Full probability-based seismic risk analysis method for tunnel under fault dislocation

Abstract

A full probability-based seismic risk analysis method for a tunnel under fault dislocation comprises: evaluating a magnitude-frequency relationship of a fault; obtaining a probabilistic seismic risk curve of a fault dislocation; calculating a series of bending moments of a tunnel lining under different fault dislocations; obtaining a series of damage index values R.sub.M of the tunnel; obtaining a vulnerability model of the tunnel damaged by fault dislocation; calculating a probabilistic risk that the tunnel crossing the fault is damaged due to the dislocation of the active fault; obtaining a probability P that the damage state is equal to or higher than a certain damage state within a specified period; and using the results to guide the assessment of the seismic risk of the tunnel crossing the fault. Modeling and analysis can be performed according to the actual situation of the tunnel crossing the fault with different factors.

Claims

1. A full probability-based seismic risk analysis method for a tunnel under a fault dislocation, comprises: step 1: determining a position, an angle, a length, and a type of an active fault that the tunnel passes through, analyzing a seismic activity of the fault, determining a minimum annual occurrence rate of earthquakes in the fault, and evaluating a magnitude-frequency relationship of the fault; step 2: evaluating a probabilistic seismic hazard of the fault dislocation by using an existing fault dislocation prediction equation according to formula (1), to obtain a probabilistic seismic hazard curve of the fault dislocation,
λ.sub.D(d)=v∫.sub.MP[D>d|m].Math.f(m).Math.dm  (1); where in formula (1), λ.sub.D(d) is an average annual exceeding rate of the fault dislocation D exceeding a certain threshold d, v is an annual average occurrence rate of earthquakes, M is an earthquake magnitude, P(D>d|m) indicates a conditional probability that the fault dislocation is greater than a given value d when the earthquake magnitude is m, and f(m) is a probability density function that the fault can produce the earthquake magnitude of m; step 3: determining basic working conditions of the tunnel crossing the fault, including an angle between the fault and the tunnel and a buried depth and soil properties of the tunnel, performing three-dimensional modeling on the tunnel crossing the fault by using a finite element model, applying the fault dislocation step by step, and calculating a series of bending moments of a tunnel lining under different fault dislocation values; step 4: calculating a limit bending moment of the lining of a tunnel segment crossing the fault according to an actual design of the tunnel, and then dividing the series of bending moments obtained in step 3 by the limit bending moment to obtain a series of damage index values R.sub.M of the tunnel; step 5: obtaining a vulnerability model of the tunnel damaged by the fault dislocation, that is, a relationship between a bending moment ratio in step 4 and a probability of causing a structure to reach different damage states, where the mathematical expression is formula (2): $\begin{array}{cc}P\left(DS\ge d{s}_i|R_M\right)=\varphi \left[\frac{1}{\beta }.Math.\ln \left(\frac{R_M}{{\overline{R}}_M}\right)\right];& \left(2\right)\end{array}$ where in formula (2), P is a cumulative vulnerability probability function of the tunnel, which describes a probability that a damage state DS of the tunnel is greater than or equal to a specific damage state ds.sub.i when a damage index value R.sub.M of the tunnel is given, R.sub.M is a median of the damage index value, β is a log standard deviation of the damage index value, and ϕ indicates a standard normal cumulative distribution function; step 6: based on the probabilistic seismic hazard curve of the fault dislocation, the damage index value of the tunnel crossing the fault, and the vulnerability model obtained in steps 2-5, calculating, according to formula (3), an annual exceeding rate of different structural damage states of the tunnel crossing the fault under an action of the fault dislocation, that is, a probabilistic risk that the tunnel crossing the fault is damaged due to a dislocation of the active fault,
λ.sub.ds.sub.i=∫.sub.DP(DS≥ds.sub.i|R.sub.M=r.sub.M(d,θ))|dλ.sub.D(d)|  (3); where in formula (3), λ.sub.ds.sub.i is the annual exceeding rate equal to or greater than a target damage state, P(DS≥ds.sub.i|R.sub.M=r.sub.M(d, θ)) is a conditional probability that the damage state DS of the tunnel is greater than the specific damage state ds.sub.i when the damage index value R.sub.M calculated by the finite element model is equal to r.sub.M under a given dislocation d and other parameters θ (including the angle between the fault and the tunnel and the buried depth of the tunnel), that is, a vulnerability function, and λ.sub.D (d) is the average annual exceeding rate of the fault dislocation; step 7: converting, based on an assumption of obeying an Poisson process, the annual exceeding rate obtained in step 6 into a probability P that the damage state is equal to or higher than a certain damage state within a specified period, using formula (4):
P=1−e.sup.−λt  (4); where in formula (4), t is the specified period of the structure, and λ is λ.sub.ds.sub.i in formula (3); and step 8: using the results of steps 6 and 7 to guide an assessment of the seismic risk of the tunnel crossing the fault.

