CN113010851B - Deep foundation pit engineering monitoring precision method based on deformation rate - Google Patents

Deep foundation pit engineering monitoring precision method based on deformation rate Download PDF

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CN113010851B
CN113010851B CN202110322067.7A CN202110322067A CN113010851B CN 113010851 B CN113010851 B CN 113010851B CN 202110322067 A CN202110322067 A CN 202110322067A CN 113010851 B CN113010851 B CN 113010851B
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王双龙
郝埃俊
宋军
吴伟理
贠银娟
张帅
黄敏
韦程文
孙曌
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Shenzhen Construction Comprehensive Survey And Design Institute Co ltd
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Abstract

The invention discloses a deep foundation pit engineering monitoring precision method based on deformation rate, which comprises the following steps: step S1: complete measurement result expression; step S2: determining deformation observation precision; the observation accuracy is to ensure that the amount of deformation that has occurred is monitored under normal operating conditions; in general, the observation precision is determined according to a deformation allowable value in a certain proportion; for foundation pit safety monitoring, important attention is paid to the deformation rate in a key construction stage of foundation pit engineering or dangerous symptoms; according to the invention, by analyzing the problem of the observation precision of the deformation rate, an observation precision calculation formula of deformation rate early warning is deduced, and the observation precision must be improved while the observation frequency is increased in a high risk period of foundation pit engineering; meanwhile, an estimation principle or an empirical rule of the observation precision is determined according to the deformation rate early warning value, and the method is economical and reasonable and has high reference value for foundation pit monitoring.

Description

Deep foundation pit engineering monitoring precision method based on deformation rate
Technical Field
The invention relates to the technical field of engineering design, in particular to a deep foundation pit engineering monitoring precision method based on deformation rate.
Background
The deformation rate early warning value is one of important control technical indexes for foundation pit engineering safety monitoring; how to determine the observation precision of the deformation rate early-warning value, so as to ensure that the tiny deformation of the foundation pit in a short time can be found, meet the requirement on the deformation rate early-warning, and the current technical standard is either undefined, or not scientific and reasonable enough or not known enough, so that the problem of the observation precision of the deformation rate early-warning value in the actual monitoring process does not draw enough attention. Because the design and calculation theory of the construction foundation pit engineering is still immature, foundation pit monitoring is an important bottom-covering work for realizing informatization construction, perfecting design scheme and guaranteeing the safety of foundation pit engineering and surrounding environment, and a deformation early warning value is an important control technical index for monitoring the safety of the foundation pit engineering; the foundation pit engineering monitoring and early warning not only needs to monitor the accumulated variation of the monitoring points, but also needs to monitor the deformation rate of the monitoring points; the deformation rate reflects the development change speed of the monitored object, and an excessive deformation rate is often a precursor of a sudden accident; therefore, it is necessary to design a method for monitoring the precision of deep foundation pit engineering based on the deformation rate.
Disclosure of Invention
The invention aims to provide a deep foundation pit engineering monitoring precision method based on deformation rate, which derives an observation precision calculation formula of deformation rate early warning by analyzing the observation precision problem of the deformation rate and indicates that the observation precision must be improved while the observation frequency is increased in a high risk period of foundation pit engineering; meanwhile, an estimation principle or an empirical rule of the observation precision is determined according to the deformation rate early warning value, and the method is economical and reasonable and has high reference value for foundation pit monitoring.
