Experimental study on the influence of seismic subsidence of loess under bidirectional loading modes

Gaofeng Che ,Ping Wang,＊ ,Qian Wang ,Xiaowu Pu ,Jinlian Ma ,Shaofeng Chai

a Key Laboratory of Loess Earthquake Engineering,CEA &Gansu Province,Lanzhou,730000,China

b Geotechnical Disaster Prevention Engineering Technology Research Center,Lanzhou,730000,China

Keywords:Loess Radial stress Axial stress Coefficient of seismic subsidence

ABSTRACT Water content,dry density,void ratio,depth of soil layer,and seismic loading may all exert influence on the seismic subsidence of loess.Many scholars have carried out seismic subsidence tests of loess to simulate the stress on soil using unidirectional (axial) vibration instead of bidirectional vibration.We conduct seismic subsidence tests of loess using two different dynamic stress loading methods,unidirectional and bidirectional dynamic stress.In addition,the effects of different dynamic stress loading modes on the development of seismic subsidence of loess are compared for a case-study in northwestern China.The results show that(1)the increasing ratio of radial stress to axial stress has exerted significant influence on the seismic subsidence coefficient of loess under the loading mode of bidirectional dynamic stress (2) there is a critical ratio of radial stress to axial stress for seismic subsidence of loess,ranging from 0.6 to 0.8;when the ratio of radial load to axial load is greater than the critical value,the effect of bidirectional load on the development of seismic subsidence is more remarkable(3)when the ratio of radial load to axial load is smaller,the seismic subsidence of loess calculated by the existing unidirectional stress loading method is safe for engineering projects.However,if the value exceeds the safety ratio range it is dangerous to conduct safety evaluations using the seismic loess subsidence.The prediction value of seismic subsidence at engineering sites directly affects the later foundation treatment and the safety of the overlying structures.The seismic subsidence calculation and evaluation method in this study may provide a scientific basis for safety evaluations of loess sites in northwestern China.

1.Introduction

Northwestern China accommodates some of the most typical loess areas and has an average seismic intensity greater than VII degree.The upper part of the loess layer is covered by a special structure characterized by large pores and weak cementation.Prominent post-earthquake subsidences are often observed in the loess areas;thus,it is important to analyze and predict the seismic subsidence scientifically and reasonably.Accurate predication may benefit in the following aspects:reduce the influence of seismic subsidence on the stability of pile foundations and buildings,meet the ASEISMIC design requirements of engineering foundations,respond to scientific and technological research on seismic safety evaluation,promote the application of advanced scientific and technological achievements to improve seismic safety evaluation,and carry out seismic safety evaluation of engineering sites.

Factors such as water content,dry density,depth of soil layer,and seismic loading can all affect the seismic subsidence of loess (Li et al.,2007;Wang et al.,2011,2020;Xu et al.,2010).Seismic waves are divided into shear,surface,and longitudinal waves.Following an earthquake,the surrounding soil is subjected to both tension and compression and shear dynamic loads.For a long time,laboratory and field experiments of seismic subsidence of loess have been carried out(Wang et al.,2010),and corresponding prevention measures have been proposed(Qiu et al.,2018).In laboratory tests,the most frequently used method to simulate soil stress is unidirectional(axial)vibration instead of bidirectional vibration proposed by Seed(Seed and Leek,1966;Seed and Idriss,1971;Seed and Peacock,1971),providing an approach to study the characteristics of seismic subsidence of loess.However,this loading method cannot effectively reflect the actual soil stress.A series of studies on the dynamic characteristics of soil under bidirectional cyclic loading have been carried out in China.For instance,Cai et al.(2008a),Cai et al.(2008b),Wang et al.(2007),and Wang et al.(2009) investigate the dynamic deformation characteristics of saturated soft clay under bidirectional cyclic loading.The results show that the strength of soil decreases quickly and the soil sample is destroyed in a small number of cycles compared with the results obtained under unidirectional cyclic loading under the influence of the cyclic stress ratio,vibration frequency,initial shear stress,and the radial cyclic stress ratio.Wang et al.(2010)probe the deformation characteristics of saturated soft clay by changing the ratio of axial load to radial load.The minimum limit cyclic strength can be obtained by using unidirectional cyclic loading instead of bidirectional cyclic loading.Huang et al.(2011) report the applicable conditions of a unidirectional triaxial test for saturated sand instead of a cyclic shear stress test for bidirectional vibration simulation.Zhang and Luo (2015) analyze the dynamic modulus and dynamic shear deformation characteristics of loess under the coupling of bidirectional cyclic loading.Furthermore,their results suggest that the initial cyclic deviator stress and the amplitude of radial dynamic loading have exerted obvious effects on the dynamic shear modulus.

