Analysis of dynamic accumulative damage about the lining structure of high speed railway’s tunnel based on ultrasonic testing technology

Based on the similar material model test of full tunnel, the theory of elastic wave propagation and the testing technology of intelligent ultrasonic wave had been used to research the dynamic accumulative damage characteristics of tunnel’s lining structure under the dynamic loads of high speed train. For the more, the dynamic damage variable of lining structure of high speed railway’s tunnel was obtained. The results shown that the dynamic cumulative damage of lining structure increases nonlinearly with the times of cumulative vibration, the weakest part of dynamic cumulative damage is the arch foot of tunnel. Much more attention should be paid to the design and operation management of high speed railway’s tunnel.

In which, E is initial elastic modulus of material, is elastic modulus of material after damage,  is continuity of material, D is damage variable of material.
According to the theory of elastic mechanics, when the concrete is undamaged, the velocity of longitudinal wave, can be shown as following: (2) In which,  is Poisson ratio,  is specific gravity of material, and the meanings of other parameters are as shown before.
It is assumed that the elastic modulus of concrete reduce to the value of , when it has been damaged, the velocity of longitudinal wave can be shown as following: Simultaneous (2) and formula (3), the relationship between p  and p  can be obtained as following: If the formula (4) has been substituted into the formula (1) , according to the assumption of equivalent strain, the relationship among the damage variable and continuity can be obtained as followings as: The value of damage variable in formula (5) can be obtained by measuring the velocity of longitudinal wave of concrete.

Test of dynamic cumulative damage for tunnel's lining structure
In order to study the dynamic accumulative damage characteristics of the lining structure of high-speed railway's tunnel under the vibration load of train. According to the design size of a tunnel on the high speed railway from Wuhan to Guangzhou, the scaled model of tunnel was made by using the particle concrete, the maximum height of model is 1.34m, the maximum width of model is 1.20m, and the lining thickness of model is 0.10m (as shown in Fig.1). By using the hydraulic servo loading system of MTS, the test of dynamic damage was carried out under the vibration loads of high speed train, in the meantime, the intelligent ultrasonic testing instrument was used to measure the velocity of ultrasonic wave for feature points of model SC1-SC4 (as shown in Fig. 2).

4.Analysis of dynamic cumulative damage
In the process of dynamic loading test, the ultrasonic velocity of feature points (SC1-SC4) ,which on the inverted arch, foot of arch, side wall and vault of tunnel are measured synchronously, and the attenuation law of ultrasonic wave velocity of feature points with the vibration times is shown in Fig.3. Based on the correlation between the changing rate of ultrasonic velocity and the damage variable of material, it can be seen that the accumulative damage of lining structure on the inverted arch, foot of arch, side wall and vault is similar. However, the cumulative damage of the inverted arch and the foot of arch is larger than that of the side wall and vault. This results are consistent with the results of theoretical analysis and engineering practice.  Fig.3 Variation trend of ultrasonic wave velocity According to the ultrasonic test, the initial velocity of ultrasonic wave is 4.12km/s. Based on the testing data of ultrasonic wave for the lining structure of tunnel, the damage variable of feature points can be calculated by formula (5) and it has been shown in Tab.1. According to the calculated values of the dynamic damage variable of feature points under different vibration times, by using the fitting method of exponential function, the dynamic accumulation damage law of the lining structure can be obtained as shown in Fig. 4

5.Conclusions
Based on the model test of tunnel with full section and the detection method of intelligent ultrasonic wave, the dynamic cumulative damage characteristics of concrete lining structure can be researched effectively, under the vibration loads of high speed train. Dynamic cumulative damage of the lining structure of high-speed railway's tunnel increases nonlinearly with the times of cumulative vibration of high-speed train. The degree of dynamic damage in different parts of the lining structure is not the same, and the foot of arch is the weakest part of tunnel.
If only consider the effect of vibration loads in operation period of high speed railway, the damage failure of tunnel's lining structure will not be occurred. If there are cracks of initial damage and coupled with the action of groundwater pressure, the dynamic damage could not be ignored ,which induced by the vibration loads of high speed train.