The aim of the invention can be achieved by the following technical scheme:
the deep foundation pit engineering monitoring precision method based on the deformation rate comprises the following steps of:
step S1: complete measurement result expression; the complete measurement result comprises a measurement result and a measurement error, wherein the measurement error expression mode adopts concepts of measuring middle error and 2 times middle error as limit error and the like, and the complete measurement result can be expressed as:
Figure BDA0002993258160000021
wherein ,
Figure BDA0002993258160000022
for the measurement result, sigma is the error in measurement, k is the standard normal distribution critical value of the significance level alpha;
step S2: determining deformation observation precision; the observation accuracy is to ensure that the amount of deformation that has occurred is monitored under normal operating conditions; in general, the observation precision is determined according to a deformation allowable value in a certain proportion; for foundation pit safety monitoring, important attention is paid to the deformation rate, namely the deformation rate is very important in the key construction stage of foundation pit engineering, or dangerous symptoms occur, or significant changes occur to influencing factors, such as rainfall and sudden changes of load around the foundation pit, and when encryption observation is needed, the deformation rate has very important meaning in early warning;
step S3: the observation accuracy of the deformation rate; assuming that the deformation rate early-warning value is v (mm/d) and the observation time interval is t (d), at the time interval of t, the deformation early-warning value should be c=vt; the observation precision must be able to distinguish the deformation c, if it is determined according to the rule of 1/10-1/20 of the accumulated deformation, it is inappropriate to require the observation precision to be too high to be realized when t is smaller, the observation error obeys the normal distribution N (mu, sigma), when the true value of the actual deformation of a monitoring point is mu at the observation time interval t (d), mu is more than or equal to c, the alarm should be given, because the true value mu cannot be obtained, it is determined by the statistical hypothesis testing method, and if mu is accepted to be more than or equal to c under a certain significance level alpha, the observation precision is an important parameter for the hypothesis test;
step S4: the observation accuracy of the deformation; nonlinear function provided with an observation X
F＝f(X 0 ,X 1 ,……,X n-1 )；
Developing linearized derivatives using the taylor formula
Figure BDA0002993258160000023
Let x be i Are mutually independent, dx i Using sigma i Instead, then
Figure BDA0002993258160000031
The relation of difference between every two observations is obtained, and the geometric deformation between any two observations is obtained;
F＝x 0 -x 1 -…-x n-1
Figure BDA0002993258160000032
Figure BDA0002993258160000033
error of any two adjacent observed deformation values
Figure BDA0002993258160000034
Step S5: checking the observation precision and the hypothesis; whether the observation precision meets the monitoring requirement or not, and timely and accurately judging the safety state of the foundation pit, wherein the safety state is required to be checked by means of statistical hypothesis; observing occasional errors obeys normal distribution X 1 ～N(μ 1 ,σ 1 ),X 2 ～N(μ 2 ,σ 2 )
In order to reduce and avoid systematic errors, it is generally required that the observation method, instrument and personnel are unchanged during each observation, and the observation is regarded as the same-precision observation sigma 1 ＝σ 2 =σ, assuming σ is known;
deformation truth value μ=μ between two monitoring 1 -μ 2 From the formula (2), the corresponding error is
Figure BDA0002993258160000035
Deformation estimator
Figure BDA0002993258160000036
Subject standard deviation +.>
Figure BDA0002993258160000037
Normal distribution->
Figure BDA0002993258160000038
When the deformation of the monitored object exceeds a certain deformation allowable value, a large safety risk exists, the monitored object is in an unstable state, and unit inspection is adopted based on the deformation characteristic of the foundation pit;
