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Dynamic stress properties of dynamic compaction (DC) in a red-sandstone soil–rock mixture embankment

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Abstract

The characteristics of dynamic stress and displacement are investigated in this study with laboratory and field tests of dynamic compaction (DC) in a red-sandstone soil–rock mixture embankment. Under four different DC energies (i.e., 1200, 1080, 960, and 840 kN m), the properties of the vertical and horizontal displacement and the dynamic stress contours at different depths induced by DC are obtained in an on-site test. The test results indicate that the effective reinforcement depth and range are approximately 4.0–6.0 and 3.0–4.0 m, respectively. When the dynamic stress in the contours is greater than 10 kPa, the dynamic stress attenuates dramatically. The regression analysis method is adopted to obtain the control equations and the parameters of settlement and dynamic stress attenuation. Based on settlement and dynamic stress data fitting method, the fitting parameters are obtained. The dimensionless analysis method is used for obtaining the design approach of the effective reinforcement depth and range for the red-sandstone soil–rock mixture embankment. The proposed design approaches are applied to the construction program of the Changji Expressway in Hunan, China. By means of long-term settlement observation of DC section K212 + 475 and ordinary section K180 + 655, the effectiveness of the red-sandstone soil–rock mixture embankment in the DC section K212 + 475 is 534.78% greater than that of the ordinary section K180 + 655, which demonstrates that the designed calculation equation and formulae are practicable.

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Abbreviations

a :

Undetermined coefficients in equation

b :

Undetermined coefficients in equation

A :

Area of tamp bottom (L2)

\(Vo\) :

Output voltage (ML2 T−3 A−1)

E :

Elastic modulus of the soil (ML−1 T−2)

\(E_{g}\) :

Bridge voltage (ML2 T−3 A−1)

\(K\) :

Sensitivity coefficient of the dynamic strain gauge

\(K_{F}\) :

Voltage gain by low-drift differential amplifier (ML2 T−3 A−1)

σ :

Dynamic stress measured by the dynamic strain gauge (ML−1 T−2)

c :

Soil cohesion (ML−1 T−2)

Δh :

Vertical deformation (L)

h :

Effective reinforcement depth (L)

H :

Fall distance of tamp (L)

k :

Fitting parameters

l :

Distance to explosion center (L)

l 0 :

Radius of charge (L)

m :

Modifying coefficient for the dynamic compaction

M :

Mass of tamper (M)

M′:

Tamper weight (ML1 T−2)

n :

Modifying coefficient for the water content

N :

Tamping times

r :

Distance to hammer bottom (L)

r 0 :

Radius of hammer (L)

ΔR :

Deformation (L)

R :

Effective reinforcement range (L)

s :

Distance between the adjacent points of the DC (L)

S 0 :

Settlement of ground surface (L)

S :

Distance between the adjacent points of the dynamic compaction (L)

D:

The diameter of the tamp pit (L)

H′:

Total depth of the soil (L)

h 0 :

Depth of the tamp pit (L)

S r :

Settlement at depth r (L)

W :

DC energy (ML2 T−2)

σ 0 :

Dynamic stress of ground surface (ML−1 T−2)

σ r :

Dynamic stress at a depth of r (ML−1 T−2)

σ a :

Dynamic stress l meters from explosion center (ML−1 T−2)

σ b :

Dynamic stress on ground induced by explosion (ML−1 T−2)

α :

Non-dimensional coefficient related to the embankment characteristics

φ :

Internal friction angle

ρ dmax :

Maximum dry density of soil (L−3 M)

ρ d :

Dry density of soil (L−3 M)

ρ 0 :

Dry density before dynamic compaction (L−3 M)

ρ 1 :

Dry density after dynamic compaction (L−3 M)

η 0 :

Porosity before dynamic compaction

η 1 :

Porosity after dynamic compaction

K 0 :

Level compactness before dynamic compaction (L)

K 1 :

Level compactness after dynamic compaction (L)

V v0 :

Pore volume before dynamic compaction (L3)

V v1 :

Pore volume after dynamic compaction (L3)

V 1 :

Tamp point volume for zone I (L3)

V 2 :

Tamp point volume for zone II (L3)

G :

Relative density and total volume of the soil

V :

Total volume of the soil (L3)

β :

Fitting parameters

ϖ :

Reduction coefficient

θ 0 :

Distributing angle of load

γ d :

Dry density (ML−3)

ω :

Water content (ML−3)

λ :

Soil type

ν :

Poisson’s ratio

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Acknowledgements

This work was supported by the National Basic Research Program of China (“973” Project) (Grant No. 2013CB036004) and the National Natural Science Foundation of China (Grant No. 51208523).

