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An improved attribute recognition method is reviewed and discussed to evaluate the risk of water inrush in karst tunnels. Due to the complex geology and hydrogeology, the methodology discusses the uncertainties related to the evaluation index and attribute measure. The uncertainties can be described by probability distributions. The values of evaluation index and attribute measure were employed through random numbers generated by Monte Carlo simulations and an attribute measure belt was chosen instead of the linearity attribute measure function. Considering the uncertainties of evaluation index and attribute measure, the probability distributions of four risk grades are calculated using random numbers generated by Monte Carlo simulation. According to the probability distribution, the risk level can be analyzed under different confidence coefficients. The method improvement is more accurate and feasible compared with the results derived from the attribute recognition model. Finally, the improved attribute recognition method was applied and verified in Longmenshan tunnel in China.

Risk management became an integral part of most underground projects during the late 1990s [

Water inrush can be described exactly by the potential energies of water leaking from karst conduit. Based on the mechanism of water inrush in karst tunnel, it can be categorized into geological flaws and no geological flaws [

There exist many perspectives on risk, and traditionally some of the perspectives have been seen as representing completely different frameworks, making the exchange of ideas and results difficult [

Risk assessment of water inrush with geological flaws normally use neural network method, AHP, FAHP, GIS, fuzzy mathematical method, attribute mathematical method, and so on [

In the risk assessment of water inrush in karst tunnels, the biggest problem is that the classification is different and the result is not rational. However, it can be effectively solved by the risk assessment model based on attribute comprehensive evaluation system, according to the principle of maximum membership degree law. Many literatures present a series of researches on the integrated attribute evaluation system model.

When using the model based on attribute synthetic evaluation system, the value of evaluation index and attribute measure influence the assessment results directly. Based on ordered partition class and attribute recognition criterion, the attribute synthetic evaluation system can effectively identify and perform comparative analysis. Also, the attribute synthetic evaluation system effectively overcomes some shortcomings of other identification methods such as fuzzy recognition theory and can effectively reduce the loss of information in a calculation. Therefore, the synthetic evaluation system attribute has been successfully applied to the risk predication, risk evaluation, and risk decision of water inrush in karst tunnel. Previous methods usually adopt a definite value. Nevertheless, the geology in karst regions is uncertain, and it has the stochastic character. Also, the attribute is uncertain too. So, there are two basic problems before the viewpoints on the stochastic rock engineering to analyze the risk assessment of water inrush.

(1) The uncertainty of geology induces the uncertainty of evaluation index value. The evaluation indices generally rely on objective factors such as hydrogeology and geology factors. The values of evaluation index are always different from each other even in the same condition. Therefore, the value of evaluation index must account for the randomness.

(2) Uncertainty of attribute measure: in the model based on attribute synthetic evaluation system, the attribute level of evaluation index is quantitatively depicted as a constant by the attribute measure. It is more reasonable using an interval compared to a constant to depict the attribute measure, ascribed to the uncertainty of attribute measure.

In this paper the statistical characteristic about the value of evaluation index and attribute measure is taken into account with respect to the uncertainty of risk assessment in water inrush. An improved attribute recognition approach is proposed to calculate probabilities of risk level utilizing attribute synthetic evaluation system and Monte Carlo sampling distribution. The results would be more scientific and reasonable compared to other methods.

Indices and criteria for risk assessment of water inrush are based on the statistical information about geology in karst tunnels, and several influencing factors of water inrush are selected as the attribute evaluation indices. Formation lithology is normalized, and strata inclination is divided into Level III and Level IV in the range of

Indices and criteria for risk assessment of water inrush in karst tunnels.

Indices for risk assessment of water inrush | Risk grade | |||
---|---|---|---|---|

IV | III | II | I | |

Formation lithology | 0~4.2 | 4.2~10.4 | 10.4~25.4 | >25.4 |

Unfavorable geological conditions | <60 | 60~70 | 70~85 | 85~100 |

Groundwater level | <10 | 10~30 | 30~60 | >60 |

Landform and physiognomy (proportion of negative landform area) | <20 | 20~40 | 40~60 | >60 |

Modified strata inclination | 0~5 | 5~10 | 10~25 | 25~45 |

Contact zones of dissolvable and insoluble rock | <60 | 60~70 | 70~85 | 85~100 |

Layer and interlayer fissures | <60 | 60~70 | 70~85 | 85~100 |

There are many uncertain factors in the evaluation of the rock engineering [

The probability distribution of strata inclination, for instance, is calculated. Suppose the actual measurement indices are

Histogram and distribution of strata inclination.

The parameters of probabilistic distribution function for indices include mean value and standard deviation which can be calculated using measurement data. If the data is a value interval, the mean value can be calculated using the value interval and the standard deviation can be calculated using

Attribute measure is the characterization that represents the level of a certain attribute of the element. As “

Linearity attribute measure curve.