setting: original assumption H 0 Mu is larger than or equal to c, and alternative hypothesis H 1 :μ<c, c is a pre-warning value c=vt of twice monitoring deformation, and pre-warning is needed when the deformation true value mu is equal to or exceeds the value c, and the value mu is smaller than the value c and is not pre-warning;
for the convenience of discussion of the hypothesis testing method, the significance level α is generally 0.10,0.05 and 0.01, so as to ensure that the first type of errors, that is, errors in which the actual deformation exceeds or equals to the allowable deformation value but is rejected, should be avoided as much as possible, so that α is as small as possible, α is 0.01, but the smaller α is, the greater the second type of error probability β is, that is, errors in which the actual deformation does not exceed the allowable deformation value but is accepted;
alpha is fixed, the same original assumption can have a plurality of detection methods, and the larger the detection efficacy 1-beta is, the better;
is provided with
Figure BDA0002993258160000041
For a checking function
When deformation amount estimation
Figure BDA0002993258160000042
Time acceptation of original assumption H 0 ,/>
Figure BDA0002993258160000043
The efficacy functions of (a) are as follows:
Figure BDA0002993258160000044
/>
so that the number of the parts to be processed,
Figure BDA0002993258160000045
obeying a standard normal distribution N (0, 1)
Figure BDA0002993258160000046
When the deformation amount μ increases, (D- μ) decreases, so
Figure BDA0002993258160000047
Also falls down;
when mu is infinitely close to C,
Figure BDA0002993258160000048
then
Figure BDA0002993258160000049
Figure BDA00029932581600000410
The geometric relationship between variables of formula (4) can be seen;
bringing (4) into (3)
Figure BDA00029932581600000411
Assuming that the probability of making the second type of error is less than the specified beta, then
Figure BDA00029932581600000412
μ<C
So that the number of the parts to be processed,
Figure BDA00029932581600000413
equivalent(s)
Figure BDA00029932581600000414
When μ approaches C infinitely, C- μ≡0, μ α Given a certain level of significance, the formula (6) is not established, i.e. the second type of errors cannot be smaller than beta, the second type of errors are large, the nano-pseudo probability is increased, H is refused 1 Accept H 0 The probability increases; from the viewpoint of monitoring safety, when the deformation true value is more and more close to the early warning value, the second error is increased, and the efficacy is reduced;
when the deformation true value mu is infinitely close to C, generally, the deformation lateral displacement of the foundation pit is not negative, D=0,
Figure BDA0002993258160000051
accept H 0 From formula (4), it can be seen that
Figure BDA0002993258160000052
μ α Is a standard normal distribution critical value mu α ＝k；
As can be seen from the formula (7), when the deformation rate is fixed, the shorter the two monitoring times is, the higher the observation precision is required, the smaller the significance level alpha is, and the higher the observation precision is required;
as a further scheme of the invention: in the step S1, the confidence level 1- α is usually 95% internationally, and k=1.96; the domestic average error of k=2, i.e. the multiple, is taken as the limit error with a confidence of 95.6%.
The invention has the beneficial effects that: according to the invention, by analyzing the problem of the observation precision of the deformation rate, an observation precision calculation formula of deformation rate early warning is deduced, and the observation precision must be improved while the observation frequency is increased in a high risk period of foundation pit engineering; moreover, by setting up the observation precision concept of 1+N, not only can the basic observation precision of foundation pit engineering monitoring be determined according to the allowable deformation quantity, but also the observation precision in different periods can be determined according to the monitoring time interval length and the deformation rate early warning value; and the method determines an estimation principle or an empirical rule of the observation precision according to the deformation rate early-warning value, is economical and reasonable, and has higher reference value for foundation pit monitoring.
Drawings
The present invention is further described below with reference to the accompanying drawings for the convenience of understanding by those skilled in the art.
