5th International Conference on and Transportation (ICCET 2015)

Test Study on Mechanical Properties of Mixture Mass of and Crushed Rocks1

Sun Wen-jun1, Song Yang1*, Guo Ke-xin1,Zhang Hai-feng2

1Hebei Engineering and Technical College, Cangzhou 061001, Hebei, China;2 Hebei University of Technology, Tianjin, 300401, China;

Keywords: ; triaxial tests; mixture mass of loess and crushed rocks; double yield surface model Abstract: Based on large-scale triaxial tests, the mechanical properties of loess and crushed rocks mixture mass of a freeway tunnel’s surrounding rocks in Hebei were studied under the consideration of crushed ’s contents. The test results indicate that with the increase of crushed rocks contents, initial slope of deviatoric and axial strain curve increases at the same confining pressure. And corresponding axial strain decreases at the maximum partial stress value. At the same time, the mixture mass shows the characteristics of crisping deformation. Additionally, with the increase of crushed rocks contents, the internal frictional angle increases but the corresponding decreases. Therefore, the mechanical constitutive relationship of loses and crushed rocks mixture mass was simulated with double yield surface model. The method for determining the model parameters of this model was put forward at the same time.

Introduction The "coarse phase" (also known as giant grain group or coarse grain group) and "fine particle phase", which constitute the mixture mass of loess and crushed rocks, have significant differences in physical properties and mechanical strength [1, 2]. The physico-mechanical properties of mixture mass of loess and crushed rocks are different from “fine-grained ” and “rock” in standard [3, 4, 5]. The definition of mixture mass of loess and crushed rocks put forward by Wenjie Xu et al [6, 7, 8] is that formed since the quatemary period, composed of block stone with certain engineering scale and higher strength, but the research on the mixture of loess and is relatively rare [7, 8].

Test analysis of tunnel’s mixture mass of loess and crushed rocks Test sample of mixture mass of loess and rocks and its physical property index. The test sample of mixture mass of loess and crushed rocks was obtained from the left line of a freeway’s tunnel in Hebei near the no.K25+240 pile. Its grain size distribution curve is shown in Fig. 1. As seen in Fig. 1, the content of the particle size which more than 10mm is about 15%. In addition, the main physical properties index of the loess are obtained by the conventional test as shown in Table 1. Firstly, there is 24h-isotropic consolidation under confining pressure. Then, triaxial shear test with no drainage was carried out under the rate of 0.5%/min axial strain. And the test readings are r according to the frequency of 0.5% axial strain.

1 This paper is supported by the Research of Education Bureau of He Bei Province（QN2015036）;Water resources research and extension project of Hebei Province（2015049）

© 2015. The authors - Published by Atlantis Press 385

100 90 Natur Natur 80 Dry 70 al al

unit Soil unit water Void 60 weight 50 samp weig conte ratio  40 d le ht  nt e (kN/m3 30 (kN/ W(% ) 20 m3) ) certain particle size /% size particle certain

Percentage of less than less of Percentage 10 mixt 0 0.1 1 10 100 ure 19.21 16.95 13.24 0.57 mass Soil particle size /mm Table 1 Physical property parameters Fig.1 Grain sizes of distribution of mixture of mixture mass

Test results analysis of mixture mass of loess and crushed rocks of As shown in Fig.2 to 4, the relationship curves between axial strain and deviatoric stress as as volumetric strain are described in triaxial shear tests with different confining pressure of three kinds of gravel content. Then, the triaxial characteristic parameters (that is angle of internal and cohesion) of tunnel’s mixture mass of loess and crushed rocks in different conditions can be obtained by the use of molar circle tangent according to triaxial shear test results with different gravel content, as shown in Table 2. In the process of increase, reduction of and distance between , and change of distribution structure are the main change of mixture mass of loess and crushed rocks.

3=100 kPa  =100 kPa 3=200 kPa 3 1000  =300 kPa 3=200 kPa 3 6

 =300 kPa 900 3=400 kPa 3  =400 kPa (%) 3

v (kPa) 800  5 q 700 4 600 toric stress stress toric 500 3 volumetric strain strain volumetric devia 400

300 2 200 100 1 axial strain  (%) 0 a 0 2 4 6 8 10 12 14 16 18 20 22 24 0 axial strain a(%) 0 2 4 6 8 10 12 14 16 18 20 22 (a) deviatoric stress ~ axial strain (b) axial strain ~ volume strain

