High in organic matter content
Peat is formed by the gradual accumulation of plant remnants, and the natural organic matter content in peat is high and variable. It has been recognized that the presence of organic matter has significant effects on engineering properties of peat. With high content of organic matter, peat exhibits high water content, large void ratio and low bulk density. Except for the difference of these conventional index properties, the organic matter itself may show some unique properties, for example compressible. Bery and Vickers (1975) have mentioned that the peat particles themselves may be compressible in their study on fibrous peat consolidation. Robinson (2003) indicated the organic matrix is compressible, which gives wrong interpretation of the primary consolidation by Terzaghi’s theory. It might be inappropriate that study on peat is still based on ideas or methods for mineral soils. An obvious initial deformation appears when loading on peat samples, which could be partly caused by organic matter compression. But no detailed studies on compressibility of organic matter in peat have been found. This may be because natural organic matter is in different forms and the structure is very complex. Usually it’s difficult even impossible to quantify the effects of organic matter on peat through a controlled experiment (Choo et al. 2015). We attempt to simulate the compression of organic matter in peat by presenting a unified empirical model. In fact, similar properties have been found in Victorian brown coal from the author’s preliminary studies (Liu et al. 2014a). Victorian brown coal is a kind of intermediate geotechnical materials (IGMs) fossilized from peat after a long time of coalification process (Hayashi and Li 2004). The form of the organic matter compression model is proposed by taking reference from some empirical creep models of soil. The following empirical equation is normally used to describe the stress and time dependent deformation behavior of soils:
$$\varepsilon = f(\sigma ,t) = f_{1} (\sigma )f_{2} (t)$$
(1)
in which f
1(σ) is to describe stress related deformation and f
2(t) is the time related deformation. Some researchers studied the creep behavior of soil based on the idea of Eq. (1) and empirical models had been proposed (Singh and Mitchell 1968; Mesri et al. 1981; Lin and Wang 1998). In these models, the stress–strain function (f
1(σ)) varies but the strain–time function (f
2(t)) usually takes the form of exponential equations. The authors propose an initial constrained modulus of organic matter E
m
to describe the stress–strain function (f
1(σ)), and still use the exponential form for the strain–time function (f
2(t)). Then a simple unified stress–strain–time model is proposed here to describe the compressibility of organic matter in peat under one-dimensional compression:
$$\varepsilon_{m} = \left( {\frac{1}{{E_{m} }}\sigma } \right)\left( {\frac{t}{{t_{1} }}} \right)^{\lambda }$$
(2)
where, ε
m
is strain of organic matter; σ is applied vertical total stress; t
1 is unit time; E
m
is initial constrained modulus of organic matter; λ is time factor.
Gas bubble entrapment
There are many conditions that engineering materials are not fully saturated and the voids are filled partly with water and partly with gas. Under the condition of a high degree of saturation, the gas phase is discontinuous and is in the form of discrete bubbles (Wheeler 1988). Due to the decomposition process, organic matter in peat can be converted into gases including carbon dioxide and methane. Under near saturated conditions, these gases accumulate into bubbles that remain trapped within peat deposit (Pichan and O’Kelly 2012). The mechanism of entrapped gas bubbles is extremely complicated. Basically the deformation of gas bubbles is controlled by pore air pressure u
g
from equation of Boyle’s law. Considering the surface tension effect between gas bubbles and water, the gas bubble pressure u
g
is not equal to water pressure u
w
in the material. Usually, the difference between the air pressure u
g
and the water pressure u
w
can be computed by Eq. (3) considering the equilibrium of gas bubbles with radius r (Schuurman 1966; Wheeler 1988):
$$u_{g} - u_{w} = 2q/r$$
(3)
where q is the surface tension and r is the radius of gas bubbles.
The temperature is considered constant during tests, the surface tension q is dependent on the temperature, therefore q is constant as well. And the diminution of surface tension q with increasing air pressure can be neglected as discussed by Schuurman (1966), so a constant value (7.4 × 10−3 N/m) of q is used in the paper.