Fig. 1 is a normal curve distribution diagram of x=μ in step S1 of the present invention;
FIG. 2 is a diagram showing the relationship between μ, C and α, β in step S5 of the present invention;
FIG. 3 is a flowchart showing the process of step S5 of the present invention
Figure BDA0002993258160000053
Schematic of the relationship with D;
Detailed Description
The technical solutions of the present invention will be clearly and completely described in connection with the embodiments, and it is obvious that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1-3, the deep foundation pit engineering monitoring precision method based on the deformation rate comprises the following steps:
step S1: complete measurement result expression; the complete measurement result comprises a measurement result and a measurement error, wherein the measurement error expression mode adopts concepts of measuring middle error and 2 times middle error as limit error and the like, and the complete measurement result can be expressed as:
Figure BDA0002993258160000061
wherein ,
Figure BDA0002993258160000062
for the measurement result, sigma is the error in measurement, k is the standard normal distribution critical value of the significance level alpha;
the confidence level 1-alpha is usually taken internationally as 95%, k=1.96; generally, k=2, namely the medium error of the double is taken as the limit error in China, and the confidence is 95.6%;
step S2: determining deformation observation precision; the observation accuracy is to ensure that the amount of deformation that has occurred is monitored under normal operating conditions; in general, the observation precision is determined according to a deformation allowable value in a certain proportion; for foundation pit safety monitoring, important attention is paid to the deformation rate, namely the deformation rate is very important in the key construction stage of foundation pit engineering, or dangerous symptoms occur, or significant changes occur to influencing factors, such as rainfall and sudden changes of load around the foundation pit, and when encryption observation is needed, the deformation rate has very important meaning in early warning;
step S3: the observation accuracy of the deformation rate; assuming that the deformation rate early-warning value is v (mm/d) and the observation time interval is t (d), at the time interval of t, the deformation early-warning value should be c=vt; the observation precision must be able to distinguish the deformation c, if it is determined according to the rule of 1/10-1/20 of the accumulated deformation, it is inappropriate to require the observation precision to be too high to be realized when t is smaller, the observation error obeys the normal distribution N (mu, sigma), when the true value of the actual deformation of a monitoring point is mu at the observation time interval t (d), mu is more than or equal to c, the alarm should be given, because the true value mu cannot be obtained, it is determined by the statistical hypothesis testing method, and if mu is accepted to be more than or equal to c under a certain significance level alpha, the observation precision is an important parameter for the hypothesis test;
step S4: the observation accuracy of the deformation; nonlinear function provided with an observation X
F＝f(X 0 ,X 1 ,……,X n-1 )；
Developing linearized derivatives using the taylor formula
Figure BDA0002993258160000071
Let x be i Are mutually independent, dx i Using sigma i Instead, then
Figure BDA0002993258160000072
The relation of difference between every two observations is obtained, and the geometric deformation between any two observations is obtained;
F＝x 0 -x 1 -…-x n-1
Figure BDA0002993258160000073
Figure BDA0002993258160000074
/>
error of any two adjacent observed deformation values
Figure BDA0002993258160000075
Step S5: checking the observation precision and the hypothesis; whether the observation precision meets the monitoring requirement or not, and timely and accurately judging the safety state of the foundation pit, wherein the safety state is required to be checked by means of statistical hypothesis; observing occasional errors obeys normal distribution X 1 ～N(μ 1 ,σ 1 ),X 2 ～N(μ 2 ,σ 2 )
In order to reduce and avoid systematic errors, it is generally required that the observation method, instrument and personnel are unchanged during each observation, and the observation is regarded as the same-precision observation sigma 1 ＝σ 2 =σ, assuming σ is known;
deformation truth value μ=μ between two monitoring 1 -μ 2 From the formula (2), the corresponding error is
Figure BDA0002993258160000076
Deformation estimator
Figure BDA0002993258160000077
Subject standard deviation +.>
Figure BDA0002993258160000078
Normal distribution->
Figure BDA0002993258160000079
