The development of urban agglomerations forces more and more often investors to build structures in areas with weak subsoil. Such areas include places with organic soil. One type of organic soil is peat. Peat has a dark colour (mostly brown or black), characteristic odour, and spongy consistency [1]. The porosity of peat and its high water content contributes to its high compressibility, low shear strength, and low stiffness [1, 2, 3, 4].
The organic soils are characterized by very high compressibility It is the reason for the large settlement of objects placed on such a subsoil. The parameter describing the compressibility is the constrained elasticity modulus [5]. The most popular method of its determination is an oedometer test [1, 3, 5]. In the test, the sample is in a metal ring which prevents horizontal deformations. The authors propose to determine this parameter by loading the soil with an overloading embankment [2, 6, 7, 8, 9, 10]. In this method, it is possible to determine the constrained elasticity modulus based on the settlement of the embankment and using the inverse problem. The paper presents two methods that allow for the determination of constrained elasticity modulus. Based on these methods, authors analysed the parameter for the quasi-stationary state for consolidation.
In order to determine the constrained modulus of elasticity of peat material during soil consolidation with an embankment, the authors used two models. The first model is based on the constant stress distribution and can be directly related to the oedometer test. The second model is based on the assumption of a uniaxial deformation state of the substrate, with a triaxial state of stress [2, 7, 9, 10].
The method assumes loads on the organic soil layer with an overloading embankment with dimensions
The stresses on the organic soil layer are determined based on the Boussinesq's theory and the principle of superposition's [2, 5, 7, 9, 10]. According to that in each analysed column, the stresses will be considered the influence of load of the all areas. More details about the assumption of this method were described in other works [2, 7, 9, 10].
The constrain elasticity modulus determined in this way can also be determined during consolidation. Changes in a settlement at the next stages of consolidation can be used to determine the modulus at any given time of the process (assumption of a quasi-stationary state).
The strain prediction based on the applied load is influenced by the state of stresses and strains in the soil. In order to determine, an appropriate soil model should be adopted (elastic, elastic-plastic, elastic-viscous plastic) and appropriate characteristics (parameters) of the subsoil should be assumed [3, 5, 14]. In addition, in numerical analysis, it is important to separate the calculation area and adopt boundary and initial conditions. In the organic soils, this problem is more complex than in the mineral soils. In most engineering cases the elastic-plastic model is used. In organic soils, this is an oversimplification, because creep also occurs in organic soil. The presented methods assume that creep does not occur.
The authors used both models to determine the constrain elasticity modulus for the quasi-stationary state for consolidation.
In this model, it was assumed that the constrained modulus of elasticity is constant throughout the calculated column of soil
Assumed column of organic soil for calculation; σ
In this model, the settlement can be determined by formula 1:
settlement of the organic soil layer [m]; load caused by the preload embankment [kPa]; thickness of the organic soil layer [m]; constrained modulus of elasticity in the considered column determined by the first model [kPa] [9, 10].
Using the inverse problem with the known settlement of the organic soil layer and a load of the embankment, the constrained modulus of elasticity can be calculated. This can be described by formula 2.
In the second model, the stresses in the organic soil layer are described according to Boussinesq's theory and the principle of superposition. The stress distribution in the soil layer is not constant:
The constrained modulus of elasticity of organic soil is constant (
Assumptions made for the model; a) calculated column in methods b) adopted coordinate system for calculations; σ
Calculations are performed on the selected point A with coordinates ( initial settlement of the organic soil layer [m] thickness of the organic soil layer [m]; constrained modulus of elasticity in the considered column determined by the second model [kPa] [9, 10]; peat porosity before overload determined by the formula (6) [12]:
dimensionless parameter given by the formula (7)[12]:
parameter includes the influence of organic soil thickness and the dimension of embankment in stresses (kN/m), defined by the formula (8):
The modulus determined by this model is the average value of the modulus in the thickness of the considered soil layer.
Two preloading embankments in Białośliwie (Poland) were analysed. These embankments were prepared and analysed by team from Warsaw University of Life Sciences and the Swedish Geotechnical Institute in the 80s of the 20th century [13, 14, 15, 16, 17, 18]. The first embankment had dimensions of 16 × 26 m at the base and the second 19.8 × 23.6 m. Both initial heights were circa 2 m. Both are placed on 4 – a metre layer of organic soil under which there is fine sand [13, 15, 16, 17, 18]. More details are in Table 1.