Author information

Authors and Affiliations

  1. School of Civil Engineering, Central South University, No. 22, Shaoshan South Road, Central South University Railway Campus, Changsha, 410075, Hunan Province, People’s Republic of China

    Zou Jin-feng, Sheng Yu-ming & Xia Zhang-qi

Authors
  1. Zou Jin-feng
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  2. Sheng Yu-ming
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  3. Xia Zhang-qi
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Correspondence to Zou Jin-feng.

Appendices

Appendix 1: Results of dynamic stress test (1200 kN m)

The x-axis in the appendixes represents time (the unit is seconds), and the y-axis represents output voltage (the unit is mV). X1 and Y11 in Appendixes 1 and 2 are the abscissa and ordinate of the peak of the curves, respectively.

Test results of dynamic stress (2 m below and 2 m left of the tamp point)

See Fig. 44.

Fig. 44
figure 44

Dynamic stress curve (2 m below and 2 m left). a The first DC. b The third DC. c The fifth DC. d The sixth DC. e The seventh DC. f The eighth DC. g The ninth DC. h The tenth DC

Full size image

Test results of dynamic stress (2 m below and 4 m left of the tamp point)

See Fig. 45.

Fig. 45
figure 45

Dynamic stress curve (2 m below and 4 m left). a The first DC. b The third DC. c The fifth DC. d The sixth DC. e The seventh DC. f The eighth DC. g The ninth DC. h The tenth DC

Full size image

Test results of dynamic stress (4 m below and 2 m left of the tamp point)

See Fig. 46.

Fig. 46
figure 46

Dynamic stress curve (4 m below and 2 m left). a The first DC. b The third DC. c The fifth DC. d The sixth DC. e The seventh DC. f The eighth DC. g The ninth DC. h The tenth DC

Full size image

Test results of dynamic stress (4 m below and 4 m left of the tamp point)

See Fig. 47.

Fig. 47
figure 47

Dynamic stress curve (4 m below and 4 m left). a The first DC. b The third DC. c The fifth DC. d The sixth DC. e The seventh DC. f The eighth DC. g The ninth DC. h The tenth DC

Full size image

Test results of dynamic stress (5 m below and 2 m left of the tamp point)

See Fig. 48.

Fig. 48
figure 48

Dynamic stress curve (5 m below and 2 m left). a The first DC. b The third DC. c The fifth DC. d The tenth DC

Full size image

Test results of dynamic stress (5 m below and 4 m left of the tamp point)

See Fig. 49.

Fig. 49
figure 49

Dynamic stress curve (5 m below and 4 m left). a The first DC. b The third DC. c The fifth DC. d The tenth DC

Full size image

Appendix 2: Results of dynamic stress test (960 kN m)

The x-axis in the appendixes represents time (the unit is seconds), and the y-axis represents output voltage (the unit is mV). X1 and Y11 in Appendixes 1 and 2 are the abscissa and ordinate of the peak of the curves, respectively.

Test results of dynamic stress below DC point

Figure 50a–c shows that dynamic stress decreases quickly and that the duration is only 0.03–0.05 s when DC energy is 960 kN m. The dynamic stress decreases from 0.883 to 0.645 mV and then to 0.027 mV at the depths of 2, 3, and 4 m, respectively, which indicates that the instance impact force caused by DC can be neglected at a depth of 4 m.

Fig. 50
figure 50

Dynamic stress curve (960 kN m). a Down 2 m. b Down 3 m. c Down 4 m

Full size image

Test results of dynamic stress around DC point

See Fig. 51.

Fig. 51
figure 51

Dynamic stress curve (960 kN m). a 2 m below and 2 m right. b 2 m below and 4 m right. c 4 m below and 2 m right. d 4 m below and 4 m right. e 2 m below and 2 m left

Full size image

Test results of dynamic stress under different tamping times (2 m below)

See Fig. 52.

Fig. 52
figure 52

Dynamic stress curve under different tamping times. a The first DC. b The second DC. c The third DC. d The fourth DC

Full size image

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Jin-feng, Z., Yu-ming, S. & Zhang-qi, X. Dynamic stress properties of dynamic compaction (DC) in a red-sandstone soil–rock mixture embankment. Environ Earth Sci 76, 411 (2017). https://doi.org/10.1007/s12665-017-6743-1

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