When the deformation of the monitored object exceeds a certain deformation allowable value, a large safety risk exists, the monitored object is in an unstable state, and unit inspection is adopted based on the deformation characteristic of the foundation pit;
setting: original assumption H 0 Mu is larger than or equal to c, and alternative hypothesis H 1 :μ<c, c is a pre-warning value c=vt of twice monitoring deformation, and pre-warning is needed when the deformation true value mu is equal to or exceeds the value c, and the value mu is smaller than the value c and is not pre-warning;
for the convenience of discussion of the hypothesis testing method, the significance level α is generally 0.10,0.05 and 0.01, so as to ensure that the first type of errors, that is, errors in which the actual deformation exceeds or equals to the allowable deformation value but is rejected, should be avoided as much as possible, so that α is as small as possible, α is 0.01, but the smaller α is, the greater the second type of error probability β is, that is, errors in which the actual deformation does not exceed the allowable deformation value but is accepted;
alpha is fixed, the same original assumption can have a plurality of detection methods, and the larger the detection efficacy 1-beta is, the better;
is provided with
Figure BDA0002993258160000081
For a checking function
When deformation amount estimation
Figure BDA0002993258160000082
Time acceptation of original assumption H 0 ,/>
Figure BDA0002993258160000083
The efficacy functions of (a) are as follows:
Figure BDA0002993258160000084
so that the number of the parts to be processed,
Figure BDA0002993258160000085
obeying a standard normal distribution N (0, 1)
Figure BDA0002993258160000086
When the deformation amount μ increases, (D- μ) decreases, so
Figure BDA0002993258160000087
Also falls down;
when mu is infinitely close to C,
Figure BDA0002993258160000088
then
Figure BDA0002993258160000089
Figure BDA00029932581600000810
The geometric relationship between variables of formula (4) can be seen;
bringing (4) into (3)
Figure BDA00029932581600000811
Assuming that the probability of making the second type of error is less than the specified beta, then
Figure BDA00029932581600000812
μ<C
So that the number of the parts to be processed,
Figure BDA00029932581600000813
/>
equivalent(s)
Figure BDA00029932581600000814
When μ approaches C infinitely, C- μ≡0, μ α Given a certain level of significance, the formula (6) is not established, i.e. the second type of errors cannot be smaller than beta, the second type of errors are large, the nano-pseudo probability is increased, H is refused 1 Accept H 0 The probability increases; from the viewpoint of monitoring safety, when the deformation true value is more and more close to the early warning value, the second error is increased, and the efficacy is reduced;
when the deformation true value mu is infinitely close to C, generally, the deformation lateral displacement of the foundation pit is not negative, D=0,
Figure BDA0002993258160000091
accept H 0 From formula (4), it can be seen that
Figure BDA0002993258160000092
μ α Is a standard normal distribution critical value mu α ＝k；
As can be seen from the formula (7), when the deformation rate is fixed, the shorter the two monitoring times is, the higher the observation precision is required, the smaller the significance level alpha is, and the higher the observation precision is required;
TABLE 1 accuracy requirement (mm) for different monitoring frequencies of deformation Rate Pre-alarm value 3mm/d
Figure BDA0002993258160000093
The time interval t of the table 1 is consistent with the standard specification, and the significance level alpha is 0.01, namely when the actual deformation is equal to or exceeds the early warning value, the probability of false is only 1%, which belongs to the extremely small probability event; when the deformation rate early warning value is 3mm/d, the building deformation and other precision are adopted for 3d and above, the observation precision is required to be improved within 2d, and the precision can be improved by adopting a method for increasing the observation times;
by analogy, when the deformation rate early-warning value is 2mm/d, building deformation standard and other precision can be adopted for 7d and more, and observation precision must be increased for 5d and less; when the deformation rate early warning value is 5mm/d, building deformation standard and other precision can be adopted for 2d and more, and the observation precision must be improved within 1 d.
The preferred embodiments of the invention disclosed above are intended only to assist in the explanation of the invention. The preferred embodiments are not exhaustive or to limit the invention to the precise form disclosed. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best understand and utilize the invention. The invention is limited only by the claims and the full scope and equivalents thereof.

