STUDY ON TIME-EFFECT OF DEFORMATION AND ITS APPLICATION IN FOUNDATION CONDITION OF HIGH-SPEED RAILWAY EMBANKMENT

Yong XIONG1，Qiang LUO1，2，Liang ZHANG1，2，Liangwei JIANG1，2，Jiangjiang ZHU1

1School of Civil Engineering，Southwest Jiaotong University，Chengdu 610031

2MOE Key Laboratory of High-speed Railway Engineering，Southwest Jiaotong University，Chengdu 610031

Abstract：Foundation condition of high-speed railway embankment is the key technology to clear the necessity of deep treatment for the foundation.Triaxial rheological tests of ground soil with low compressibility are carried out，and the samples are instating of optimal water rate and 100％compaction degree.Strain-time history curves under different deviatoric stresses are got，and then the time-effect of strain of samples is analyzed，the relationship between foundation condition and shear strength parameters is emphatically discussed.Research indicates that：The ratio between deviatoric stress threshold of strain time-effect and the ultimate deviatoric stress is 10％，for soil with low compressibility.The envelope equation of stress circles that are in time-effect critical state is derived，according to geometric relationships of stress circles in time-effect critical state and stress circles in limit equilibrium state.Combining the actual stress state of foundation soil at different depths under embankment，foundation condition of high-speed railway embankment is calculated at the standard that the thickness of the soil layer which has obvious time-effect deformation is not more than 5 m.The research results provide guidance for the selection of treatment for ground with low compressibility.

Keywords：high-speed railway，time-effect，deviatoric stress threshold，foundation condition

Email：313960770@qq.com

1　Introduction

High-speed railway has been large-scale construction in China，how to make sure the high-speed railway operate safety in a long term has become a prominent problem at the present stage[1]，finding out the evolution behavior and law of dynamic performance of basic structure in high-speed railway system during the long-term operation is the key to solving this problem.Particularly for subgrade，the evolution behavior foundation settlement under static load plays a decisive role on the development law of subgrade’s post settlement.So，it’s very necessary to study the load threshold of time-effect which determines whether the deformation of foundation has time-effect.

Time-effect deformation of foundation soil under static load belongs to the category of creep deformation.Kie[2]proposed stress threshold of the blocked deformation and creep deformation of soil；Vyalov’s research[3]shows that soil has a creep limit，when the load is less than the creep limit，and creep will not happen；Sun[4]carried a serious of creep experiment using Shanghai soft soil，and proposed a concept that when the load is less than a certain value，soil deformation has no time-effect；Fan[5]got the liner relationship between stress threshold of creep limit and confining pressure of soft rock by triaxial rheological tests；Vucetic[6]pointed out that almost no obvious plastic deformation occurs in the soil when actual cyclic shear strain of soil is less than critical cyclic shear strain；Singh and Mitchell[7]are proposed to use the parameter m（m=∆logε′/∆logt）to reflect time effect of soil creep，and got a conclusion that the value of m for normal consolidated clay are between 0.7to 1.2 at 30％-90％ of ultimate strength.Most of above researches can’t quantitatively distinguish time-effect of deformation，Xiong[8]proposed“power criterion” to describe time effect of deformation，and quantitatively distinguished whether soil deformation has time effect.

In this paper，triaxial rheological tests will be carried out ，deviatoric stress threshold of time-effect for ground soil with low compressibility will be got by adopting “power criterion”，and the envelope equation，related to shear strength parameters of ground soil，of stress circles in time-effect critical state can be derived.So that，after calculating the stress state of ground soil at different depth，the thickness of ground soil that with time-effect can be distinguished.When the thickness is no more than 5 m，deep treatment for the foundation is not necessary.Thus，foundation condition under different high embankments will be obtained.

2　Power Criterions

According to the concept of creep limit，long-term strength and relative instantaneous strength in archeology of soil mechanics，Xiong[8]divides creep into four categories of fast convergence，slow convergence，slow divergence and rapidly divergence，and propose “power criterion”，as listed in the Table1，to distinguish the four categories，taking the power exponent P in Equation（1）as the core parameter.

v（t）∞t−P　　（1）

3　Triaxial Rheological Tests

Applying GDS system，triaxial rheological tests（CD）are carried out；the consolidation time is 24 h.The deviatoric stresses are 47 kPa，95 kPa，190 kPa，285 kPa and 570 kPa，each loading lasts 50-100 h，and the confining pressure is 100 kPa.Sample is in optimal moisture content of 10％ and compaction coefficient K of 1.00.The size of sample is d（50 mm）× h（100 mm）.Physical properties of foundation soil to be tested are shown in Table 2.

So，plastic strain time-history curves of sample under different deviatoric stresses during experiment can be obtained，as shown in Figure 1.

Because of the limitation of accuracy of the test system and the small of strain，the error is too large to calculate average strain rate，so Equation（1）needed to be used to fitting to obtain power exponent.In order to satisfy the initial condition of finite deformation rate，Equation（1）should be calculated into Equation（2），in which，T is determined by the test time of 1％，namely，T=1 h.

s（t）=a（t+T）−P+1/（−P+1）+b　　（2）

So，the power exponent of P，corresponding to 47 kPa，95 kPa，190 kPa and 285 kPa，is obtained as 2.48，1.83，1.27 and 1.26 by fitting the curves in Figure 1 according to Equation（1）and（2）.In accordance with ultimate deviatoric stress of 759 kPa，the law that power exponent of P varies with the normalized ratio of λ is shown in Figure 2，from which we known that，the ratio λ，corresponding to P=2，is about 10％for silt soil with low compressibility.

