J. Cent. South Univ. Technol. (2008) 15(s1): 381-385
DOI: 10.1007/s11771-008-384-1
Mechanism and calculation method of rheological settlement of high-filled embankment
WANG Zhi-chao(王智超)1, 2, LUO Ying-she(罗迎社)3, TANG Song-hua(唐松花)1
(1. Institute of Fundamental Mechanics and Material Engineering, Xiangtan University, Xiangtan 411105, China;
2. College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, China;
3. Institute of Rheological Mechanics and Material Engineering, Central South University of Forestry and Technology, Changsha 410004, China)
Abstract: The characteristics of high-filled embankment rheological settlement were analyzed; mechanical calculation model of high-filled embankment rheological settlement during constructing and running period was also put forward. Combining the macroscopic and microscopic deformation properties of the engineering soil grain, its constitutive model was set up and its characters were fully revealed, at the same time, its practical calculation formula under the action of dead-weight load was derived, which is feasible by analysis and comparison.
Key words: high-filled embankment; rheological settlement; calculation method
1 Introduction
In recent years, along with the stretching of the express-way gradually to the Midwest districts of China, more and more high-filled embankments have appeared, the common difference of elevation height of filling interface is 6-10 m, the maximum always surpasses 18 m. Comparing the general embankment, it possesses these characters: the height of filling and post- construction settlement quantity is great; the time of post-construction settlement is long, etc. It becomes an important subject in highway constructing scientific field in the Midwest districts how to calculate and predict effectively its post-construction settlement and eliminate the harm of its settlement.
Owing to the soil being an engineering material of multiphase, anisotropy, inhomogeneity and discontinuity, its settlement problem is quite complex and unsolved up-to-date. At present, the semitheoretical-semiempirical settlement calculation method (layerwise summation method) is still used in designing the highway subgrade in our country[1]. This is a simple and easy method, but it cannot reveal the settlement mechanism, furthermore, the lateral soil mass deformation cannot be considered in calculating, and the difference between the calculating result and practical measured values is great. So that the non-linear elastoplastic model which is adopted to promote the original settlement calculation method was put forward[2]. But because the principal problem in post-construction settlement is an ageing one, the above method cannot reflect this feature. Along with the development in the field of computer and artificial intelligence, some scholars tried to apply this calculating method to treating the practical measured settlement data through computer numerical treatment to predict the final settlement of embankment[3], which avoided intentionally the constitutive model problem of complex geo-material, and could use the finite data to comprehensively reflect the approximate laws of embankment settlement. However, it would be short of the inherent law deduction, which could only provide one reference as the empirical method. Obviously it is unreliable to the important and complex problems of high-filled embankment settlement. Therefore starting from the mechanism of high-filled embankment settlement and combining the features of macroscopic and microscopic deformation of the engineering soil grain, in this work the constitutive model of high-filled embankment rheological settlement was set up, and the research on the problem of high-filled embankment post-construction settlement was made on the basis of the existent mature calculating theory, which has stronger pertinence and theoretical and practical significance.
2 Characteristics of high-filled embankment rheological settlement
2.1 Unity of traditional consolidation and rheological settlement
According to the traditional consolidation theory (both Terzaghi consolidation theory and 3-D Biot
consolidation theory), it considers that the embankment soil settlement quantity S, under the action of load, could be divided into three parts in the light of its deformation feature: immediate settlement Sd, consolidation one Sc and secondary consolidation one Ss, the calculation formula is
S = Sd + Sc + Ss (1)
where the consolidation settlement is the deformation caused by the dissipation of excess pore water pressure, while the secondary consolidation settlement is the result of the creep produced by the soil skeleton after the finishing of the excess pore water pressure dissipation. In engineering, the secondary consolidation settlement is always neglected because of its less. But its existence reveals to a certain extent the consolidation theory being imperfect. Owing to the time effectiveness of soil mass deformation being objective, how to reveal its essence in theory, an approach was made from the angle of rheology. Taking Kelvin Model (the most simple binary element rheological model, where [N] denotes dashpot body, [H] denotes spring body) as an example, at the instancy of applied external force, all the load is borne by [N] body, while [H] body has not any displacement, and does not bear external force. As time goes on, [H] body should share a part of load. The deformation would not be stable until all the load is borne by [H] body. However, the traditional consolidation theory considers that at the instancy of applied load, it is all borne by the pore water (air). As the time goes on, external force gradually is transferred to the soil grain skeleton; consolidation does not end until the excess pore water pressure dissipates fully. The discovery is from the comparison of the two theories, the starting points are different, but they are similar in mechanism. The action done by the pore water (air) in consolidation theory and [N] element in rheological model are the same in mechanism[4]. As the rheological model can simultaneously reflect the various parts of the soil mass deformation: instantaneous deformation, attenuated creeping deformation, viscous flowing deformation and accelerative creeping deformation. It can be considered that the course of embankment rheological settlement would contain the traditional consolidation settlement, namely traditional embankment consolidation settlement is one part of embankment rheological settlement.
