CN114462185A - 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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CN114462185A
CN114462185A CN202111438409.8A CN202111438409A CN114462185A CN 114462185 A CN114462185 A CN 114462185A CN 202111438409 A CN202111438409 A CN 202111438409A CN 114462185 A CN114462185 A CN 114462185A
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tunnel
formula
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peck
data
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CN114462185B (en
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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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Qingdao University of Technology
China Construction Fifth Engineering Bureau Co Ltd
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China Construction Fifth Engineering Bureau Co Ltd
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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 tunneliData; 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. The scheme takes the five-dimensional space effect of surface subsidence as a rule, introduces time factors and step length factors on the basis of a three-dimensional subsider of the surface, and establishes a Peck formula in the five-dimensional spaceThe dynamic development law of the earth surface settling tank along with construction disturbance and time process can be more accurately described in the five-dimensional space, so that the defects of earth surface settling in the aspect of research on the dynamic change law are overcome, the prediction of earth surface settling 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 space form of an earth surface settling tank 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 global related fields.
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 BDA0003382574280000011
In general, when using a formula to predict, K value and V value are obtained from the data of the conventional engineeringlValue and then substituted into the processed formula
Figure BDA0003382574280000012
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 morphology of a ground surface subsider caused by tunnel construction aiming at the defect that the traditional Peck formula cannot predict ground surface subsidence in a construction stage, and the evaluation of the ground surface subsidence under the combined action of time-containing factors and shield step length factors is realized.
The invention is realized by adopting the following technical scheme: 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 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 and excavating each ring in the longitudinal direction of the tunnelSpecific volume loss rate eta, and formation loss rate V per unit length of tunnel in the transverse directioniData;
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 BDA0003382574280000021
wherein: viThe soil stratum loss per unit length; smaxThe maximum subsidence value of the earth surface is obtained; 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 distance of the ground surface point along the tunnel, namely the longitudinal distance, of the origin (point o in the attached figures 1 and 2); 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, i.e.:
Figure BDA0003382574280000022
if the boundary condition t is 0, S (t) is solved to S (t)∞(1-e-ct)；
(2) Introduce hypothesis 2: the traditional Peck formula yields the final settlement of the earth's surface, i.e.:
Figure BDA0003382574280000023
further obtaining:
Figure BDA0003382574280000024
(3) and (3) verification: when t is 0, S (x, 0) is 0, and the practical situation is met;
when t → ∞ is reached,
Figure BDA0003382574280000025
the practical situation is met;
(4) when t is equal to τ, the rock with width dy and area w (y) is suddenly mined at S, and the rock subsidence dS caused by the tiny mining is:
Figure BDA0003382574280000031
when the mining width reaches L,
Figure BDA0003382574280000032
determining the area of the micro rock excavated in the propelling process:
Figure BDA0003382574280000033
wherein, A is shield structure machine cutter head area, and D is shield structure machine cutter head diameter, then has:
Figure BDA0003382574280000034
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 tunneliMonitoring point settlement values S (x);
2) deformation and least squares analysis were performed on the traditional Peck formula:
Figure BDA0003382574280000035
mixing lnS (x) and
Figure BDA0003382574280000036
set to regression variables for analysis, set lnSmaxFor the constant term after regression, let
Figure BDA0003382574280000037
Linear coefficient after regression;
3) obtaining a regression equation:
Figure BDA0003382574280000038
Figure BDA0003382574280000039
Figure BDA00033825742800000310
and collecting the historical settlement data lnS (X) collected in step 1)i) And the distance X of the monitoring point according to the central line of the tunneliIs substituted into the regression equation to calculate Sxx、Sxy、Syy；
4) Order:
Figure BDA00033825742800000311
Figure BDA00033825742800000312
substituting regression equation data and the monitoring point data in the step 1) to calculate
Figure BDA00033825742800000313
5) By calculated Sxx、Sxy、SyyThe result is substituted into the following formula: (ii) a
Figure BDA0003382574280000041
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 the 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 BDA0003382574280000042
Values, wherein:
Figure BDA0003382574280000043
Figure BDA0003382574280000044
based on the obtained data, the stratum loss rate V of unit length is obtainedi；
6) Calculating the volume loss rate eta caused by excavation of each longitudinal ring of the tunnel:
Figure BDA0003382574280000045
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, the Peck formula in the five-dimensional space is established, 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 research of 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 in 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 subsidence is not only distributed in X, Y, Z three dimensions, but also continuously evolves with two dimensions of shield tunnel tunneling step length (L) and time (T). 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 principle, corrects the traditional Peck formula, introduces time factors and step length factors, and establishes the Peck formula in the five-dimensional space, so that the dynamic development rule of the surface subsidence tank along with construction disturbance and 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 the absolute value of R is larger than 0.8, the area is judged to be suitable for predicting the surface subsidence by using a Peck formula, and the next operation is carried out;
step B, obtaining the area A of the shield cutter head, the volume loss rate eta caused by each ring of longitudinal excavation of the tunnel and the stratum loss rate V of the transverse unit length of the tunneliData;
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 BDA0003382574280000051
wherein: viThe soil stratum loss per unit length; smaxThe 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 origin of the earth surface point data calculation(point o in fig. 1 and 2) distance along the tunnel run, i.e. 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 tunneliMonitoring point settlement values S (x);
2) performing formal change and least square analysis on the conventional Peck formula
Figure BDA0003382574280000052
Taking logarithm at two ends of the formula to obtain a deformation formula:
Figure BDA0003382574280000061
mixing lnS (x) and
Figure BDA0003382574280000062
set to regression variables for analysis, set lnSmaxFor the constant term after regression, let
Figure BDA0003382574280000063
Linear coefficient after regression;
3) by a mathematical method, a regression equation is obtained:
Figure BDA0003382574280000064
Figure BDA0003382574280000065
Figure BDA0003382574280000066
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 tunneliSubstituting into regression equation of step 3), calculating Sxx、Sxy、Syy；
5) Order:
Figure BDA0003382574280000067
Figure BDA0003382574280000068
substituting the regression equation data in the step 4) and the monitoring point data in the step 1) to calculate
Figure BDA0003382574280000069
6) S calculated by the previous stepxx、Sxy、SyySubstituting the result into a linear correlation coefficient R of the linear regression equation;
Figure BDA00033825742800000610
if R is greater than 0.8, the earth surface settlement can be predicted by a Peck formula in the area; if R <0.3, judging that the subsidence of the region is not suitable to be predicted by using a Peck formula; in other cases, the prediction results are moderately correlated, and the prediction results can be self-judged whether to be used as reference or not.
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 is 0, it means that there is not a linear correlation between the two variables, and if R is 1 or-1, it means that the two variables are strictly phenomenologically related, and the absolute value approaches 1, which means that the stronger the correlation between the two variables, the better the applicability of the Peck equation, and the closer the absolute value approaches 0, which means that the lower the correlation between the two variables, the worse the applicability of the Peck equation.
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 BDA00033825742800000611
Value of wherein
Figure BDA00033825742800000612
Figure BDA00033825742800000613
Based on the obtained unit length stratum loss rate Vi；
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 BDA0003382574280000071
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) final settlement of the ground surface for shield tunnel construction:
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, i.e.:
Figure BDA0003382574280000072
if the boundary condition t is 0, S (t) is solved to S (t)∞(1-e-ct)；
(3) Introduce hypothesis 2: the traditional Peck formula yields the final settlement of the earth's surface, i.e.:
Figure BDA0003382574280000073
substituting to obtain:
Figure BDA0003382574280000074
and (3) verification: when t is 0, S (x, 0) is 0, and the practical situation is met;
when t → ∞ is reached,
Figure BDA0003382574280000075
the practical situation is met;
wherein:
Vi-amount of soil formation loss per unit length;
Smax-is the maximum subsidence value of the earth's surface;
i-is the width of the surface settling tank;
Figure BDA0003382574280000076
i.e. under xoz spaceThe surface subsidence four-dimensional expression;
(3) let ViWhen 1, then:
Figure BDA0003382574280000077
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 is equal to τ, the rock with width dy and area w (y) is suddenly produced at S, and as shown in fig. 1, the rock subsidence dS caused by the tiny mining is
Figure BDA0003382574280000081
When the mining width reaches L,
Figure BDA0003382574280000082
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 BDA0003382574280000083
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 BDA0003382574280000084
since the segment is disposed for each ring (step length), the volume loss rate for each ring (step length) is defined as η:
Figure BDA0003382574280000085
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 BDA0003382574280000086
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.