There is often no linear relationship between the influencing factors and the risk of water inrush in karst tunnel. So, when the attribute recognition model is applied to comprehensive risk evaluation of water inrush, the evaluation results of attribute recognition model based on linear measure function often have relatively large errors. Thus, the reliability of the evaluation results is reduced. However, it is better to depict the attribute measure by a limited value interval rather than a certain value. This means that the attribute measure perturbs in the value interval. The disturbing region is called attribute measure belt. In the attribute measure belt, the attribute measure value of the element on the starting point or terminal point is 0 or 1, while the value of the element on the middle is 0.5. Therefore, if the value of the element is 0 or 1, it is the clearest point; if the value is 0.5, it is the fuzziest point. That is to say, it is on the middle point between 0 and 1. When the value of a point is certain, its value of attribute measure is 0 or 1, the attribute measure belt will be tentatively determined, as shown in Figure

Trigonal attribute measure curve.

Suppose

Domain elements of attribute measure.

Grade | Attribute measure | ||
---|---|---|---|

| | 0.5 | |

| | | |

| | | |

| | | |

| | | |

The attribute measure function is not arbitrary, but it must follow three principles [

The value of risk index for water inrush in karst tunnels is achieved through statistical probability distribution based on the method in Section

Value of

Index values | Index vectors | |
---|---|---|

Formation lithology | | |

Unfavorable geological conditions | | |

Groundwater level (m) | | |

Landform and physiognomy (proportion of negative landform area) | | |

Modified strata inclination (°) | | |

Contact zones of dissolvable and insoluble rock | | |

Layer and interlayer fissures | | |

The random number

Multiple indices synthetic attribute measure vector

Distribution maps can be expressed by using programming software MATLAB. Then the risk level can be further assessed through agglomeration and overlap degree of the distribution maps.

The risk assessment model of water inrush in karst tunnels based on attribute synthetic evaluation system is applied in Jigongling tunnel at construction contract section K19 + 509 to K19 + 539 [

Based on the values about the geological and hydrogeological conditions in Jigongling tunnel at construction contract section K19 + 509 to K19 + 539, the evaluation process can be performed considering uncertainty about the index and attribute measure as follows.

(1) For the time being, normal distribution can be used to deal with the uncertainty problem. Based on the values of indices [

Parameters of probabilistic distribution for index

Mean | Standard deviation | ||
---|---|---|---|

Formation lithology | | 75 | 1.5 |

Unfavorable geological conditions | | 60 | 1.5 |

Groundwater level (m) | | >75 | 1.5 |

Landform and physiognomy (proportion of negative landform area) | | 40 | 1.5 |

Modified strata inclination (°) | | 16 | 1.5 |

Contact zones of dissolvable and insoluble rock | | 70 | 1.5 |

Layer and interlayer fissures | | 65 | 1.5 |

(2) According to parameters in Table

(3) Single index attribute measure matrix: single index attribute measure of each stochastic vector is computed by using the method in Section

(4) Multiple indices synthetic attribute measures matrix is calculated with (

Histogram of the synthetic attribute measures of risk grade.

Based on the histogram, synthetic attribute measures of risk grade analysis are depicted as follows.

(1) The probability of risk follows a sequence of Level III < Level I < Level IV < Level II. It is noticed that the risk of level II is most likely to occur compared to other risk levels.

(2) The probabilities of risk Level III and Level I overlap with each other from 0.1 to 0.15. The probability of risk Level II is approximately three times larger or higher than that of risk Level I and 4 times compared to that of risk Level III. Hence, considering the single probability of synthetic attribute measure, the risk level is probably Level II.

(3) Based on the synthetic attribute measures in Figure

Risk evaluation risk level under different confidence coefficients.

Risk level | Confidence coefficient |
---|---|

Risk Level I | |

Risk Level I or risk Level II; slanting risk Level I | |

Risk Level I or risk Level II; slanting risk Level II | |

Risk Level II | |

Risk Level III or risk Level II; slanting risk Level II | |

Risk Level III or risk Level II; slanting risk Level III | |

Risk Level III | |

Risk Level IV or risk Level III; slanting risk Level III | |

Risk Level IV or risk Level III; slanting risk Level IV | |

Risk Level IV | |

Histograms of probability of risk level.

There are three reasons why the risk evaluation results of water inrush is Level I in design stage and modified into Level II in construction stage [

Probabilistic distribution of value indices.