The influence of radial dynamic load and phase difference on the development of dynamic shear modulus of loess is given.Compared with bidirectional cyclic loading,substantial research results show that the development rate of dynamic residual deformation and dynamic shear are obviously not equivalent to the unidirectional cyclic loading method in simulating seismic action.Although some studies have been carried out on the dynamic properties of soils under bidirectional cyclic loading,reports on the development of seismic subsidence of loess under bidirectional cyclic loading are rare.It remains unknown whether the development trend of seismic subsidence and the prediction value of seismic subsidence of loess are the same as the existing test results and prediction value.

The prediction value of earthquake subsidence of an engineering site directly affects the later foundation treatment and the safety of the overlying structures.To evaluate the safety of a loess site,a WF-12440 dynamic triaxial-torsional shear test instrument is used in this study.The seismic subsidence tests of loess are conducted under two different dynamic stress loading modes,unidirectional cyclic loading and bidirectional cyclic loading.The effects of different dynamic stress loading modes on the development characteristics of loess seismic subsidence are explored in detail.

2.Methodology

2.1.Test sample

A WF-12440 dynamic triaxial-hollow cylinder torsional shear test system produced by the WF company is used in this study.All the soil samples are taken from a brick factory in Qianshi,Beiyuan Township,Linxia County,Gansu Province.The soil layer is uniform with a depth of 13 m and belongs to Q3loess,and the color is yellow brown.Considering the influence of individual differences in soil structure on the test results,to ensure the homogeneity of the samples,physical parameters such as the actual water content and density of the undisturbed loess are taken as the reference in the experiment.The basic physical properties of the soil sample are shown in Table 1.

The grain size distribution curve of the soil sample is shown in Fig.1.

2.2.Test methods and conditions

The size of the test sample is Φ 50 mm × 100 mm.To simulate the residual deformation of soil after an earthquake,we analyze soil properties and overburden load,and select KC=1.69 as the consolidation ratio.The samples are consolidated under bias pressure,σ1c=200 kPa,σ3c=118 kPa.After the samples are consolidated,the seismic subsidence tests under unidirectional cyclic loading and bidirectional cyclic loading are carried out.The loading wave belongs to equivalent sine wave with a 1 Hz frequency,and the ratio of radial dynamic stress to axial dynamic stressis 0,0.4,0.6,0.8,and 1.0 respectively.The experimental conditions are shown in Table 2.

Table 1 Basic physical properties of the soil sample.

Table 2 Experimental conditions.

2.3.Stress analysis

The unidirectional cyclic load is adopted to simulate an earthquake activity.Under the confining pressure and the axial load,the shear deformation of the sample is caused by the shear stress on the 45°plane.A soil stress diagram is shown in Fig.2(a).When the axial and radial cyclic loads are applied to simulate the earthquake activity,both shear stress and normal stress on the 45°shear plane of the sample are observed under the bidirectional loads.The stress diagram of the sample under this loading condition is shown in Fig.2(b).

3.Results

3.1.Influence of different dynamic stress loading methods on seismic subsidence coefficient of loess

Fig.1.Grain size distribution curve of the soil sample.

The coefficient of seismic subsidence obtained from the seismic subsidence test is expressed by residual strain and can be obtained under different dynamic stress loading modes.The curve of seismic settlement coefficient of soil with the change of residual strain (εp) and dynamic stress(σd) is shown in Fig.3.

From Fig.3 it can be seen that with the increase of axial load,the seismic subsidence coefficient of loess shows an increasing trend under the two different dynamic stress loading modes.However,the magnitude of the seismic subsidence coefficient of loess under different radial load and axial load stress ratios is different.

