# A Practical Design Method for Reducing Postconstruction Settlement of Highway Subgrade Induced by Soil Creep

Authors: Fei Zhou; Tangdai Xia; Bingqi Yu; Fan Xia; Fan Yu
Journal: Geofluids
 (2021)

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## Abstract

The postconstruction settlement of the bridge approach is usually uneven, which could create a bump in the roadway. Indeed, this is a typical situation at the end of the bridge approach and requires a solution. One of the main causes of postconstruction settlement is the creep of soil. This paper is aimed at generalizing a new design method for controlling highway postconstruction settlement by replacing subgrade with expanded polystyrene (EPS). In the new method, the creep coefficient can be calculated based on the Yin-Graham EVP model. Thus, the relationship between the overloading ratio (OLR) and overconsolidation ratio (OCR) is obtained. The new method involves five steps: (a) determine the creep coefficient based on the relationship between the creep coefficient and over consolidation ratio, (b) divide the ground into a suitable number of sublayers, (c) select groups of different overloading ratios and then calculate the average values of the additional stress and overconsolidation ratio for each sublayer under different OLRs, (d) calculate the postconstruction settlement under different OLRs, and (e) determine the replacement capacity for different sections. This method can be used for quantitative design according to different requirements of postconstruction settlement of foundation. Taking Huzhou Avenue as an example, the case study illustrates the calculation process of the new method in detail.


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## Body

## 1. Introduction

The bridge approaches provide a smooth transition of cars from roadway pavements to bridge structures. However, the postconstruction settlement of bridge approaches is usually uneven, which could create a bump in the roadway. Indeed, this is a typical situation at the bridge approach and requires a solution.The bump at bridge-head is a complicated technical problem. The creep of soil is one of the main causes of postconstruction settlement. The soil exhibits creep properties. Compared with primary consolidation settlement, creep settlement is small but significant, especially for soft clay. In the past several decades, extensive studies have been conducted on the creep of soft clay. Ladd et al. [1] first proposed the question of whether creep settlement occurs in the process of primary consolidation settlement. And there are two different views on whether the creep occurs during primary consolidation. They summed them up as Hypothesis A and Hypothesis B. Hypothesis A holds that creep occurs only in the secondary consolidation stage, and no creep occurs in the primary consolidation stage. Mesri et al. [2–4], Wang et al. [3], and Mesri and Vardhanabhuti [4] support Hypothesis A. However, Hypothesis B believes that the soil creep is caused by its own viscosity and occurs from the beginning of the primary consolidation process. It is supported by Bjerrum [5], Stolle et al. [6], Nash and Ryde [7], Yin et al. [8], Suklje [9], Bouchard et al. [10], Berre and Iversen [11], Leoni et al. [12], Karim et al. [13], and Nash and Brown [14]. As is known, with the effective stress changes, the creep always exists actually, which means that Hypothesis B is reasonable. Based on Hypothesis B and the equivalent time concept, Yin and Graham [15–18] proposed a 1D elastic viscoplastic (EVP) model for creep behavior, which can be used to calculate the creep settlement. According to the EVP model, the creep coefficient is closely related to the over consolidation ratio (OCR).Some compression tests [19–21] have shown that the creep coefficient decreases with the increase of OCR. Therefore, the use of a preload larger than the final construction load is an effective method to reduce postconstruction settlement [22–26]. However, in the actual project, for some sections, the preloading period is insufficient so that it is difficult to achieve the original effect within the time limit of the project. The method of replacing part of subgrade with lightweight materials to reduce the permanent load of subgrade can solve the problem [27, 28]. Expanded polystyrene (EPS) is one of the high-quality lightweight materials [29]. EPS has the characteristics of ultralightweight, compressibility resistance, self-reliance, water resistance, flame retardant, and so on. The density of the EPS material is generally 0.2 ~ 0.3 kN/m3, which is equivalent to 1/100~1/60 of the soil density. EPS has high compressive strength and varies with density, so it can be used as an embankment filling material in the elastic range of 80~140 kN/m2. EPS is a synthetic resin foam containing independent bubbles that do not absorb water. The physical properties and mechanical indexes of the EPS material change little in the aging process, excellent aging resistance, and its aging life is more than 60 years.It is important to determine the appropriate thickness of EPS to control the postconstruction settlement but there are only few studies in this area. Chen et al. [30] suggest that consolidation, compression, and other parameters can be calculated according to the monitoring data, and the calculation program of foundation settlement reflecting the process of overloading-unloading and reloading should be compiled. Then, the relationship between different capacities of lightweight material and postconstruction settlement is obtained. Thus, the thickness of the lightweight material can be determined according to the allowable postconstruction settlement. Many factors are considered in this method, but it is difficult to be generalized and applied in engineering due to its complex calculation. Jiang et al. [31] come up with a formula to calculate the thickness. However, this formula also relies on monitoring data and the postconstruction settlement is only estimated according to the measured data. Therefore, this formula may not be used in the stage of design.This paper is aimed at proposing a new practical design method for controlling highway postconstruction settlement by replacing subgrade with EPS. First, the functional relationship between the creep coefficient and overconsolidation ratio is established by fitting the one-dimensional compression test data. Second, the relationship between the overloading ratio (OLR) and overconsolidation ratio (OCR) is deduced. Then, groups of different OLR are selected and the postconstruction settlement under different OLRs is calculated. This method can be used for quantitative design according to different requirements of postconstruction settlement of foundation. And it can make the OLR greater than 1.3 without the limitation of foundation stability.