4　Critical Stress State Equation of Time effect

According to mohr-coulomb yield criterion，stress circles that are in time-effect critical state are obtained through reducing the diameter of stress circles that are in limit equilibrium state at the ratio of deviatoric stress threshold and ultimate deviatoric stress，as shown in Figure 3，the envelope equation of stress circles that are in time-effect critical state is expressed to be Equation（3），and фcr，ccrarecalculated by Equation（4）and（5）.

τ=σtan фcr+ccr　　（3）

sin фcr=sinф/[（1-sinф）/λ+sinф]　　（4）

ccr=ctanфcr/tan ф　　（5）

[σ1]=σ3tan2（π/4+фcr/2）+2ccrtan（π/4+фcr/ 2）　　（6）

Analyzing foundation soil below the midline of subgrade，the stress state can be described in Figure 4，taking no consideration of σ2.

Observational data[9，10]show that，in deep strata below the surface 500 m，the value of k（k=σc1/σc3）is generally greater than 1.In shallow strata，low compressibility soil，formed in the alluvial process from high-order area，show the characteristics of strong structure and strong over consolidation[11]，and the over-consolidation ratio（OCR）is more than 2 in the range of 15 m depth[12]，and we know[13]，k0=µ/（1−µ）=0.67，so that，Thus，when calculatingσc3，k is taken as 1，namely σc3=σc1.Taking into account k might slightly bigger，∆σ3is ignored as compensation，so that σ3=σc3=σc1.So Equation（6）can be derived into Equation（7），in which，γ is the weight of foundation soil，h is the height of embankment.

[σ1]=γhtan2（π/4+фcr/2）+2ccrtan（π/4+фcr/ 2）　　（7）

Meanwhile，σ1=σc1+∆σ1，σc1=γh，∆σ1can be calculated by Equation（8）[13]，which is derived from q，applying for the situation showed in Figure 5.For the foundation soil below the midline of subgrade，the additional stress load of embankment can be departed as showed in Figure 6.

In which，n=z/b，m=x/b.

5　Foundation Condition

From Figure 3，we know that，if actual stress circles intersect the envelope of τ=σtan фcr+ccr，time-effect of deformation occurs.In other words，if σ1≥[σ1]，deformation will be with time effect；On the contrary，if σ1≤[σ1]，deformation is no time effect.So，foundation can be divided along depth into two kinds of layers，the upper emerges deformation with time effect and lower with no time effect，as is shown in Figure 7.Thus，Equation（9）can be used to calculate the thickness of time-effect layer.

σ1=[σ1]　　（9）

It is generally believed that when the thickness of time-effect layer is no more than 3-5 m，the ground just need to be treated simply，and deep reinforcing measure is not necessary.Taking this as principle，the requirement of foundation for embankment can be calculated out，and it is generally called foundation condition of embankment，from which we can know that whether the foundation need deep treatment.

Foundation under embankment of double-line ballastless track high-speed railway is taken as calculating example.Calculating data of embankment and foundation is showed in Table 3.Subgrade width（2b）is 13.6 m，embankment slope ratio（i）is 1：1.5，weight（γ1）of embank stuff in is 20 kN/m3.Physical indicators of foundation soil is showed in Table 2，weight（γ2）is 19.8 kN/m3.Additional stress ∆σ1（h=5 m）is also calculated.

Critical control Equation（10）for embankments with different heights can be got via Equation（9）：

156=99tan2（π/4+фcr/2）+2ccrtan（π/4+фcr/2）

215=99tan2（π/4+фcr/2）+2ccrtan（π/4+фcr/2）

275=99tan2（π/4+фcr/2）+2ccrtan（π/4+фcr/2）

335=99tan2（π/4+фcr/2）+2ccrtan（π/4+фcr/2）

394=99tan2（π/4+фcr/2）+2ccrtan（π/4+фcr/2）

So，for foundation under embankments of 3 m，6 m，9 m，12 m and 15 m，a certain фcrhas a minimum ccr，satisfying the thickness of time-effect layer is no more than 5 m.Then，via Equation（4）and（5），ф and c corresponding tocrф and ccrcan be got，which will tell us that deep treatment is not necessary.The results are collected in Table 4 and Figure 8.

The ultimate strength parameters（c，φ）of foundation soil have obvious influence on the compression layer thickness with time effect，and φ is the most obvious influence factor.For embankment of 3 m，6 m，9 m，12 m and 15 m，the influence of φ is more and more remarkable，because the slope in Figure 7 are 6 kPa/°，9 kPa/°，12 kPa/°，16 kPa/° and 19 kPa/°.

When the height of embankment is 3 m，foundation soil of low compressibility probably satisfies the condition，just some shallow treatments needed.But for the height of embankment is more than 3 m，it is really needed to treat the foundation in deep treatments.

6　Conclusions

This paper deals with foundation condition of high speed railway embankment，researches the time-effect characters of foundation soil.Some conclusions can be drawn below：For silt soil of low compressibility，the ratio of time-effect deviatoric stress threshold and ultimate deviatoric stress is about 10％ determined by“power criterion”.The envelope equation that stands for time-effect critical state is derived to be τ=σtan фcr+ccr，and sinфcr=sinф/[（1-sinф）/]sinλ+ф，ccr=ctanфcr/tan ф.For the height of embankment is 3 m，foundation condition is c+6ф-281＞0，when the height is 6 m and more，deep treatment need to be adopted generally.

Acknowledgement

The authors wish to acknowledgethe support and motivation provided by National 973Project of China（No.2013CB036204），and Natural Science Foundation of China Youth Fund Project（No.51408491）.

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ICRE2016-International Conference on Railway Engineering