Fig.2 Triaxial tests results of mixture mass with 10% crushed rocks

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3=100 kPa 3=100 kPa

3=200 kPa  =200 kPa 1000 7 3 3=300 kPa (%)  =300 kPa

v 3  (kPa) 900 3=400 kPa

q 3=400 kPa 6 800

700 5 ic stress stress ic 600 4 500 volumetric strain strain volumetric

deviator 400 3

300 2 200 1 100 0 0 0 2 4 6 8 10 12 14 16 18 20 22 24 0 2 4 6 8 10 12 14 16 18 20 22 24 (a) deviatoric stress ~ axial strain (b) axial strain ~ volume strain

axial strain  (%) axial strain  (%) a a Fig.3 Triaxial tests results of mixture mass with 20% crushed rocks

3=100 kPa 3=100 kPa

1000  =200 kPa 7 3=200 kPa 3 (%)  =300 kPa 3=300 kPa 3 v 900  3=400 kPa 6 3=400 kPa

(kPa) 800 q 700 5 600 4 500 volumetric strain strain volumetric 400 3

deviatoric stress stress deviatoric 300 2 200 1 100 0 0 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 axial strain a(%) axial strain a(%) (a) deviatoric stress ~ axial strain (b) a xial strain ~ volume Fig.4 Triaxial tests results of mixture mass with 30% crushed rocksstrain

normal peak intensity residual intensity intensity internal cohesion internal index Cohesion friction angle force friction angle gravel content c(kPa) (°) c(kPa) (°) 10% 26.89 65.34 25.14 62.64 20% 27.67 61.12 26.43 53.21 30% 28.84 51.90 28.24 51.40 Table 2 Index of shear strength for mixture mass

Research on constitutive model of the mixture mass of loess and crushed rocks At present, the constitutive model of mixture mass of loess and crushed rocks mainly bases on the constant elasticity modulus and Poisson’s ratio. Currently, after the soil mass reaches its yield, the description of yield surface mainly contains shear yield surface and volume collapse yield surface. And double yield surface which combined by two of them is commonly used. The p p hardening parameter of the yield surface is plastic volume strain v and the shear stains , taking the plastic shear stain and plastic shear stain into consideration. In this paper, the model of mixture mass of loess and crushed rocks is simulated by the double yield surface model.

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Shear yield surface of mixture mass of loess and crushed rocks.

p yield trace ( ＝6%) yield trace (  ＝4%)

s 1000 1000 /kPa /kPa 900 900 q

q 800 800 700 700 stress stress stress stress 600 600

500 500 400 400 300 300 200 200 100 100 100 200 300 400 p/kPa500 600 700 100 200 300 400 p/kPa500 600 700

1000 1000 900 900 800 800 700 700 600 600

500 500 /kPa 400 400 /kPa q

q 300 300 200 200 stress stress 100 stress 100 yield100 trace200 ( ＝3008%) 400 500 600 700 yield100 trace200 ( ＝30010%)400 500 600 700

p/kPa p/kPa Fig.5 Trace of plastic strain change for mixture mass with 10% crushed rocks And then the fitting results of the corresponding stress yield trace by hyperbolic function with plastic shear strain of mixture mass of loess and crushed rocks is 4%, 6%, 8% and 10% under different gravel contents in Table 3.

Natur Natur al unit Dry unit al Soil Void weigh weight water sampl ratio t   conte e d e (kN/m (kN/m3) nt 3) W(%) mixtu re 19.21 16.95 13.24 0.57 mass critical paramet shearing hyperbolic yield Hyperbolic yield er cohesion state strain function function parameters c(kPa) (%) parameters a b line slope mixture mass M 4 -0.0005 3.3479 gravel content 6 -0.00091 1.5433 65.34 1.1365 10% 8 -0.00074 1.4352 10 -0.00034 2.243 4 -0.0005 3.4164 gravel content 6 -0.00042 2.6933 61.12 1.2008 20% 8 -0.0003 2.0475 10 -0.00026 1.8188 4 -0.00026 1.845 gravel content 6 -0.0005 3.3479 51.90 1.3615 30% 8 -0.00091 1.5433 10 -0.00074 1.4352 Table 3 The shear yield surface parameters for mixture mass considering different contents of crushed rocks

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Conclusion An indoor large triaxial tests carried out for the mechanical properties of mixture mass of loess and crushed rocks of a freeway’s tunnel in Hebei. The impact of gravel on loess mass was analyzed by changing its content. And then, the stress and strain characteristics of mixture mass of loess and crushed rocks were simulated by using double yield surface model. And main conclusions of this paper are as followed:(1) The deviatoric stress increases obviously with the increase of gravel content under the same confining pressure, especially when the gravel content increases to 30%. (2) Mixture mass of loess and crushed rocks has brittle characteristics when the gravel content gradually increases from 10% to 20% and 30%. And when gravel content increases to 30%, the internal friction angle of mixture mass of loess and crushed rocks increases by 7.3%, while the cohesion decreases by 20.6%. (3) Put forward the double yield model to simulate the mixture mass of loess and crushed rocks and determine the model parameters.

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