## 2. Creep Coefficient of Overconsolidated Soil

Buisman proposed the concept of secondary consolidation coefficient (Cα). As is shown in Figure 1, it is believed that the e−lgt curve is close to a straight line after primary consolidation. The slope of the straight line part i is defined as secondary consolidation coefficient Cα.
(1)Cα=e0−e1lgt1−lgt0,where t0 is the time at the end of primary consolidation and t1 is any time after the end of primary consolidation.Figure 1
Primary consolidation and secondary consolidation of normally consolidated soil.However, Equation (1) is not applicable to the overconsolidated soil because overconsolidated soil has finished primary consolidation before test. In 1964, Crawford [32] conducted normally consolidated soil compressive rheological tests and plotted e−lgp curves of different consolidation times. In 1967, Bjerrum made a creep diagram. As is shown in Figure 2, he divided the displacements which he observed in the actual engineering into “instant compression” and “delayed compression” and proposed that the delayed compression can be described with parallel lines in e−lgσ space.Figure 2
Bjerrum’s creep diagram.Based on Bjerrum’s creep diagram, Yin-Graham proposed the 1-D EVP model, and the total strains can be written as follows:(2)εz=εzo+λVlnσz′σzo′+ψVlnte+toto,where εzo is a reference strain and εz is the total strain. σzo′ is a reference stress that corresponds, respectively, to the strain at the beginning of loading. For normally consolidated soil, σzo′ corresponds to strain εzo. V is the specific volume of the soil (1+e), that is, the volume occupied by unit volume of solids. So λ=Cc/2.303 and ψ=Cαe/2.303, where Cc and Cαe are the compression index and creep coefficient under logarithmic coordinates. Here, we call Cαe “creep coefficient” instead of the “secondary consolidation coefficient”, because Equation (2) considers creep occurs during and after “primary consolidation.” And to is a parameter that can be measured by one-dimensional compression test, which is usually taken as unit time or the boundary point between the primary consolidation and secondary consolidation [33]. te is called the equivalent time as defined by Yin and Graham.According to Equation (2), the void ratio e, the effective stress σ, and the equivalent te have a unique relationship.
(3)e=eo−Cclgσz′σzo′−Cαelgte+toto.As is shown in Figure3, no matter if it is normal consolidation soil or overconsolidated soil, the zero point of time is taken as the loading start time of its corresponding normal consolidation condition. For example, point 2 in Figure 3 is under overconsolidation condition, and its corresponding normal consolidation condition is point 5 on the normal consolidation line. The time corresponding to point 5 is the beginning time. And te is the equivalent time that is from point 5 to point 2. Such a time coordinate system combines normal consolidation and overconsolidation into a unified time coordinate system, so it is called an absolute time coordinate system. Now, te can be found from
(4)Cαe0lgte+toto=Cc−Celgσz′σzo′,where Cαe0 is the normal consolidation soil creep coefficient and Ce is the expansion coefficient. From which
(5)te=toσz′σzo′Cc−Cs/Cαeo−to.Figure 3
Equitimee−lgp curves.Let(6)OCR=σz′σzo′,δ=Cc−CsCαeo.te can be expressed as follows:
(7)te=toOCRδ−to.According to Equation (7), te is a parameter related to OCR, and it can reflect the stress history and the state of soil. For overconsolidated soil, the creep coefficient of overconsolidated soils can be expressed as
(8)Cαe=e1−e2lgte2+to/te1+to=e1−e2lgte1+Δt+to/te1+to=e1−e2lg1+Δt/te1+to,where te1 and te2 are the equivalent time; e1 and e2 are the void ratios at equivalent time te1 and te2, respectively; and △t is the current load duration from te1 to te2.According to Equations (7) and (8), the creep coefficient is not a constant. It can be expressed as a function with overconsolidation ratio.
(9)Cαe=fOCR.