2.2 Features and influence factors of high-filled embankment rheological settlement
The obvious feature of the high-filled embankment lies in “highness” (see Fig.1), i.e. the filling quantity is great, and leads to the gravity load on the foundation top-surface being great, caused by which, the internal force is far greater than that caused by the load of vehicles in running period. Therefore, the gravity load of high-filled embankment is the main reason which causes rheological settlement. Its settlement quantity S contains two sorts: 1) the settlement S0 caused by the embankment filling height and compaction should be controlled in the period of construction; 2) the settlement St caused by time effectiveness, which is the main reason of the post-construction settlement. The calculation formula is
S = S0 + St (2)
Seeing from the embankment settlement field monitoring result of “Chang-Zhang and Heng-Zao expressway” in Ref.[5], in the range of the similar filling rate and observational time, it would increase with the increment of the filling height for the embankment rheological settlement and average rheological settlement deformation rate (see Fig.2), the rheological effect is more obvious. Furthermore, its rheological settlement still has the close relation with the soil earthiness of the filling (see Table 1). The relative grain size of filling with shale is larger, pore is larger, grain grading is worse, its average settlement quantity is greater. It is thus evident that all the filling height, soil earthiness and gradation of high-filled embankment are important factors which affect its rheological settlement.
As to the study of soil microscopic structure，its macro anti-deformation capability has relations with microscopic grain configuration, distributive feature, porosity and contact belt distribution characteristics[6].
Fig.1 Schematic diagram of cross section composition of high-filled embankment
Fig.2 Fitting curves of change of embankment settlement and filling height[5]
Table 1 Statistics of different filling earthiness settlements[5]
Through plentiful test of clay soil, it has discovered that: 1) clay soil microscopic structure deformation in pressure generally goes through three stages: structure recovery stage (internal force≤0.1 MPa), structure reconstruction stage (0.1 MPa＜internal force≤0.4 MPa), structure solidification stage (internal force＞0.4 MPa or 0.8 MPa); 2) On the micro-level, clay soil macro deformation mainly displays in pore configuration adjustment and grain shape change, and the changes of other structure factors (such as directivity, grain diameter etc.) have little influence on it; 3) Owing to the existence of pore water and gas in soil micro structure, the structure adjustment of clay soil during its rheological consolidation is closely related to initial state and pore water permeability. At present, the relationship between soil grain microscopic structure parameters and its macro physical quantity still cannot directly be established, but the conclusion obtained by experiment can provide reference for construction of constitutive model of high-filled embankment rheological settlement.