As shown in Fig.3(a),when the ratio of radial load to axial load is 0.4,the effect of radial load on seismic settlement coefficient of loess is not obvious,and the seismic settlement coefficient of loess under unidirectional load is larger than that under bidirectional load.With the ratio of radial load to axial load increasing to 0.6 in Fig.3(b),the axial load is less than 90 kPa and the coefficient of seismic subsidence of loess is larger under unidirectional load.When the axial load exceeds 90 kPa,the seismic subsidence coefficient under bidirectional load is greater than that under unidirectional load.Increasing the ratio of radial load to axial load to 0.8 in Fig.3(c),the effect of bidirectional load on the seismic settlement coefficient of loess is obvious and the critical value of the seismic subsidence coefficient under unidirectional load is larger than that under bidirectional load,which decreases from 90 kPa in Fig.3(b)to 50 kPa.When the axial load exceeds 50 kPa,the seismic subsidence coefficient under bidirectional load is larger than that under unidirectional load.When the ratio of radial load to axial load increases to 1.0 in Fig.3(d),the effect of the bidirectional load on the seismic settlement coefficient of loess is significant;as the axial load increases,the seismic settlement coefficient of loess becomes extremely larger than that of unidirectional load.

The test results show that the development trend of the seismic subsidence coefficient of loess is directly influenced by different dynamic stress loading modes,and the effect of the bidirectional loading mode on the seismic subsidence coefficient of loess cannot be ignored.With the increase of the ratio of radial load to axial load,the effect of radial load on the seismic settlement coefficient of loess is strengthened.Thus,the bidirectional load mode has exerted a significant effect on the seismic subsidence coefficient of loess.

3.2.Prediction and evaluation of seismic subsidence of loess under different dynamic stress loading modes

The seismic subsidence of loess is predicted with a depth of 20 m,and the seismic subsidence of loess under different dynamic stress loading modes is shown in Table 3.

It can be seen from Table 3 that under different seismic intensities,when the stress ratio of radial load to axial load is greater than 0.8,the maximum seismic subsidence of loess is greater than that of the existing unidirectional load.Especially when the seismic intensity of the loess site reaches degree IX,the difference in seismic subsidence of loess under bidirectional and unidirectional loads is extremely large,and the predicted seismic subsidence is 1.4 times of that caused by unidirectional load.

According to Table 3,the seismic subsidence curve of loess is shown in Fig.4.

Table 3 Prediction of seismic subsidence of loess under different seismic intensities.

Fig.4 suggests that the seismic subsidence of loess increases with the increase of seismic acceleration.When the ratio of radial load to axial load is less than 0.8,the seismic subsidence of loess calculated by the existing loading method of unidirectional load is on the higher.In this case,existing prediction methods of seismic subsidence can be used in engineering.As the ratio of radial load to axial load increases,the seismic subsidence of loess increases sharply with the increase of seismic acceleration,and the amount of seismic subsidence calculated by this method is larger than that obtained by existing test methods.Specifically when the acceleration is large,the difference between the seismic subsidence of the loess and that of the unidirectional loading method becomes distinctly different.The predicted value of the seismic subsidence of loess obtained from the existing loading method is selected to guide the site safety evaluation of the actual project.,and the predicted value is relatively small compared with the actual value.

The test results show a critical ratio of radial load to axial load in the seismic subsidence of loess.When the ratio is greater than the critical value,the seismic subsidence of loess calculated under the existing unidirectional loading mode is obviously small,and the prediction of seismic subsidence of loess under different intensities is not accurate,possibly posing great threat to the engineering safety.The range of the critical ratio of the radial load to the axial load is between 0.6 and 0.8 under the existing evaluation system.Previous investigations indicate that there exists a critical cyclic stress ratio and a radial cyclic stress ratio for Hangzhou saturated soft clay based on the dynamic deformation characteristics of saturated soft clay under bidirectional cyclic loading (Cai et al.,2008a,2008b;Wang et al.,2007;Wang and Chen,2010).When the ratio of radial load to axial load exceeds the corresponding critical ratio,the bidirectional cyclic load accelerates the deformation of the soil.In addition,Wang et al.(2010)found a critical ratio of radial load to axial load in saturated soft clay;when the ratio is less than this value,the results of unidirectional cyclic loading can replace those of bidirectional cyclic loading.Relevant studies show that there exists a critical ratio of soil mass under bidirectional cyclic loading,and the unidirectional cyclic load cannot provide a precise simulation which can reflect true force condition of soil.The ratio of critical radial load to axial load given by Wang et al.(2010)is 0.5,similar to the results in this study but still with a certain numerical difference.The slight difference is possibly due to the combined effect of a list of factors.For example,the structure of loess differs from that of soft clay,the strength of saturated soil is lower than that of unsaturated soil,and the critical value of deformation and failure is smaller.

