A simplif i ed method for prediction of embankment settlement in clays

Chunlin Li*

InstituteofCivilEngineering,TonglingUniversity,Tongling244000,China

A simplif i ed method for prediction of embankment settlement in clays

Chunlin Li*

InstituteofCivilEngineering,TonglingUniversity,Tongling244000,China

A R T I C L E I N F O

Articlehistory:

Received 22 October 2013 Received in revised form

23 November 2013

Accepted 9 December 2013

Simplif i ed method

Settlement prediction

Embankment

Consolidation theory

Clayey soil

The prediction of embankment settlement is a critically important issue for the serviceability of subgrade projects, especially the post-construction settlement. A number of methods have been proposed to predict embankment settlement; however, all of these methods are based on a parameter, i.e. the initial time point. The difference of the initial time point determined by different designers can def i nitely induce errors in prediction of embankment settlement. This paper proposed a concept named “potential settlement” and a simplif i ed method based on the in situ data. The key parameter “b” in the proposed method was verif i ed using theoretical method and fi eld data. Finally, an example was used to demonstrate the advantages of the proposed method by comparing with other methods and the observation data.

? 2013 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. All rights reserved.

1. Introduction

The one-dimensional (1D) consolidation equations proposed by Terzaghi are the cornerstone of soil mechanics. Settlement calculated using Terzaghi’s 1D consolidation theory (Terzaghi, 1925) has been widely used, but it is not always effective due to the uncertainty of coeff i cient (Asaoka, 1978). Many methods for settlement prediction based on observation data have also been proposed, for example, Asaoka method, hyperbolic method (Tan et al., 1991), parabola method (Xu and Xu, 2000), and in situ tests (Bergado et al., 1991). The Asaoka method and hyperbolic method are widely used due to their simplicity (Anderson et al., 1994; Tan, 1994, 1995, 1996). However, limitations still exist in both methods that the initial time point is necessary to be determined fi rst; and the difference of the initial time point determination can signif i cantly inf l uence the accuracy of the settlement prediction. Therefore, this paper proposed a simplif i ed method based on the Terzaghi’s 1D consolidation equation irrelevant to the initial time point and compared it with other methods to verify its effectiveness.

2. Theory of Asaoka’s method

In 1978, Asaoka proposed a new settlement prediction method, the philosophy of which is based on “observational procedure”. The theory is derived from 1D consolidation equation. He combined Mikasa’s (1965) equation with Terzaghi’s (1925) equation, and obtained the vertical strain as

where ε(t,z) is the vertical strain ofzat timet;TandFare unknown functions of time;cvis the coeff i cient of consolidation.

With the two boundary conditions, i.e. drainage from both top and bottom boundaries and upward drainage, the following equations can be derived:

whereSis the settlement,His the thickness of clay stratum, andˉε is the vertical strain at initial time.

The discrete time can be introduced as

where Δtis the equal time interval.

Fig.1.Hyperbolic plots of Terzaghi theory (after Tan, 1995).

From Eqs. (2) and (3), the settlement at timejcan be written as

whereSjandSj-1are the settlements at timejandj- 1; β0, β1are unknown parameters.

When the state is stable, the fi nal settlementSfcan be obtained by the following equation:

whereSfis the fi nal settlement.

From Eq. (5), we realize that the fi nal settlement is the intersection of relationship line betweenSjandSj-1with 45°line in theSj-Sj-1plot.

IfSjandSj-1are substituted bySfin Eq. (4), Eq. (4) can be simplif i ed to

And the settlementS(t) at timetcan be calculated as follows:

whereS0is the settlement at the initial time.

In Eq. (7),S0should be determined fi rstly before settlement prediction. The different values ofS0can result in different values ofS(t), thus the precision depends greatly on the selection of the initial time. However, the selection of the initial time point will be different by different designers, which can cause the deviation of settlement calculation.

Fig.2.Hyperbolic plots of fi eld settlement (Tan, 1995).