Entrapped gas could be exist as the form of small bubbles compared with average particle size or large gas voids. Wheeler (1988) and Pietruszczak and Pande (1996) discussed the difference between the two kinds of gassy soils. When the gas bubbles are small compared with peat particle size, the bubbles fit within the normal void spaces and the radius of curvature of gas–water interface is equal to the radius r of the bubble. At the opposite extreme, gas bubbles are much larger than peat particle size, which generates a large gas-filled void. Then the gas–water interfaces are formed by lots of small menisci which bridge the gaps between the particles. The radius of curvature of these menisci is not necessarily equal to the radius r of the bubble. As a simplification, the size of small gas bubbles is assumed to be trapped within the voids of peat grains.
Electron microscope scanning tests of peat from different places have been carried out by some researchers. Lv et al. (2011) obtained the results that the average void diameter is about 10 μm and the large void is up to 25 μm diameter for peat samples from northern east China. Xiong (2005) and Liu et al. (2014b) got the average void diameter is about 13.65 μm for peat samples from Kunming. A void diameter range of 3–20 μm is obtained by Wang (2013)and their tested peat samples are from Hangzhou, east China. Considering the void size of peat, the radius r of gas bubbles can be determined and it should be smaller than void sizes. An average initial radius r
0 of gas bubbles are used in the following case studies.
Without considering gas dissolution and exsolution, the gas phase in peat is considered as ideal gas and the deformation obeys Boyle’s law (Schuurman 1966), which is:
$$(P_{a} + 2q/r_{0} )V_{g0} = (P_{a} + 2q/r + u_{w} )V_{g}$$
(4)
where V
g
is gas volume in peat and r is the radius of gas bubbles, the subscript 0 represents the initial value of each parameter; P
a
is the atmospheric pressure.
Three phase composition of peat
Peat has complex textures and physical composition, and peat solid phase can be considered as a mixture of organic matter and minerals. Even under conventional saturated condition, small gas bubbles can also be trapped within the voids of peat grains. Landva and Pheeney (1980) described the characteristics of three phase peat based on a series of electron microscope scanning tests. The author also proposed a similar conceptual model on Victorian brown coal which is a kind of organic material fossilized from peat (Liu et al. 2014a). Based on discussions of above sections, we know that peat can be considered as a three phase mixture and in the state of quasi-saturated. Especially, the solid phase of peat should be divided into mineral part and organic matter part. A schematic diagram of the special three phase composition of peat is shown in Fig. 1. Some parameter definitions and assumptions are made as follows.
As usual analysis method of one dimensional consolidation theory, a representative element with unit volume dxdydz is taken here to do the analysis. The unit element is assumed to satisfy both the basic assumptions of Terzaghi’s theory and assumptions in above discussions. The special three phase composition as shown in Fig. 1 is adopted for the unit element. Similar to the definition of conventional void ratio e, some parameter definitions are made as follow.
$$e_{m} = \frac{{V_{m} }}{{V_{s} }}\quad e_{g} = \frac{{V_{g} }}{{V_{s} }}\quad e_{w} = \frac{{V_{w} }}{{V_{s} }}$$
(5)
$$a = e_{m} + e_{g} + e_{w}$$
(6)
where, e
w
, e
g
and e
m
are defined as volume ratios of water, gas and organic matter, respectively; V
w
, V
g
, V
m
and V
s
are water volume, gas volume, organic matter volume and mineral volume, respectively; and a is the ratio of the changeable volume to the volume of the incompressible solid minerals, which is the sum of e
w
, e
g
and e
m
.
Usually the basic geotechnical indexes of peat are known quantities including density of peat (ρ), water content (ω), organic matter content (ω
m
) and unit weight of peat solid phase (γ
p
), then above defined parameters can be calculated with mass and volume conservation for a certain peat sample.
Under above definitions, conventional void ratio e can be calculated as:
$$e = \frac{{e_{g} + e_{w} }}{{1 + e_{m} }}$$
(7)
A parameter β is defined as the ratio of initial organic matter volume (V
m0
) to initial total volume (V
0
), that is:
$$\beta = \frac{{V_{m0} }}{{V_{0} }} = \frac{{e_{m0} }}{{1 + a_{0} }}$$
(8)
The gas volume content is defined as:
$$S_{g} = \frac{{V_{g} }}{V} = \frac{{e_{g} }}{1 + a}$$
(9)
where, V is the total volume.