Evaluation of segment convergence and settlement of subway shield tunnel in water-rich complex stratum

4.1. Analysis of variation law of convergence value data

From Table 2 and Fig. 2, the clearance convergence cumulative change of the measurement points of each segment section is different. Most of the segments at the monitoring section are squeezed by the surrounding soil, and the convergence deformation of the horizontal inward contraction occurs in the direction of the clearance. A small part of the section deformation is horizontal outward expansion. The point with the largest cumulative change is GGJ928, and the cumulative displacement is 2.41 mm within the safe and controllable range.

Fig. 2Cumulative value curve of segment convergence deformation

4.2. Engineering convergence data distribution pattern

Table 3 shows the convergence deformation values on each typical monitoring section. The statistical analysis software SPSS is used to test the normality of the engineering data in the table to determine whether the convergence data obeys the normal distribution [9, 10]. The test results are shown in Table 3.

Table 3 uses Kolmogorov-Smirnov and Shapiro-Wilk methods to test the data. The results show that the significance values $Sig.$ of both are greater than 0.05, indicating that the monitored data conform to the normal distribution.

4.3. Test for accidental errors in convergent data

Based on the theory of probability and statistics, the monitoring data of segment convergence in Table 3 is analyzed, and the characteristics of accidental error are tested, so as to judge whether the convergence data is accidental error or systematic error [11].

(1) Test method and formula of random error characteristics.

1) Hypothesis: specify the specific test content of the null hypothesis $H_0$;

2) Determine the test statistic: select the corresponding statistic according to the hypothesis content;

3) Determined the rejection region of $H_0$: under the condition that the significance level $\alpha$ (0$<\alpha <$1) is determined, the rejection region corresponding to the critical value is obtained.

The rejection region of positive and negative error signs number test is:

The rejection region of positive and negative error allocation order test is:

The rejection region of error value and test is:

The rejection region of the maximum error value test is:

4) Make a judgment: if the critical value meets the range of the rejection region, reject $H_0$; Otherwise, accept $H_0$ and pass the test.

(2) The estimated standard deviation of convergence value was calculated by statistical theory $m=$ ±1.10 mm, and the significance level $\alpha =$0.0455 was used to test the following error characteristics of convergence monitoring data.

1) Positive and negative error signs number test.

Proposing the null hypothesis $H_0$: the number of positive and negative error signs is equal; The positive error number is $S_{\alpha }=$ 11, the negative error number is ${S_{\alpha }}^{\text{'}}=$ 25, then $\left|S_{\alpha }-{S_{\alpha }}^{\text{'}}\right|=$ 14, and the critical value is $2\sqrt{n}=2\sqrt{36}=$ 12, that is $\left|S_{\alpha }-{S_{\alpha }}^{\text{'}}\right|>2\sqrt{n}$, $H_0$ is rejected, which does not conform to the symmetry of accidental error.

2) Positive and negative error allocation order test.

Proposing the null hypothesis $H_0$: the alternations number of the same or opposite sign of the adjacent two errors is equal; The number of two adjacent errors with the same sign is $S_{\theta }=$ 21, the number of adjacent error with opposite sign is ${S_{\theta }}^{\text{'}}=$ 14, then $\left|S_{\theta }-{S_{\theta }}^{\text{'}}\right|=$ 7, and the critical value is $2\sqrt{n-1}=2\sqrt{35}=$ 11.8 ≈ 12, that is $\left|S_{\theta }-{S_{\theta }}^{\text{'}}\right|<2\sqrt{n-1}$, the null hypothesis $H_0$ is accepted and the test is passed.

3) The sum of error values test.

Proposing the null hypothesis $H_0$: the mean error is zero; The sum of all monitored values is $\left|S\right|=$ 12.61, and the critical value is $2\sqrt{nm}=2\sqrt{36}\times \left(\pm 10\right)=$±13.2, that is, $\left|S\right|<2\sqrt{nm}$, the null hypothesis${\mathrm{H}}_0$is accepted and the test is passed.

4) The maximum error value test.

Proposing the null hypothesis $H_0$: The critical value of limit error is $2m=$ ±2.2 mm; The maximum closure difference in all monitoring values is $\left|S_i\right|=$ 2.41 mm, then $\left|S_i\right|>2m$, that is, the error value at the GGJ928-1 monitoring point is abnormal, $H_0$ is rejected, which does not conform to the boundedness of accidental errors.

Through the above error characteristics test, it can be seen that the convergence value data does not satisfy the symmetry and boundedness of accidental errors, and there are two rejection terms. Firstly, the number of positive and negative error signs is tested and $H_0$ is rejected, indicating that the probability of positive and negative errors with equal absolute values is different. It is considered that these deformation values have systematic tendency characteristics.

4.4. Comprehensive analysis of convergence data

Through the normality test and error characteristic test, the convergence value data obeys the normal distribution, and does not conform to the characteristics of accidental error. It is considered that the tunnel segment has a systematic tendency in the direction of clearance convergence, and there is a relative dynamic deformation with an offset of –0.35 mm horizontally inward extrusion.

5.1. Analysis of settlement data of segmental vault

From Table 4 and Fig. 3, It can be seen that the change rate of the cumulative settlement of the whole vault fluctuates greatly, and in the process of shield construction, the segments at most monitoring sections have vertical upward displacement deformation in the vertical direction, resulting in floating phenomenon, and the segment vault at a few sections has normal settlement. The point with the largest cumulative change is GGC1000, and the cumulative displacement is 3.10 mm, which does not reach the warning value.

5.2. Data analysis of segment arch bottom settlement

From Table 5 and Fig. 4, it can be seen that except for the large fluctuation of individual monitoring point data caused by construction, the overall change rate of the settlement curve of the arch bottom is relatively gentle. Most of the segments on the monitoring section are in normal settlement, and only a few sections have a certain uplift at the bottom of the tunnel segment. Among them, the point with the largest cumulative change is GDC864, with a cumulative displacement of –3.96 mm, which does not reach the warning value.

Through the normality and error characteristics of the settlement values at the top and bottom of the arch, it can be seen that the settlement data obeys a normal distribution and does not satisfy the requirements of symmetry, boundedness and compensation for chance errors. Both the top and bottom of the arch have a rigid absolute deflection with offsets of +0.64 mm and –0.45 mm respectively.

Fig. 3Cumulative value curve of segment vault settlement

Fig. 4Cumulative value curve of segment arch bottom settlement

5.3. Comprehensive evaluation of the project

Through the statistical analysis and test of the convergence and settlement data of the segment, and according to the judgment of the deformation state in Table 1, it can be seen that the project belongs to the comprehensive deformation phenomenon of the 2, 4 and 8 cases. The deformation of the tunnel segment is judged as follows: in the direction of clearance convergence, the segment is squeezed by the surrounding soil to produce a relative dynamic deformation of –0.35 mm horizontally inward, and the rigid absolute deformation of the vertical upward 0.64 mm of the vault and the vertical downward –0.45 mm of the arch bottom is accompanied.