The above description is only a preferred embodiment of the present invention, and not intended to limit the present invention in other forms, and any person skilled in the art can apply the above modifications or variations to the present invention without departing from the scope of the present invention.

Claims (5)

1. The method for estimating the five-dimensional evolution of the space form of the surface subsider caused by tunnel construction is characterized by comprising the following steps of:
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 ring of longitudinal excavation of the tunnel and the stratum loss rate V of the transverse unit length of the tunneliData;
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 FDA0003382574270000011
wherein: viThe soil stratum loss per unit length; smaxThe 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 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, 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, i.e.:
Figure FDA0003382574270000012
if the boundary condition t is 0, S (t) is solved to S (t)∞∞(1-e-ct)；
(2) Introduce hypothesis 2: the traditional Peck formula yields the final settlement of the earth's surface, i.e.:
Figure FDA0003382574270000013
further obtaining:
Figure FDA0003382574270000014
(3) and (3) verification: when t is 0, S (x, 0) is 0, and the practical situation is met;
when t → ∞ is reached,
Figure FDA0003382574270000015
the practical situation is met;
(4) when t is equal to τ, the rock with width dy and area w (y) is suddenly mined at S, and the rock subsidence dS caused by the tiny mining is:
Figure FDA0003382574270000021
when the mining width reaches L,
Figure FDA0003382574270000022
determining the area of the micro rock excavated in the propelling process:
Figure FDA0003382574270000023
wherein, A is shield structure machine cutter head area, and D is shield structure machine cutter head diameter, then has:
Figure FDA0003382574270000024
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 A, the judgment mode 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 tunneliMonitoring point settlement values s (x);
2) deformation and least squares analysis were performed on the traditional Peck formula:
Figure FDA0003382574270000025
mixing lnS (x) and
Figure FDA0003382574270000026
set as regression variable for analysis, let ln SmaxFor the constant term after regression, let
Figure FDA0003382574270000027
Linear coefficient after regression;
3) obtaining a regression equation:
Figure FDA0003382574270000028
Figure FDA0003382574270000029
Figure FDA00033825742700000210
and collecting the historical settlement data lnS (X) collected in step 1)i) And the distance X of the monitoring point according to the central line of the tunneliSubstituting into regression equation to calculate Sxx、Sxy、Syy；
4) Order:
Figure FDA00033825742700000211
Figure FDA0003382574270000031
substituting regression equation data and the monitoring point data in the step 1) to calculate
Figure FDA0003382574270000032
5) By calculated Sxx、Sxy、SyyThe result is substituted into the following formula: (ii) a
Figure FDA0003382574270000033
Wherein, R is a linear correlation coefficient of the linear regression equation.
4. 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 A, if the calculated | R | is less than 0.3, the fitting degree of the curve of the sedimentation tank in the area and the Peck formula is considered to be low, and then the sedimentation in 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.
5. 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 3, 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 FDA0003382574270000034
Values, wherein:
Figure FDA0003382574270000035
based on the obtained data, the stratum loss rate V of unit length is obtainedi；
3) Calculating the volume loss rate eta caused by excavation of each longitudinal ring of the tunnel:
Figure FDA0003382574270000036
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.
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