicates that the two variables are strictly phenomenologically related, and if the absolute value approaches 1, it indicates that the correlation between the two variables is stronger, the applicability of the Peck formula is better, and if the absolute value approaches 0, it indicates that the applicability of the Peck formula is worse.
In the step B, three data types are obtained as follows:
7) The area A of the cutter head of the shield machine can find an accurate value in a project file of a construction unit;
8) In the calculation step A
Figure GDA00038339156600000611
Value of wherein
Figure GDA00038339156600000612
Based on the obtained data, the stratum loss rate V of unit length is obtained i ；
9) Calculating the volume loss rate eta caused by excavation of each ring (step length) in the longitudinal direction of the tunnel, wherein more than a plurality of groups of earth surface settlement observation data are needed, the stratum loss after least square fitting of shield propulsion n-ring earth surface monitoring points is divided by the number of shield propulsion rings, and the stratum loss is fitted with a plurality of groups of data by adopting a least square method;
Figure GDA0003833915660000071
and summarizing the volume loss rate eta of a plurality of groups of different propulsion ring numbers, and taking the average value of the volume loss rate eta.
In the step C, a specific manner of correcting the Peck formula is as follows:
(1) Note S ∞ And (3) constructing the final settlement amount of the earth surface for the shield tunnel:
introduce the assumption 1: the subsidence rate at a surface point is proportional to the difference between the final subsidence at that point and the instantaneous subsidence at that point, i.e.:
Figure GDA0003833915660000072
if the boundary condition t =0 is introduced, S (t) =0, and S (t) = S is obtained by solving ∞ (1-e -ct )；
(3) Introduce hypothesis 2: the traditional Peck formula yields the final settlement of the earth's surface, i.e.:
Figure GDA0003833915660000073
substituting to obtain:
Figure GDA0003833915660000074
and (3) verification: when t =0, S (x, 0) =0, which satisfies the practical situation;
when t → ∞ is reached,
Figure GDA0003833915660000075
the practical situation is met;
wherein:
V i -amount of soil formation loss per unit length;
S max -is the maximum subsidence value of the earth's surface;
i-is the width of the surface settling tank;
Figure GDA0003833915660000076
namely, the expression of the surface subsidence four-dimensional under the xoz space;
(3) Let V i =1, then:
Figure GDA0003833915660000077
the expression is further converted into a unit earth surface subsidence basin expression taking a peck formula as a prototype, and the unit earth surface subsidence basin along the x axis is not different from that along the y axis according to the alternate symmetry of coordinates and the specific physical significance of earth surface subsidence;
when t = τ, the rock with width dy and area w (y) is suddenly extracted at S, and the subsidence dS of the rock caused by the tiny mining is shown as fig. 1
Figure GDA0003833915660000081
When the mining width reaches L,
Figure GDA0003833915660000082
considering the practical engineering significance of shield tunneling, as shown in fig. 2, the area of the micro rock excavated in the propelling process is as follows:
Figure GDA0003833915660000083
wherein A is the area of the cutter head of the shield machine, and D is the diameter of the cutter head of the shield machine;
Figure GDA0003833915660000084
since the segment is disposed for each ring (step length), the volume loss rate for each ring (step length) is defined as η:
Figure GDA0003833915660000085
further, the design of a Peck formula in a five-dimensional space into a piecewise function along the x axis and the y axis is obtained as follows
Figure GDA0003833915660000086
And further, the dynamic change rule of the earth surface along with time and shield propulsion can be obtained, and the purpose of more accurately describing the dynamic development rule of the earth surface settling tank along with construction disturbance and time process in a five-dimensional space is achieved.
While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention.