Claims (1)

1. The deep foundation pit engineering monitoring precision method based on the deformation rate is characterized by comprising the following steps of:
step S1: complete measurement result expression; the complete measurement result comprises a measurement result and a measurement error, wherein the measurement error expression mode adopts a measurement middle error and a middle error which is 2 times as a limit error concept, and the complete measurement result can be expressed as follows:
Figure FDA0004162489530000011
wherein ,
Figure FDA0004162489530000012
for the measurement result, sigma is the error in measurement, k is the standard normal distribution critical value of the significance level alpha;
step S2: determining deformation observation precision;
step S3: the observation accuracy of the deformation rate; assuming that the deformation rate early-warning value is v, and the observation time interval is t, then at the time interval of t, the deformation early-warning value should be c=vt; the observation precision must be able to distinguish the deformation c, if the observation error is determined according to the rule of 1/10-1/20 of the accumulated deformation, the observation error is compliant with normal distribution N (mu, sigma), when one monitoring point is in the observation time interval t and the true value of the actual deformation is mu theta, mu is more than or equal to c, the early warning should be carried out;
step S4: the observation accuracy of the deformation; nonlinear function provided with an observation X
F＝f(X 0 ，X 1 ，......，X n-1 )；
Developing linearized derivatives using the taylor formula
Figure FDA0004162489530000021
Let x be i Are mutually independent, dx i Using sigma i Instead, then
Figure FDA0004162489530000022
The relation of difference between every two observations is obtained, and the geometric deformation between any two observations is obtained;
F＝x 0 -x 1 -…-x n-1
Figure FDA0004162489530000023
Figure FDA0004162489530000024
error of any two adjacent observed deformation values
Figure FDA0004162489530000025
Step S5: checking the observation precision and the hypothesis; observing occasional errors obeys normal distribution X 1 ～N(μ 1 ，σ 1 )，X 2 ～N(μ 2 ，σ 2 )
In order to reduce and avoid systematic errors, the observation method, instrument and personnel are required to be unchanged during each observation, and are regarded as the same-precision observation sigma 1 ＝σ 2 =σ, assuming σ is known;
deformation truth value μ=μ between two monitoring 1 -μ 2 From the formula (2), the corresponding error is
Figure FDA0004162489530000026
Deformation estimator
Figure FDA0004162489530000031
Subject standard deviation +.>
Figure FDA0004162489530000032
Normal distribution->
Figure FDA0004162489530000033
Setting: original assumption H 0 : mu is larger than or equal to c, and alternative hypothesis H 1 : μ is more than or equal to c, c is a twice-monitored deformation early warning value c=vt, and early warning is performed when the deformation true value μ is equal to or exceeds the value c, and μ is less than the value c and is not early warning;
for ease of discussion of hypothesis testing methods, a significance level α of 0.10,0.05,0.01 is desirable;
is provided with
Figure FDA0004162489530000034
For a checking function
When deformation amount estimation
Figure FDA0004162489530000035
Time acceptation of original assumption H 0 ,/>
Figure FDA0004162489530000036
The efficacy functions of (a) are as follows:/>
Figure FDA0004162489530000037
so that the number of the parts to be processed,
Figure FDA0004162489530000038
obeying a standard normal distribution N (0, 1)
Figure FDA0004162489530000039
When the deformation amount μ increases, (D- μ) decreases, so
Figure FDA00041624895300000310
Also falls down;
when mu is infinitely close to C,
Figure FDA00041624895300000311
then
Figure FDA00041624895300000312
Figure FDA0004162489530000041
The geometric relationship between variables of formula (4) can be seen;
bringing (4) into (3)
Figure FDA0004162489530000042
Assuming that the probability of making the second type of error is less than the specified beta, then
Figure FDA0004162489530000043
μ＜C
So that the number of the parts to be processed,
Figure FDA0004162489530000044
equivalent(s)
Figure FDA0004162489530000045
When μ approaches C infinitely, C- μ≡0, μ α Given by the significance level, the formula (6) is not established, the nano-pseudo probability is increased, and H is refused 1 Accept H 0 The probability increases;
when the distortion value mu approaches C infinitely, taking d=0,
Figure FDA0004162489530000046
accept H 0 From formula (4), it can be seen that
Figure FDA0004162489530000047
μ α Is a standard normal distribution critical value mu α ＝k；
As can be seen from the expression (7), when the deformation rate is constant, the shorter the two monitoring times, the higher the observation accuracy is required, and the smaller the significance level α is, the higher the observation accuracy is required.
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