Fig.2.Soil stress under different dynamic loads.

Fig.3.Seismic subsidence coefficient curves of loess under different dynamic stress loading modes(a)dynamic stress loading σdh/σdv=0.0 and 0.4;(b)dynamic stress loading σdh/σdv=0.0 and 0.6;(c) dynamic stress loading σdh/σdv=0.0 and 0.8;(d) dynamic stress loading σdh/σdv=0.0 and 1.0.

Fig.4.Seismic subsidence curves of loess under different loading modes.

The influence of different dynamic stress loading modes on the development of seismic subsidence of loess is due to the fact that the shear stress and normal stress on the 45°plane of the sample are tiny when the axial load is small.Whether the load is unidirectional or bidirectional,the influence of the dynamic stress on the development of loess seismic subsidence is not significant.As the axial load increases,when the ratio of radial load to axial load is small and in a certain range,the normal stress of the sample under bidirectional load is smaller,and the seismic subsidence of loess under unidirectional load is larger.This is because the shear stress of the sample under unidirectional load is larger than that under bidirectional load.As the ratio of radial load to axial load increases,the normal stress of the sample under the bidirectional load increases substantially and the effect of bidirectional loading on the seismic subsidence of loess becomes much greater than that of unidirectional loading.

4.Discussion and conclusions

Loess seismic subsidence tests are conducted under two different dynamic stress loading modes:unidirectional cyclic loading and bidirectional cyclic loading.Furthermore,the influence of different dynamic stress loading methods on the development of seismic subsidence of loess is compared.

(1) As the ratio of radial load to axial load increases,the effect of radial load on the seismic subsidence coefficient of loess is strengthened,and the effect of the bidirectional loading mode on the seismic subsidence coefficient of loess becomes obvious and cannot be ignored.

(2) There is a critical ratio of radial load to axial load in seismic subsidence of loess which ranges from 0.6 to 0.8;when the ratio exceeds the critical ratio,the effect of bidirectional cyclic load on the development of seismic subsidence of loess becomes more prominent.

(3) When the ratio of radial load to axial load is small,the seismic subsidence of loess calculated by the existing loading method of unidirectional load is safe for engineering projects.In contrast.when the ratio exceeds a certain value,the prediction value of seismic subsidence of loess derived from the existing load method is selected to guide the site safety evaluation of actual projects,and the prediction value is smaller than the actual value.

Numerous factors may affect the development of the post-earthquake loess subsidence,and the influence of different ratios of radial load to axial load on the development of subsidence is a typical one.In this study,the development of seismic subsidence of loess under different dynamic stress loading modes with the same water content and density has been studied.For future works,it is necessary to explore the characteristics of seismic subsidence development of loess under the combined effect of water content,dry density,soil depth,and dynamic stress.Such comprehensive studies could enhance the calculation accuracy and the evaluation of seismic subsidence of loess,thereby providing a robust scientific basis for the safety evaluation of loess sites.

Acknowledgement

The project is sponsored by the open foundation for Key Laboratory of Loess Seismic Engineering of China Earthquake Administration (KLLEE-17-001),Basic Scientific Research Operating Expenses of the China Earthquake Administration (2018IESLZ08),Spark Program of China Earthquake Administration (XH20058Y),Key Research and Development Program of Gansu Province (18YF1FA101),and the National Natural Science Foundation of China(U1939209,51578518&51778590).