Analysis of Using the Empirical Model of Organic Soil Consolidation to Predict Settlement

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.

MATHEMATICAL DESCRIPTION OF METHODS

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 B × L. The settlement should be measured in the consolidation process. The embankment is divided into smaller rectangular calculation areas. The calculations are made at points based on the discretization of the embankment. There is a column of organic soil (peat) below each area. The layer of organic soil (peat) has thickness H_T. The column of organic soil is loaded from the top by an embankment layer (σ₀). It was assumed that the layer below organic soil is not compressible [2, 7, 9, 10].

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.

2.1.

First model

In this model, it was assumed that the constrained modulus of elasticity is constant throughout the calculated column of soil $(Em_1 = const and \frac{\partial E}{\partial E} = 0)$ (Em\_{\it 1} = const\;{\rm{and}}\;{{\partial E} \over {\partial E}} = 0) , the stress distribution in the soil is constant σ_z = σ₀ = const and the influence of the load from other calculation areas are not taken into account. All assumptions were shown in Figure 1 [2, 9, 10].

Assumed column of organic soil for calculation; σ0 – loading by the preload embankment (kPa); σ_z – stresses in the soil in the column under consideration (kPa); H_T – organic soil thickness (m); E_{m_1} – constrained modulus of elasticity of peat material in the column under consideration; determined by the first model (kPa); A – analysed point (−); h_n – the height of the embankment (m); γ – the unit weight of the embankment (kN/m³); z – the axis of depth [9, 10]

In this model, the settlement can be determined by formula 1: (1) $s = \frac{σ_{0}}{E_{m_1}} H_{T}$ s = {{{\sigma _0}} \over {{E_{m\_1}}}}{H_T} where: s

settlement of the organic soil layer [m];

σ₀

load caused by the preload embankment [kPa];

H_T

thickness of the organic soil layer [m];

E_{m_1}

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. (2) $E_{m_1} = \frac{σ_{0}}{s} H_{T}$ {E_{{m\_1 }}} = {{{\sigma _0}} \over s}{H_T} Above mentions topics were described more extensively in [9, 10].

2.2.

Second model

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: σ_z = f(x, y, z), ∂_σz / ∂z ≠0.

The constrained modulus of elasticity of organic soil is constant (E_{m_2} = const; ∂E_{m_2}/∂z= 0) and depends on settlement related to Meyer's approach [11, 12]. The assumptions are summarized in Figure 2.

Assumptions made for the model; a) calculated column in methods b) adopted coordinate system for calculations; σ₀ – loading by the preload embankment (kPa); σ_z – stresses in the soil in the column under consideration (kPa); H_T – organic soil thickness (m); E_{m_2} – constrained modulus of elasticity of peat material in the column under consideration; determined by the second model (kPa); A, analysed point (−); h_n – the height of the embankment (m); γ – the unit weight of the embankment (kN/m³); z – the axis of depth [10]

Calculations are performed on the selected point A with coordinates (x_A, y_A), where x_A ∈ 〈0;B〉 and y_A ∈ 〈0;L〉. The calculations take into account the settlement of the elementary volume of organic soil. This is described in formula 3: (3) $\frac{ds}{dz} = \frac{σ_{z} (x, y, z)}{M (x, y)}$ {{ds} \over {dz}} = {{{\sigma_z}\left( {x,y,z} \right)} \over {M\left( {x,y} \right)}} As M(x,y) the Meyer approach [11,12] on the change in constrained modulus of elasticity M(s) for the peat substrate was adopted by formula 4: (4) $M (s) = M_{0} {[1 - \frac{s}{n_{0} H_{T}}]}^{- κ}$ M\left( s \right) = {M_0}{\left[ {1 - {s \over {{n_0}{H_T}}}} \right]^{ - \kappa }} By solving equation (3) and taking into account dependence (4), the constrained modulus of elasticity of organic soil can be written: (5) $E_{m_2} = \frac{J_{i} (κ - 1)}{[(H_{T} n_{0} - s) {(1 - \frac{s}{H_{T} n_{0}})}^{- κ} + (- H_{T} n_{0} + s_{0}) {(1 - \frac{s_{0}}{H_{T} n_{0}})}^{- κ}]}$ {E_{{m\_2}}} = {{{J_i}\left( {\kappa - 1} \right)} \over {\left[ {\left( {{H_T}{n_0} - s} \right){{\left( {1 - {s \over {{H_T}{n_0}}}} \right)}^{ - \kappa }} + \left( { - {H_T}{n_0} + {s_0}} \right){{\left( {1 - {{{s_0}} \over {{H_T}{n_0}}}} \right)}^{ - \kappa }}} \right]}} where: s₀

initial settlement of the organic soil layer [m] s₀ = 0;

H_T

thickness of the organic soil layer [m];