The first embankment | The second embankment | |
---|---|---|
Dimension at the base | 16 × 26 m | 19.8 × 23.6 m |
Initial height | 2.0 m | 2.2 m |
Material of embankment | MSa | MSa |
Bulk density of embankment | γ =17.5 kN/m3, | γ =18.18 kN/m3, |
Height of organic soil layer | 4.0 m | 4.0 m |
Type of organic soil | 2 m of peat and 2 m of gyttja | 4 m of peat |
Water content of organic soil | Peat – |
|
Bulk density | Peat – γ =10.5 kN/m3 |
Peat – γ =10.5 kN/m3 |
Organic matter content | Peat – |
Peat – |
On the basis of field and laboratory tests, the known properties of the soil. Consolidations were observed based on cyclic geodetic measurements of benchmarks installed in the soil at the top of the organic soil layer for about a year. This process was observed at 3 measurement points under their centre [13, 15, 16, 17, 18].
The locations of the settlement measurement points in the embankments are shown in Figure 3.
Scheme of embankments with the arrangement of measuring benchmarks [3, 16, 17]
During the consolidation of organic soils, the load on the embankment will change due to the displacement of groundwater, which in organic soils is usually equal to their thickness. The total stresses that the embankment will exert on the organic soil over time can be determined by the formula (9):
the unit weight of the embankment; the effective unit weight of of the embankment; the initial height of the embankment; settlement in time [3].
The initial stresses by embankment 1 on the subsoil are σ
The changes of stresses working on the subsoil σ
The change of stresses working on the subsoil σ(
The changing settlement in time
For all measurement points of both embankments, the constrain elasticity modulus of the organic soil layer during its consolidation was calculated according to models 1 and 2. Assuming quasi-steady states, the final settlement was assumed during the calculations as each successive settlement in time.
The values of the constrain elasticity modulus of the layer of organic soil located under the embankments, determined with the described models for the measurement points in known time, are presented in Fig. 6.
The constrain elasticity modulus: a. for the first embankment; b. for the second embankment
From the analysis, it can be seen that during consolidation, the constrained elasticity modulus increases for each model used. The modulus values stabilize around day 125÷150 when the load transfer to the soil skeleton and the pore pressure in the soil disappears. Model 1 for determining the constrain elasticity modulus is based on the linear Terzaghi theory [5, 19]. Assuming vertical soil deformation during consolidation, vertical filtration in a separated soil column is in accordance with the principles of the consolidation theory [5, 19].
In addition, the constrained elasticity modulus of organic soil over time, determined by model 2, is based on the already completed consolidation process (stabilized settlement). Model 2 takes into account the triaxial stress state in the uniaxial strain state.
In model 1, the dependence of the consolidation description, assuming additionally the effects of soil deformation and vertical filtration in the column [5, 19]. However, these simplifications result in multiple overestimations of the constrain elasticity modulus in the corners of the embankment, despite their good accordance of settlement under its centre in the case of the embankment founded on a shallow organic subsoil (the embankment in Białośliwie).
The paper presents two models determining the organic soil constrained elasticity modulus on the basis of overloading it with an embankment.
The first method assumes a constant stress distribution from the external load in the peat layer and a constant compressibility modulus (
Analysis of the constrain elasticity modulus changing in time for quasi-steady states was performed for the cases of previously examined embankments in Białośliwie [13, 15, 16, 17, 18].
The analysis showed that it can be used not only to determine the compressibility modulus of organic soils but also in the analysis of soil consolidation taking into account the buoyancy of the load layer.
Both compressibility modulus increase with their duration. Model 1 showed the best compliance with respect to the oedometric modulus for both analysed embankments. The analogy of the results is a consequence of the assumptions made in method 1, i.e. Terzaghi's consolidation theory. Using model 2, which determines the constrain elasticity modulus of organic soils based on field studies, can be used to forecast embankment subsidence using the observation method during the implementation of investments in the design and build mode.
The calculations and analysis performed (in theory) prove that the original models can be used in practical calculations of the constrained elasticity modulus of organic soils. What's more, they can also be used in the analysis of subsoil consolidation, taking into account the displacement of water.
When considering the constrain elasticity modulus of the organic soil, the one-dimensional strain state is considered, despite the state of spatial stress. This fact can be used in the “design and build” technology. The constrained modulus is determined from the embankment overload and will represent the actual deformations – volumetric deformations (including other deformations that actually occurred) during the consolidation.
The rheological aspect is not included directly in this publication. In this paper, the uniaxial strain state was taken into account to the triaxial stress state, taking into account vertical stresses (which are greater than horizontal ones). The plan of further research provides for determining the influence of the embankment geometry on determining the value of the constrained modulus of the organic soil, taking into account rheological phenomenon and parameters..