Claims (3)

1. A method for estimating five-dimensional evolution of space form of an earth surface settling tank caused by tunnel construction is characterized by comprising the following steps:
step A, judging the application condition of a Peck formula of a region to be researched:
1) Collecting historical settlement data of monitoring points of an area to be researched, wherein the settlement data comprises a distance X from the monitoring points to a tunnel center line i Monitoring point settlement values S (x);
2) Deformation and least squares analysis were performed on the traditional Peck formula:
Figure FDA0003833915650000011
mixing ln S (x) and
Figure FDA0003833915650000012
set as regression variable for analysis, let ln S max For the constant term after regression, let
Figure FDA0003833915650000013
Linear coefficient after regression;
3) Constructing a regression equation and obtaining a linear correlation coefficient R of the regression equation:
Figure FDA0003833915650000014
Figure FDA0003833915650000015
Figure FDA0003833915650000016
and the historical settlement data lnS (X) collected in the step 1) is collected i ) And monitorMeasuring distance X of points according to tunnel center line i Substituting into regression equation to calculate S xx 、S xy 、S yy ；
4) Order:
Figure FDA0003833915650000017
Figure FDA0003833915650000018
substituting regression equation data and the monitoring point data in the step 1) to calculate
Figure FDA0003833915650000019
5) By calculated S xx 、S xy 、S yy The result is substituted into the following formula:
Figure FDA00038339156500000110
wherein, R is a linear correlation coefficient of a linear regression equation;
6) If the earth surface settlement is suitable to be predicted by a Peck formula, the next operation is carried out:
if the calculated | R | <0.3, the fitting degree of the curve of the settling tank in the area and the Peck formula is considered to be low, and then the settlement of the area is judged to be inappropriate and is predicted by the Peck formula; if the calculated | R | is greater than 0.8, the fitting degree of the curve of the settling tank in the area and the Peck formula is considered to be high, and the area is judged to be suitable for predicting the surface settlement by the Peck formula;
step B, obtaining the area A of the shield cutter head, the volume loss rate eta caused by each longitudinal ring excavation of the tunnel and the stratum loss rate V of the transverse unit length of the tunnel i Data;
and step C, correcting the traditional Peck formula to obtain the Peck formula in the five-dimensional space so as to achieve the effect of accurately predicting the influence of time and step length on the surface settlement:
Figure FDA0003833915650000021
wherein: v i The soil stratum loss per unit length; s. the max The maximum subsidence value of the earth surface is obtained; i is the width of the surface settling tank; eta is the volume loss rate caused by the excavation of each longitudinal ring of the tunnel; s is the surface sedimentation value; s is the excavated length of the tunnel; x is the vertical distance, namely the transverse distance, of the ground point data tunnel center line; y is the distance of the ground surface point along the tunnel direction, namely the longitudinal distance; c is a proportionality coefficient, and t represents time; a is the cutter head area of the shield machine; l is the step length; tau represents the time of unit excavation;
and D, substituting the data obtained in the step B into a five-dimensional space Peck formula to obtain the dynamic change rule of the earth surface along with time and shield propulsion.
2. The method for estimating the five-dimensional evolution of the space form of the earth surface settling tank caused by tunnel construction as claimed in claim 1, wherein the method comprises the following steps: in the step C, the Peck formula is modified in the following specific manner:
(1) Note S ∞ And (3) constructing the final settlement amount of the earth surface for the shield tunnel:
introduce the assumption 1: the subsidence rate at a surface point is proportional to the difference between the final subsidence at that point and the instantaneous subsidence at that point, i.e.:
Figure FDA0003833915650000022
if the boundary condition t =0 is introduced, S (t) =0, and S (t) = S is obtained by solving ∞ (1-e -ct )；
(2) Introduction hypothesis 2: the traditional Peck formula yields the final settlement of the earth's surface, i.e.:
Figure FDA0003833915650000023
further obtaining:
Figure FDA0003833915650000024
(3) And (3) verification: when t =0, S (x, 0) =0, which satisfies the practical situation;
when t → ∞ is reached,
Figure FDA0003833915650000025
the practical situation is met;
(4) When t = τ is assumed, a rock with width dy and area w (y) is suddenly mined at S, and the rock subsidence dS caused by the micro mining is assumed as follows:
Figure FDA0003833915650000026
when the mining width reaches L the time when mining is completed,
Figure FDA0003833915650000027
determining the area of the micro rock excavated in the advancing process:
Figure FDA0003833915650000031
wherein, A is shield structure machine cutter head area, and D is shield structure machine cutter head diameter, then has:
Figure FDA0003833915650000032
and further, a Peck formula in a five-dimensional space is obtained and is designed into a piecewise function along the x axis and the y axis.
3. The method for estimating the five-dimensional evolution of the space form of the earth surface settling tank caused by tunnel construction as claimed in claim 1, wherein the method comprises the following steps: in the step B, the data is obtained in the following manner:
1) Determining an accurate value in a project file of a construction unit by using the cutter head area A of the shield machine;
2) According to step A
Figure FDA0003833915650000033
A value, wherein:
Figure FDA0003833915650000034
based on the obtained data, the stratum loss rate V of unit length is obtained i ；
3) Calculating the volume loss rate eta caused by excavation of each longitudinal ring of the tunnel:
Figure FDA0003833915650000035
and summarizing volume loss rate eta of a plurality of groups of different propulsion ring numbers, and taking the average value of the volume loss rate eta.
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