E_{m_2}

constrained modulus of elasticity in the considered column determined by the second model [kPa] [9, 10];

n₀

peat porosity before overload determined by the formula (6) [12]: (6) $n_{0} = 1 - \frac{1}{12} σ^{\frac{1}{3}}$ {n_0} = 1 - {1 \over {12}}{\sigma ^{{1 \over 3}}}

dimensionless parameter given by the formula (7)[12]: (7) $κ = 2,2 σ^{- \frac{1}{18}}$ \kappa = 2,2{\sigma ^{-{1 \over {18}}}}

J_i

parameter includes the influence of organic soil thickness and the dimension of embankment in stresses (kN/m), defined by the formula (8): (8) $\begin{array}{l} J_{i} = \int_{0}^{B} (\int_{0}^{L} (\int_{0}^{H_{T}} σ_{z} dz) dy) dx = \\ = \frac{σ_{0}}{2 π} (A_{i} + B_{i} + C_{i} + D_{i} + E_{i} + F_{i}) \end{array}$ \matrix{ {{J_i} = \mathop \smallint \nolimits_0^B \left( {\mathop \smallint \nolimits_0^L \left( {\mathop \smallint \nolimits_0^{{H_T}} {\sigma _z}dz} \right)dy} \right)dx = } \hfill \cr {\;\;\;\; = {{{\sigma _0}} \over {2\pi }}\left( {{A_i} + {B_i} + {C_i} + {D_i} + {E_i} + {F_i}} \right)} \hfill \cr }

where the parameters A_i, B_i, C_i, D_i, E_i, F_i are variable expressions. Equations describing those expressions have been previously described by the authors in [9, 10].

The modulus determined by this model is the average value of the modulus in the thickness of the considered soil layer.

THE PRACTICAL USE OF MODELS

3.1.

Description of the embankments overload – literature analysis

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 20^th 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.

Table 1.

The details of embankments [13, 15, 16, 17, 18]

	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	w = 418% (peat);w= 135% (gyttja)	Peat – w = 426%
Bulk density	Peat – γ =10.5 kN/m³Gyttja – γ =13.5 kN/m³	Peat – γ =10.5 kN/m³
Organic matter content	Peat – I_ż = 99%;Gyttja – I_ż = 44.25%	Peat – I_ż = 90%

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]

3.2.

Analysis of the constrain elasticity modulus based on the literature

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): (9) $σ_{0} (t) = γ (H_{n} - s (t)) + γ^{'} s (t)$ {\sigma _0}\left( t \right) = \gamma \left( {{H_n} - s\left( t \right)} \right) + \gamma 's\left( t \right) where: γ

the unit weight of the embankment;

γ’

the effective unit weight of of the embankment;

H_n

the initial height of the embankment;

s(t)

settlement in time [3].

The initial stresses by embankment 1 on the subsoil are σ₀ = 35 kPa and for the second σ₀ = 40 kPa. The effective unit weight the embankment no 1 is γ’= 9.21 kN/m³ and for no 2 is γ’ = 9.21 kN/m³ [13, 15, 16, 17, 18].

The changes of stresses working on the subsoil σ₀(t) taking into account the pore pressure and settlement in time s(t) for embankments 1 and 2 at the measurement points is presented in Figure 4 and 5.

The change of stresses working on the subsoil σ(t) and settlement in time s(t) for embankments

The changing settlement in time s(t) for embankments

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).

SUMMARY

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 (E_m1) throughout the column. The second model assumes that the stress distribution from the external load in the organic soil layer is variable. This method also takes into account the dependence of the constrain elasticity modulus (E_m2) on the value of peat settlement M=M(s) according to Meyer [11, 12]. For each elementary design volume of organic soil. In this method, the constrained elasticity modulus changes with the settlement.

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..

eISSN:: 2720-6947
Idioma:: Inglés

Calendario de la edición:: 4 veces al año
Temas de la revista:: Architecture and Design, Architecture, Architects, Buildings

RSS Feed de revista

Analysis of Using the Empirical Model of Organic Soil Consolidation to Predict Settlement

Publicado en línea: 20 jul 2023

Páginas: 111 - 117

Recibido: 15 ene 2023

Aceptado: 27 mar 2023

DOI: https://doi.org/10.2478/acee-2023-0020

Palabras clave
Compressibility of organic soil, Consolidation of organic soils, Constrained modulus, Modulus of elasticity, Peat

© 2023 Zygmunt Meyer et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Analysis of Using the Empirical Model of Organic Soil Consolidation to Predict Settlement

Publicado en línea: 20 jul 2023

Páginas: 111 - 117

Recibido: 15 ene 2023

Aceptado: 27 mar 2023

DOI: https://doi.org/10.2478/acee-2023-0020

Palabras claveCompressibility of organic soil, Consolidation of organic soils, Constrained modulus, Modulus of elasticity, Peat

© 2023 Zygmunt Meyer et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Palabras clave
Compressibility of organic soil, Consolidation of organic soils, Constrained modulus, Modulus of elasticity, Peat