Fig.3.The determination of parameterbin the section K5+800.

3. Theory of hyperbolic method

The hyperbolic method proposed by Tan et al. (1991) has its origins in the rectangular hyperbolic fi tting method proposed by Sridharan and Rao (1981) and Sridharan et al. (1987). According to the Terzaghi’s theory of consolidation (1925), the settlementtime relationship can be expressed usingUandTv. The relationship betweenTv/UandTvis shown in Fig. 1. From Fig. 1, we can see that the linear portion is betweenU60andU90, which can be represented as

where α is the slope and β is the intercept of the hyperbolic plot.

Based on the fi eld data (Tan, 1995), the relationship between settlement δ and timetis shown ast/δ vs.tin Fig. 2.

The slopes ofs60ands90can be determined by

wheresiand αiare the initial slope of linear segment in Figs. 1 and 2, respectively. So the fi nal settlement δfcan be calculated by the following equation:

Fig.4.The determination of parameterbin the section K6+180.

The limitation of this method is also the determination of the initial time point, since this method is based on the initial slope of the settlement; the difference of the initial time point can result in the difference of settlement. The constant-load condition was assumed in the hyperbolic method, thus the settlement before the end of loading cannot be predicted. During the loading period, the settlement rate varies widely, and the initial slope is diff i cult to judge. Sun et al. (2002) proposed a method of initial point determination by the regression analysis of observation data, but it is somewhat complicated to be applied in practice.

4. Proposed method

As discussed above, Asaoka’s method and the hyperbolic method are not very adequate for the prediction of embankment settlement, since some parameters are diff i cult to be determined and the initial time is a subjective choice. Most of settlements are the results of consolidation, so consolidation theory is commonly used to predict the settlement. As mentioned previously, Terzaghi’s 1D consolidation theory is not always effective due to the uncertainty of coeff i cient determination, but the trend of the settlement is constant, thus an improved method for predicting the trend of the settlements is necessary.

According to the loading levels, the settlement induced by loads can be calculated using Terzaghi’s 1D consolidation equation. The settlement at a given time can be computed as

Fig.5.The determination of parameterbin the sections (a) K6+300 and (b) K6+260.

wheres∞is the fi nal settlement,stis the settlement at timet, andbis an unknown coeff i cient.

In order to simplify the calculation, we def i ne the “potential settlement” as

wherespis the potential settlement, which will happen in the future, suggesting the difference between current and fi nal settlements.

In Eq. (13), the parametersbands∞of Terzaghi’s 1D consolidation equation should be determined fi rstly. The parameterbcan be obtained from in situ data and Asaoka’s method, as described below.

From Eq. (13), it is clear that the relationship between ln[spπ2/(8s∞)] andtis linear, so parameterbcan be determined from the observation data. On the scale, the parameterbrepresents the slope of the straight line.

It is well-known that the parameterbrepresents the conditions of drainage in Terzaghi’s 1D consolidation equation, which can be calculated using the consolidation coeff i cient and drainage length under two kinds of drainage conditions, as shown in Table 1.

It is important to discuss the consistency of the parameterbacquired by theoretical analysis data and the observation data to ensure the effectiveness of the proposed method. Five sampling positions were chosen in the sections of K5+800–K7+320 ofAnyang–Xinxiang Highway. The parameterbdetermined by theoretical method in Table 1 is showed in Table 2.

Based on the observation data, the parameterbcan be obtained according to proposed method, and calculation results of the parameterbare presented in Figs. 3–7.

By comparing the values ofbin Figs. 3–7 and Table 2, the parameterbcalculated using the consolidation theory is consistent with the proposed method under two drainage conditions (drainage from both top and bottom boundaries and upward drainage), so the parameterbcan be derived using the proposed method.

With the parameterbobtained by Eq. (13), the potential settlement can be calculated from the fi nal settlements∞and the observational settlement at timet. The key to predict settlement is to obtain the value ofs∞. Although the Asaoka’s method has some restriction, the fi nal settlement predicted by this method is very precise (Anderson et al., 1994),s∞may be calculated by Asaoka’s method.