2. The full probability-based seismic risk analysis method for the tunnel under the fault dislocation according to claim 1, wherein in step 2, the fault dislocation is a bedrock dislocation or a surface dislocation; and wherein x-axis of the hazard curve is a maximum surface dislocation of the fault, and y-axis of the hazard curve is the annual exceeding rate corresponding to the dislocation.

3. The full probability-based seismic risk analysis method for the tunnel under the fault dislocation according to claim 1, wherein in step 3, the finite element model is Flac3D or ABAQUS; a range of applying the fault dislocation step by step is 0 m to 1 m, once every 0.01 m; and R.sub.M is the bending moment ratio equated to an actual bending moment divided by the limit bending moment.

4. The full probability-based seismic risk analysis method for the tunnel under the fault dislocation according to claim 1, wherein in step 7, the specified period is a design period.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is an example magnitude and frequency relation diagram of a full probability-based seismic risk analysis method for a tunnel under fault dislocation according to the present invention;

(2) FIG. 2 is a schematic diagram of an example hazard curve of the full probability-based seismic risk analysis method for a tunnel under fault dislocation according to the present invention;

(3) FIG. 3 is an example finite element model diagram of the full probability-based seismic risk analysis method for a tunnel under fault dislocation according to the present invention;

(4) FIG. 4 is an example dislocation and bending moment ratio diagram of the full probability-based seismic risk analysis method for a tunnel under fault dislocation according to the present invention; and

(5) FIG. 5 is a schematic diagram of an example vulnerability curve of serious structure damage in the full probability-based seismic risk analysis method for a tunnel under fault dislocation according to the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(6) The present invention is further described below, but the present invention is not limited thereto.

Example

(7) A tunnel that passes through a strike-slip fault having a width of 31 km and a length of 50 km is known. Seismicity information of the fault: the upper limit of the earthquake magnitude is 7, the lower limit is 5, and the b value is 0.83. The tunnel has a lining thickness of 0.6 m and a burial depth of 20 m, and the angle between the tunnel strike and the fault strike is 90°; the tunnel has a weight of 25 kN*m.sup.−3, an elastic modulus of 33.5 GPa, and a Poisson's ratio of 0.2. Soil layers have a weight of 20 kN*m.sup.−3, an elastic modulus of 0.55 GPa, a Poisson's ratio of 0.3, and a cohesion of 0.25 MPa. The fault soil layer at an internal friction angle 22° has a weight of 19 kN*m.sup.−3, an elastic modulus of 0.35 GPa, a Poisson's ratio of 0.35, a cohesion of 0.1 MPa, and an internal friction angle of 20°.

(8) Calculate:

(9) Step 1): the annual average occurrence rate V.sub.5 of earthquakes is 0.56, and the obtained relationship between magnitude and frequency is as shown in FIG. 1;

(10) Step 2): fault dislocation prediction equation: lgD=1.0267*M−7.3973;

(11) A probabilistic cut-off model is

(12) $f\left(m\right)=\{\begin{array}{cc}\frac{\beta \exp \left[-\beta \left(m_u-m_0\right)\right]}{1-\exp \left[-\beta \left(m_u-m_0\right)\right]}& \left(m_0\le m\le m_u\right)\\ 0& \left(\mathrm{other}\right)\end{array}$

(13) Parameters are brought into formula (1) to obtain a risk curve, as shown in FIG. 2;

(14) Step 3): establish an ABAQUS finite element model, as shown in FIG. 3;

(15) Step 4): find the relationship between the dislocation and the bending moment ratio, as shown in FIG. 4;

(16) Step 5): obtain a vulnerability curve, as shown in FIG. 5, and obtain vulnerability curve information, as shown in Table 1;

(17) TABLE-US-00001 TABLE 1 Mean and variance table of vulnerability curve Damage level Mean Variance Serious damage 2,9883 0,13075

(18) Step 6): according to the information obtained in steps 2-5, using formula (3), calculate the annual exceeding rate of serious damage to the tunnel crossing the fault: λ.sub.ds=0.005;

(19) Step 7): based on formula (4), the probability of serious damage to the tunnel crossing the fault is P=39.4% when the specified period is 100 years.

(20) It should be noted that those of ordinary skill in the art may further make variations and improvements without departing from the conception of the present invention, and the variations and improvements all fall within the protection scope of the present invention.