General descriptions

The relationships between hydraulic gradient and seepage velocity for bimsoil samples with different RBPs are shown in Figure 5.34. As shown in Figure 5.34, samples with various heights were tested from 40 to 200mm. It can be seen that the seepage velocity increases with increasing hydraulic gradient, and the increment rate for bimsoil samples with a RBP of 60% is most evident. In addition, for the samples with various RBPs,

Technical flowchart for study on the slenderness ratio flow tests for bimsoil samples

Figure 5.33 Technical flowchart for study on the slenderness ratio flow tests for bimsoil samples.

the seepage velocity decreased with the increase of sample height. These results implied that the permeability coefficient of bimsoils is variational and not constant, and it depends on the hydraulic gradient. This result is consistent with the study of Wang et al. (Wang et al., 2016a): the permeability law of bimsoils does not comply with Darcy’s law. With the increase of sample height, the curves tended to be stable. This indicates that the seepage field in inhomogeneous bimsoil becomes steady gradually after a certain flow distance; the flow distance is an important factor influencing the flow characteristics. What is more, the critical sample height is different for samples with various RBPs.

The non-Darcy’s flow of bimsoils

When water flows in bimsoils, with the increase of seepage velocity, the flow characteristic becomes non-Darcian, and the link between the seepage velocity and pressure gradient of Darcy’s law becomes nonlinear (i.e., the bimsoil permeability depends on the seepage velocity). This dependency is influenced by the randomly distributed rock

The relationship between hydraulic gradient and seepage velocity for sampleswithheightfrom40to200 mm.(a-d)TheRBPis30%,40%,50%,and60%, respectively

Figure 5.34 The relationship between hydraulic gradient and seepage velocity for sampleswithheightfrom40to200 mm.(a-d)TheRBPis30%,40%,50%,and60%, respectively.

blocks in the bimsoil samples. To interpret this phenomenon well, an empirical equation was proposed by Forchheimer (1901) to correct for the nonlinearity of Darcy’s law. During the flow process in bimsoil, each stage of the stable value of the hydraulic gradient and seepage velocity is performed with a binomial fitting, and a modified version of Darcy’s law can be obtained as below (Wang et al. 2015a):

where p is the fluid mass density; Ca is the acceleration coefficient; / is the volume force of unit mass; V is the seepage velocity; % = dp/dx is the pressure gradient; and coefficient /? is termed the non-Darcy flow factor, m_l, also known as the inertial coefficient, inertial resistance, or turbulence factor. Both /? and к are regarded as material constants of the Forchheimer’s equation in the range of its validity.

When the duration of the path of the fluid flow in bimsoil samples is long enough, the flow reaches stability, so dVIdt = 0 . Theoretical analysis shows that when ignoring the compressibility of the liquid, the pressure gradient presents a uniform distribution. As a result, we rewrite the expression of the pressure difference as follows:

where pbase and Ihop are the hydraulic pressure at the outlet and inlet of the bimsoil sample, respectively, and H is the height of the sample, which is the length of the flow path.

Neglecting the mass force, in case the sample is not very large, the expression for Eq. (5.3) can be written as follows:

Using the experimental data above, the polynomial fitting equations for the typical specimens with different specimen heights are listed in Tables 5.10-5.13. Figure 5.35 plots the curve fitting results of sample height from 40 to 200 mm, with an RBP of 30%, 40%, 50%, and 60%, respectively. The correlation coefficient of all equations is good with a correlation coefficient larger than 0.9. From Eq. (5.4), we can obtain the non- Darcy permeability coefficient and the non-Darcy flow /? factor accordingly.

Table 5.10 The non-Darcy’s flow equations for typical specimens with a rock block percentage of 30%, using the Forchheimer equation

Specimen no.

Bimsoil 30-l(H = 40mm)

25.4676

57.28886

0.03966

0.975

Bimsoil_30-1 (H = 60mm)

27.3673

46.06427

0.03691

0.977

Bimsoil 30-l(H = 80mm)

37.5564

36.6585

0.02689

0.990

Bimsoil_30-I(H = 100mm)

37.7689

25.86399

0.02674

0.977

Bimsoil 30-l(H= 120mm)

37.2458

25.04659

0.02712

0.980

Bimsoil 30-l(H = 140mm)

38.612

26.41917

0.02616

0.981

Bimsoil_30-I(H = 160mm)

38.827

27.59595

0.02601

0.979

Bimsoil_30-I(H = 180mm)

37.0617

27.39719

0.02725

0.980

Bimsoil_30-I(H = 200mm)

37.6457

26.13581

0.02683

0.976

Table 5.11 The non-Darcy’s flow equations for typical specimens with a rock block percentage of 40%, using the Forchheimer equation

Specimen no.

Bimsoil_40-1 (H = 40 mm)

33.21934

79.41739

0.0304

0.991

Bimsoil_40-1 (H = 60 mm)

44.2489

54.85734

0.02283

0.957

Bimsoil_40-1 (H = 80mm)

55.9207

46.08953

0.01806

0.978

Bimsoil 40-l(H = 100mm)

56.86151

38.04205

0.01776

0.986

Bimsoil_40-1 (H = 120mm)

56.6892

29.67069

0.01782

0.976

Bimsoil 40-l(H = 140mm)

58.2059

30.95381

0.01735

0.990

Bimsoil 40-l(H = 160mm)

58.0889

30.68529

0.01739

0.989

Bimsoil 40-l(H = 180mm)

56.72037

30.81588

0.01781

0.957

Bimsoil_40-I(H = 200mm)

57.1004

28.84796

0.01769

0.977

Table 5.12 The non-Darcy’s flow equations for typical specimens with a rock block percentage of 50%, using the Forchheimer equation

Specimen no.

Bimsoil 50-1 (H =

40 mm)

17.45548

48.85914

0.05786

0.996

Bimsoil 50-2(H =

60 mm)

21.70822

36.53996

0.04653

0.992

Bimsoil_50-3(H =

80 mm)

27.27899

25.15432

0.03702

0.991

Bimsoil 50-4(H =

100 mm)

33.96639

27.1969

0.02974

0.991

Bimsoil_50-5(H =

120 mm)

34.12356

26.77677

0.0296

0.992

Bimsoil 50-6(H =

140 mm)

34.85317

26.23295

0.02898

0.990

Bimsoil_50-7(H =

160 mm)

33.23728

27.15362

0.03039

0.992

Bimsoil_50-8(H =

180 mm)

34.50031

26.9832

0.02928

0.992

Bimsoil_50-9(H =

200 mm)

33.54192

26.56346

0.03011

0.993

Table 5.13 The non-Darcy’s flow equations for typical specimens with a rock block percentage of 60%, using the Forchheimer equation

Specimen no.

Bimsoil_60-1 (H =

40 mm)

12.5917

30.10298

0.08021

0.997

Bimsoil_60-2(H =

60 mm)

16.2290

22.59943

0.06223

0.993

Bimsoil_60-3(H =

80 mm)

18.3969

17.88247

0.0549

0.988

Bimsoil_60-4(H =

100 mm)

19.2867

17.64004

0.05237

0.990

Bimsoil_60-5(H =

120 mm)

21.6305

17.5256

0.04669

0.987

Bimsoil_60-6(H =

140 mm)

20.9707

17.21499

0.04816

0.989

Bimsoil_60-7(H =

160 mm)

21.9001

16.46893

0.04612

0.988

 
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