Centrifuge modeling of dynamic response of high fill slope by using generalized scaling law

Highlights

• Generalized scaling law is re-organized to improve the similitude of dynamic strain.

• A slope with prototype height of 100 m is studied by method of “modeling of models”.

• Seismic amplification in slope results from soil nonlinearity and non-uniform strata.

• High fill slopes with non-uniform strata are more vulnerable to earthquake motions.

Abstract

The development of physical modeling for mega engineering prototypes requires sophisticated use of the capability of current centrifuge facilities. In this study, centrifuge model tests were performed to investigate the dynamic response of high fill slope by using generalized scaling law in an improved way. Firstly the two-stage generalized scaling law was partly re-organized by considering the separate similitude of dynamic strain for the virtual 1 g field, to solve the inherent problem of the scaling of soil strain when the derived prototype strain exceeded some important thresholds. Then a series of centrifuge model tests were conducted under different centrifugal accelerations to model a high fill slope with a prototype height of 100 m by the approach of “modeling of models”. Dynamic responses under sine waves with different amplitudes were monitored and the re-organized generalized scaling law was validated for nonlinear dynamic response with shear strain less than 1%. It was observed that site amplification of high fill slope was affected by both soil nonlinearity and soil strata non-uniformity, where soil nonlinearity led to smaller acceleration amplification under stronger excitation and soil strata non-uniformity contributed to the acceleration de-amplification and larger displacement amplification at the weak sublayer. The large dynamic displacement near the slope surface consequently contributes to the development of lateral cracks after strong shaking. Seismic response under earthquake motions revealed that high fill slope with inclined non-uniform strata was characterized by multiple vibration modes and lower fundamental frequency, which was more vulnerable to earthquake motions with abundant frequency components. This study provides a more physically meaningful use of the similitude of dynamic stress-strain relation in centrifuge modeling for large-scale geotechnical problems under dynamic loadings.

Introduction

Airports built upon high fill slopes in highly seismic active regions are typical mega engineering projects in challenging geological environments. As shown in Fig. 1, there is a plan to construct many airports on high fill slopes in mountainous areas of China by 2020 (Cao et al., 2011; Yao et al., 2015; Zhang et al., 2017a, Zhang et al., 2017b). Field investigations indicate that these airports are built on relatively high (50 m–100 m) slopes under complicated geological conditions (see Table 1). As the bedrock of the engineering site in mountains or hills is usually covered by a layer of residual soils or heavily weathered rocks, and then rockfill materials are filled upon it, which typically forms a non-uniform “bedrock-weak sublayer-rockfill” strata for the airport. These airports frequently suffer from earthquake attacks. For example, the Jiuzhai-huanglong airport performed well during the May 12, 2008 Wenchuan earthquake (M_w = 7.9) (Xu et al., 2004), while the site amplification of ground motion in high fill slope of Kangding Airport led to the cracks and roofs falling at the terminal buildings during the 2014 Kangding earthquake (M_w = 5.9) (see Fig. 2(a)) (People's Daily Online, 2014). The worse case is, massive landslide occurred on the high fill slope of Panzhihua airport in October 3, 2009 under the coupled influences of the August 30, 2008 Panzhihua earthquake (M_w = 5.7) and the subsequent heavy rainfall (see Fig. 2(b)) (Wang et al., 2013). The seismic response and stability of high fill slopes become one of the major concerns in engineering practices (e.g., Chen et al., 2014; Lin et al., 2015). Although some existing codes consider the importance of the influences of the filling height and the existence of weak sub-layer on the seismic safety of high fill slopes, they seldom provides detailed guidelines either qualitatively or quantitatively (e.g., Comite European de Normalization (CEN), 2004; Federal Emergency Management Agency (FEMA), 2005; New Zealand Society on Large Dams (NZSOLD), 2015; U.S. Department of the Interior Bureau of Reclamation (USBR), 2015), which makes the seismic design of high fill slopes more challenging. The seismic response of high fill slopes under strong earthquakes becomes an urgent research need to play as the basis for developing these codes and guidelines.

From geotechnical research to engineering practice, physical modeling is widely adopted to study the fundamental mechanics of ground and geotechnical structures according to the conventional centrifuge scaling law (e.g., Garnier et al., 2007), and to provide benchmark data for verification of numerical analysis (Tang et al., 2014; Zhou et al., 2017; Zhang et al., 2018). In some cases when the scaling law could be satisfied, the prototype behavior could be directly modeled (e.g., Deng et al., 2011; Hung et al., 2018).

Usually, the length scaling factor (ratio between prototype to physical model) in dynamic centrifuge modeling ranges from 10 to 100, and the dimension of modeled prototype is less than 80 m (e.g., Rayamajhi et al., 2015). Since the size of physical model is restricted by the capacity of experimental facilities, it is very difficult to directly model mega geotechnical engineering problems with the length scaling factor ranging from 100 to 1000 (i.e., at the level of hundreds of meters at prototype). Therefore the sophisticated use of the currently available facilities with advanced scaling law to develop new methods of physical modeling seems more promising with regard to the large scale prototype problems (Iai et al., 2005; Tobita et al., 2011, 2012). Iai et al. (2005) developed the generalized scaling law for dynamic centrifuge tests that allows available facilities to model dynamic response of much larger prototypes. The generalized scaling law contains two stages: at the first stage, a prototype is scaled down into a virtual model based on the scaling relations in a 1 g field (Iai, 1989); at the second stage, the virtual model is further scaled down to a physical model in a Ng field by using conventional centrifuge scaling law. Thus a large length scaling factor could be achieved. Recently Park and Kim (2017) applied the generalized scaling law to assess the seismic safety of cored rockfill dams with the height over 100 m. Nevertheless, in view of the fact that scaling factor of strain in generalized scaling law is always lager than unity, the stress-strain behavior of the prototype problem might be different from that observed in the model if the derived prototype strain exceeds some important thresholds (e.g., the threshold strain about 0.01% that represents the change in soil behavior from elastic to plastic (Chang et al., 2015; Dobry and Abdoun, 2015) or the threshold strain about 5–10% at shear failure).

This study firstly re-organized the two-staged generalized scaling law by designating the similitude of dynamic strain to unity from the centrifuge model to the virtual 1 g field, to partly solve the abovementioned inherent problem of the scaling of soil strain. Then a series of centrifuge model tests were performed to model a high fill slope with the prototype height of 100 m. The applicability of the proposed partly re-organized generalized scaling law was investigated under different centrifugal accelerations by the approach of “modeling of models” (Schofield, 1980). A series of sine waves and earthquake motions with different amplitudes were applied to the model. The seismic response of high fill slope with complex geotechnical structure was analyzed in both time and frequency domains and some interesting findings were presented.