Based on the theory and parameter analysis mentioned above, the procedure of this method is summarized as follows:

Fig.6.The determination of parameterbin the sections of (a) K7+106 and (b) K7+110.

Table1The value ofbunder different drainage conditions (after Zhang et al., 2005).

Fig.7.The determination of parameterbin the section K7+320.

(1) The fi nal settlements∞is calculated by Asaoka’s method.

(2) The potential settlementspis obtained using the observation data ands∞.

(3) The linear relationship between ln[spπ2/(8s∞)] andtis plotted, and the slope of this line isb.

Table2Parameterbcalculated by consolidation theory.

Fig.8.The relation between fi lling thickness and time.

Fig.9.Determination ofs∞by Asaoka’s method.

Fig.10.Determination of the parameterbwith the present method.

Fig.11.Results comparison of different methods with the observation data.

(4) Settlement at a given time can be obtained by substituting the value ofs∞andbto Eq. (12).

5. Case study

In order to investigate the accuracy of the proposed method, the calculated results using the proposed method were compared with the observational data of Anyang–Xinxiang Highway. Then a statistical analysis was carried out to analyze the difference of results between proposed method and the observation data.

In the case of the present study, the relationship between roadbed fi lling thickness and time is shown in Fig. 8, ands∞was obtained by Asaoka’s method in this case (Fig. 9), while the parameterbcan be obtained by proposed method (Fig. 10).

According to Eq. (12), we have

The comparison among the proposed method, Asaoka’s method, hyperbolic method and the observation data shows that the results by proposed method are closer to the observation data than Asaoka’s method and hyperbolic method (Fig. 11).

6. Conclusions

Compared with other methods, the proposed method has a better adaptability to soil conditions. For instance, the proposed method is more accurate than hyperbolic method when settlement of embankment is quite small (i.e. the soil layer is relatively good); and the proposed method is more accurate than Asaoka’s method, especially in the early stages of the post-construction settlement on soft clay. Of course, the proposed method also has its limitations, and the accuracy of settlement prediction mainly depends on both the accuracy of the observation data and the proper choice of the discrete time step (Δt). In this study, major conclusions can be drawn as follows:

(1) The proposed method is simple and the fi nal settlement can be obtained using two fi gures (Figs. 9 and 10).

(2) The parameterbwas calculated using the theoretical method and the observation data under two kinds of drainage conditions. The comparison illustrates that the proposed method is suitable under different drainage conditions.

(3) The results calculated by proposed method are verif i ed by the comparison with other methods and fi eld data in Fig. 11, andthe results calculated by the proposed method is closer to the observations than other two typical methods.

(4) The trend of the settlement is constant and the precision of settlement acquired by the proposed method is not dependent of the initial time point selection, so it can be applied to predicting the embankment settlement at any time.

Conf l ict of interest

The author does not have any possible conf l icts of interest.

Acknowledgements

This paper is a part of the project “Universities Natural Science Research Project in Anhui Province” (KJ2011Z375), which is supported by Department of Education of Anhui Province. The author wishes to express his gratitude for the support given to this work.

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Dr. Chunlin Li is Associate Professor in the Institute of Civil Engineering of Tongling University in China. He got his M.S. degree in Geotechnical Engineering from Zhengzhou University, China, in 2003, and Ph.D. in Geotechnical Engineering from Southeast University, China, in 2012. His research interests are focused on road nondestructive examination, the basic characters of soft soil for subgrade, and soil disturbance characteristics for underground engineering constructions. He has participated in a large number of projects in design and construction of subgrade and pavement, including the Wuxi Subway Line Project No. 1.

*Tel.: +86 13856250392.

E-mailaddress:lichunlin111@126.com

Peer review under responsibility of Institute of Rock and Soil Mechanics, Chinese Academy of Sciences.