Indices | | | | | | | | |
---|---|---|---|---|---|---|---|---|

XJ3K1 + 525-XJ3K1 + 485 | Mean | 60 | 55 | 120 | 30 | 16 | 65 | 60 |

Standard deviation | 0.83 | 0.83 | 1.5 | 0.83 | 0.83 | 1.5 | 1.5 | |

| ||||||||

XJ3K1 + 485-XJ3K1 + 445 | Mean | 70 | 65 | 120 | 30 | 20 | 70 | 65 |

Standard deviation | 0.83 | 0.83 | 1.5 | 0.83 | 0.83 | 1.5 | 1.5 | |

| ||||||||

XJ3K1 + 445-XJ3K1 + 405 | Mean | 75 | 85 | 120 | 30 | 40 | 75 | 80 |

Standard deviation | 0.83 | 0.83 | 1.5 | 0.83 | 0.83 | 1.5 | 1.5 | |

| ||||||||

XJ3K1 + 405-XJ3K1 + 365 | Mean | 78 | 80 | 120 | 30 | 40 | 70 | 75 |

Standard deviation | 0.83 | 0.83 | 1.5 | 0.83 | 0.83 | 1.5 | 1.5 | |

| ||||||||

XJ3K1 + 365-XJ3K1 + 325 | Mean | 65 | 70 | 120 | 30 | 30 | 65 | 60 |

Standard deviation | 0.83 | 0.83 | 1.5 | 0.83 | 0.83 | 1.5 | 1.5 |

The Chengdu-Lanzhou railway is located in Chengdu and Lanzhou in China, the bridges and tunnels ratio of which reaches up to 86.05%. The project crosses through three fracture zones: the Longmenshan fracture zone, Minjiang fracture zone, and Qinling fracture zone. Therefore, the construction project has a great risk of geological disaster.

Longmenshan tunnel is located in the Longmenshan fracture zone in the Chengdu-Lanzhou railway. It is approximately 20 km long, with the maximum buried depth of 1445 m. The tunnel traverses the Peijiang river systems and the central fault belt of Longmenshan Mountain. The geological structure is relatively complex, and the topographical map is described as Figure

Topographical map of the tunnel.

Based on the geology and hydrogeology of test sections, risk of water inrush is assessed. The test section is divided into five regions and risk of water inrush is evaluated in each region. The probability distributions of value indices in each region are presented in Table

Through the calculation of the model considering uncertainties, the histograms of the probabilities of water risk level in each region are shown in Figure

Considering the confidence coefficient taken as 0.6–0.7, the possible risk levels with different confidence coefficients are shown in Table

Possible risk level in each region.

Risk level | Confidence coefficient | Risk evaluation results | |
---|---|---|---|

XJ3K1 + 525-XJ3K1 + 485 | Level III | | Level III |

XJ3K1 + 485-XJ3K1 + 445 | Risk Level III or risk Level II; slanting risk Level III | | level III |

XJ3K1 + 445-XJ3K1 + 405 | Risk Level I or risk Level II; slanting risk Level I | | Risk level I |

XJ3K1 + 405-XJ3K1 + 365 | Risk Level I or risk Level II; slanting risk Level II | | Risk level II |

XJ3K1 + 365-XJ3K1 + 325 | Risk Level III or risk Level II; slanting risk Level II | | Risk level II |

Histograms of probability of risk level in each region.

According to the possible risk levels and confidence coefficient, the risk evaluation results of water inrush are listed in Table

The excavation of number 3 inclined shaft in Longmenshan tunnel was constructed at sections XJ3K1 + 485. During the advanced drilling of borehole at XJ3K1 + 439, water seepage suddenly flowed (see Figure

Water inrush of practical situation.

Water seepage at XJ3K1 + 439

Water flow at XJ3K1 + 439

Water inrush at XJ3K1 + 439

The uncertainty analysis on the risk assessment attribute model of water inrush in karst tunnels was performed in this paper. Based on the uncertainties of evaluation index and attribute measure, an attribute recognition method improvement is developed and more information can be provided for decision-makers.

The probabilities of risk grade indicate that the risk evaluation results are also influenced by the confidence coefficients. While the confidence coefficient selects different value, the risk evaluation result may be different.

By comparing with attribute recognition model, this paper successfully explained the reason that the risk evaluation is different between design stage and construction stage. Basically, there are two influencing factors: (1) uncertainties of values of evaluation index and attribute measure and (2) different confidence coefficients.

The method presented was then applied in Longmenshan tunnel at section of XJ3K1 + 085-XJ3K1 + 485. Based on the new method, the risk evaluation results of water inrush show that the risk level of water inrush is very high, and sure enough water inrush occurs at section XJ3K1 + 445. So, the results used in this method to predict the risk level of water inrush in the construction of Longmenshan tunnel are in accord with the actual situation and have high reliability.

The method about uncertainties can also be utilized in other recognition models. The probability distributions of evaluation index values and attribute measures will be more objective and reasonable through big data analysis. In addition, it is very important to gain the confidence coefficient objectively.

The authors declare that they have no competing interests.

The authors would like to acknowledge the financial support from the National Basic Research Program of China (973 Program, no. 2013CB036005), the National Natural Science Foundation of China (nos. 51527810, 51309234, 51308543, 51309233, 51304219, and 51409258), and the Natural Science Foundation of Jiangsu Province (BK20130065). The authors also acknowledge the financial support from the Open Foundation of State Key Laboratory for Geomechanics and Deep Underground Engineering (SKLGDUEK1403) and the China Postdoctoral Science Foundation (2015M570451).