3 Calculation method of high-filled embank- ment rheological settlement
3.1 Mechanical calculation model of high-filled embankment
The mechanical calculation model of high-filled embankment rheological settlement has important connections with construction modes. During the current construction, it used to adopt the manner of layered filling and then compacting layer by layer. The physical and mechanical properties of filling soil and foundation soil have very great difference with compacting treatment, so the two research objects should be selected and be analyzed respectively (see Fig.3). Origin O is control point of middle line in highway alignment design, AB is ground line before construction, and CD is a certain ground line during layered filling. The total settlement S of embankment is
(3)
Fig.3 Schematic diagram of mechanical calculation model of high-filled embankment
3.2 Construction of constitutive model of high-filled embankment rheological settlement
The two states of pre and post compacting are mainly considered for filling soil of embankment. When the filling soil is in the state of pre-compacting, it is a kind of loose media; its constitutive model construction is mainly based on mass conservation, and also needs to be combined with controlling index (degree of compaction) of subgrade construction:
(4)
where γs is the unit weight of filling soil before compaction; 
is the maximal dry unit weight of compacting soil in room; 
is the average compaction degree of filling soil, it has relations with water content of soil, grain diameter, and degree of saturation[7]; V and V′ are the volume of filling soil before and after compaction respectively. When the filling soil is in the state of post-compacting, the deformation of filling soil tends to be stable according to the known experimental data. So it can be regarded as a rigid material in this state:
ε→0 (5)
For the foundation soil, it is difficult to find a common constitutive model, which can reflect its various kinds of properties, because it is greatly affected by its forming history and natural environment factor. However, it is objective for the rheology of its settlement increases depended on time. Assuming that it is a kind of rheological viscoelastic material, the constitutive model of one-dimension rheology is adopted to simplify the question, its general formula is
(6)
where the value identification of n, m, {p1, ???, pn} and {q1,???, qm}[8] needs to be combined with the microcosmic deformation characteristics of foundation soil, and also refers to the experiment and theoretical derivation method of the traditional consolidation theory. Taking three elements standard solid model (H-K) as an example (as Fig.4), its rheological equation is
(7)
Fig.4 Three elements standard solid model (H-K) (a) and creep curve (b)
Under the constant stress σ, using initial condition ε0 = σ/E0, there is
(8)
(9)
where E0, E1 and η1 are gained by experiment, due to that the constitutive model of subgrade soil is not totally an one-dimension linear rheological relationship, so those parameters need to be modified to
, 
and 
, combining with the measured data when calculating the settlement, in order to give a more accurate prediction. Comparing Eqns.(1) and (8), it can find that there is some corresponding relation between them. This shows that the rheological constitutive model can reflect the three components of traditional settlement at the same time.
3.3 Simplified calculation method of high-filled embankment rheological settlement
Because the construction of filling embankment always adopts the method of compacting its edge firstly and its middle last, it is helpful for controlling its horizontal displacement. In order to simplify the calculation, the horizontal displacement of embankment is neglected during compacting, then
(10)
Supposing that the additional internal force caused by the gravity load of embankment in the foundation soil is σz, there is
(11)
The total settlement of embankment is
(12)
where σz can be calculated by improved Bossiness solution, and its solution distribution can also be obtained by FEM method in the complex problems.
4 Results
1) The problem of high filled embankment settlement is discussed, and the traditional consolidation settlement is compared with rheological settlement. The results show that traditional embankment consolidation settlement is one part of embankment rheological settlement.
2) The deduced calculation formula of embankment settlement can reflect rheological settlement phenomenon, but in order to simplify calculation, only one-dimension linear rheological settlement problem is analyzed here. However, the problem of three-dimension inhomogeneous nonlinear rheological settlement remains to be studied by using FEM method and more reasonable rheological constitutive model.
References
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[4] SUN Jun. Geo-material rheology and its application in engineering [M]. Beijing: Architecture Industry Press, 1999. (in Chinese)
[5] XU Xiao-yu. Research on settlement character and prediction method for high embankment [D]. Changsha University of Science and Technology, 2005. (in Chinese)
[6] HU Rui-lin, et al. Quantitative microstructure models of clayey soils and their engineering behaviors [M]. Beijing: Geological Publishing House, 1995. (in Chinese)
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(Edited by YANG Hua)
Foundation item: Project(06C843) supported by the Scientific Research Fund of Hunan Provincial Education Department, China
Received date: 2008-06-25; Accepted date: 2008-08-05
Corresponding author: WANG Zhi-chao, PhD; Tel: +86-732-8293694; E-mail: wzc98231@163.com
