2. Key Laboratory of High-Speed Railway Engineering, Ministry of Education, Chengdu 610031, China;
3. China Railway Eryuan Engineering Group Co. Ltd., Chengdu 610031, China
Reinforced soil retaining walls have the excellent characteristics of economy, aesthetics, and seismic performance as compared to traditional gravity structures. Among them, the latter characteristic has been verified by earthquakes, such as the Hyogo-ken Nambu earthquake. Tatsuoka F. et al., (1996) found the Tanata wall (a geosynthetic-reinforce soil retaining wall) at the epicenter had displacements of only 10cm, and the gravity retaining walls near it were destroyed. Ling H.I. et al., (2001) found that reinforced soil retaining walls suffered mostly local damage and many non-reinforced retaining walls collapsed in the Chichi earthquake.
To study the mechanical and deformation characteristics of reinforced soil retaining walls, researchers have carried out a lot of studies: Jiang Yan et al. (2016) found that the secondary reinforcements could effectively reduce the pull forces in primary geogrid layers and the facing displacement. Using the numerical software PLAXIS 2D, Sukmak K. et al., (2016) found that the soil-structure interaction could affect the horizontal deformation sensitively. Huang C.C. et al., (2006) carried out a calculation using the two-wedge method and Newmark sliding method and compared the value with that measured in the Chichi earthquake; Ling H.I.et al., (2010) used numerical simulation method to study the dynamic response of reinforced earth retaining walls under seismic loadings. Latha G.M. et al., (2008) carried out several shaking table tests to study the effect of backfill relative density on reinforced soil retaining walls.
To guide the design of reinforced soil retaining walls, many countries have published corresponding seismic design specifications, such as the Code for Seismic Design of Railway Engineering (CSDRE) (The National Standards Compilation Group of the People's Republic of China, 2006) in China and the FHWA Code. To quantify the difference between these two design codes, the author carried out a calculation to analyze the differences in inertial force, dynamic earth pressure, and safety factors.
1 DESIGN CODES 1.1 Code for Seismic Design of Railway EngineeringThere is no specific design instruction for reinforced soil retaining walls in the CSDRE. Combined with the Code for design on retaining structures of railway subgrade in China, seismic design of reinforced soil retaining walls consists of two parts: internal stability calculation and external stability calculation. When evaluating the external stability, the entire reinforced zone is treated as a gravity wall. The loads include the inertial force of reinforced zone P, dynamic earth pressure F, and the gravity of reinforced zone W, etc. The dynamic earth pressure F is calculated using the Mononobe-Okabe method and P is calculated using the following equation:
$ P = \eta {A_g}\lambda m $ | (1) |
where, η is the correction factor for horizontal earthquakes, A_{g} is the peak ground acceleration, λ is the amplification factor, and m is the wall mass.
The influence of the inertial force P_{1} of the active zone needs to be taken into account in the dynamic pullout stability calculation of the reinforcements.
1.2 FHWAExternal stability analysis and internal stability analysis should also be carried out in the FHWA Code. The inertia force P used in the external calculation is expressed as:
$ P = 0.5{k_{av}}W $ | (2) |
where k_{av} is the average peak ground acceleration. In addition, the height of the action point of the earth's pressure F is h/2. For internal stability, the FHWA Code divides reinforced zone into active zone and resistant zone using Rankine rupture surfaces for extensible reinforcement as shown in Fig. 3.
Calculations were carried out for a reinforced soil retaining wall with wall height h=6.0m, facing width b=0.3m, reinforcement length l=4.2m, vertical spacing of the reinforcement S_{v}=0.6m, bulk unit weight of the backfill γ_{s}=18kN/m^{3}, and friction angle φ=35°.
2.1 Comparison of External AnalysisFig. 4 shows the relationship of k_{h} and P calculated from the CSDRS and the FHWA Code. The inertial force P calculated from the above codes increases linearly with the horizontal acceleration coefficient, and the values calculated from the CSDRS are larger than those calculated from the FHWA Code. The difference between these two methods is mainly caused by the acceleration values used in calculations. For example, the CSDRS corrects the acceleration by η=0.25. However, the inertia force P is reduced by a half in the FHWA Code.
Fig. 5 shows the relationship of k_{h} and F calculated by the CSDRS and the FHWA Code. As shown in Fig. 5, F calculated by the former is much smaller than those calculated by the latter and the elevation of the action point of F obtained according to the former is also higher. The above results are still caused by the small acceleration used in the CSDRS. Besides, as the elevation of the action point is higher, the wall's overturning safety factor is usually smaller calculated from the FHWA Code.
Since the inertial force and the earth pressure calculated from the FHWA Code is greater than those by the CSDRS, so the former method leads to a lower safety factor, and the difference between them is more obvious with the horizontal acceleration coefficient as shown in Fig. 6.
As shown in Fig. 7, although the shape of the active zone is different according to the CSDRE and the FHWA Code, the area values are not much different, and the values calculated from the former is slightly smaller, leading to the inertia force P_{1} of the active zone calculated by the CSDRE is also smaller. As shown in Fig. 8, since P_{1} calculated from the FHWA Code is larger, the reinforcement strain, T is larger.
To analyze the similarities and differences in the seismic design of reinforced earth retaining walls by the FHWA Code and the CSDRE, an example was used for analysis and the following conclusions are obtained:
(1) The inertial force, earth pressure and tensile force calculated from the CSDRE are less than those from the FHWA Code.
(2) Although the M-O method is recommended to calculate the dynamic earth pressure, the FHWA Code recommends a higher earth pressure action point than the CSDRE.
(3) The safety factor calculated from the FHWA Code is smaller than that from the CSDRE.
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