## 3. The Relationship between Overconsolidation Ratio (OCR) and Overloading Ratio (OLR)

The maximum value of load in the past, namely, the preload, divided by the present value of load, is defined as the overload ratio (OLR). Overload ratio (OLR) was proposed to reflect overload state, which can be expressed as follows:(10)OLR=popf,where po is the preload, that is, the load under the condition of overload preloading. pf is the present value of load, that is, the final construction load on the ground surface.The maximum value of effective stress in the past, namely, the preconsolidation pressure, divided by the present value of effective value of effective stress, is defined as the overconsolidation ratio (OCR).(11)OCR=σcσ0,where σo is the present effective stress and σc is the preconsolidation pressure.When the load on the ground surface changes, the stress state of each point in the soil stratum will change, and OCR will also change. For example, as is shown in Figure4, point A is under normal consolidation condition before loading. That is, σo is equal to γiz.Figure 4
Cross-section of EPS filling.In soil mechanics, when loadpo is applied to the ground surface, the vertical additional stress σm is equal to αpo. Here, α is the additional stress coefficient which can be calculated based on the depth of soil and the load distribution type. It is convenient that we can look up the additional stress coefficient table to determine its value. And when final load pf is applied to the ground surface, the vertical additional stress σf is equal to αpf. So, the OCR of point A can be expressed as follows:
(12)OCR=σo+σmσo+σf=γiz+αpoγiz+αpf.As is shown in Figure4,
(13)H=h+Δh+hs,(14)pf=γh+γEΔh+γshs,(15)po=γH=γh+Δh+hs,where γ, γE, γi, and γs indicate the unit weight of filling soil, EPS, soft soil, and pavement, respectively; h, △h, and hsindicate the thickness of soft soil, EPS, and pavement, respectively; and H is the designed height of embankment fill.Let us establish the relationship between the OCR and OLR. Based on Equations (10) and (11),
(16)OCR=γiz+αγh+Δh+hsγiz+αγh+γEΔh+γshs=γiz+αγh+αγE+γ−γEΔh+αγs+γ−γshsγz+αγh+γEΔh+γshs=1+γ−γEΔh+γ−γshsγh+γEΔh+γshs+γiz/α,(17)OLR=γh+Δh+hsγh+γEΔh+γshs=γh+γE+γ−γEΔh+γs+γ−γshsγh+γEΔh+γshs=1+γ−γEΔh+γ−γshsγh+γEΔh+γshs.According to Equations (14) and (15).
(18)1OCR−1−1OLR−1=γizαγ−γEΔh+γ−γshs.Let(19)βz=γizαγ−γEΔh+γ−γshs.Thus, OCR, OLR, andz have a relationship:
(20)OCR=1+11/OLR−1+βz.


## 4. The New Method for Controlling Postconstruction Settlement

### 4.1. Procedures of Applying the Practical Design Method

The new method for controlling postconstruction settlement involves the following 5 steps:(a)
Determine the creep coefficient. Based on the Yin-Graham EVP model, the functional relationship between the creep coefficient and overconsolidation ratio is established by fitting the one-dimensional compression test data(b)
Divided the ground into a suitable number of sublayers. Each sublayer within a same soil layer should not be overly thick. The thickness of each sublayer should be controlled within 2 m-4 m. For each sublayer, it is assumed that pressure is uniformly distributed(c)
Select groups of different OLRs and calculate the average values of the additional stress and OCR for each sublayer under different OLRs. The OLR usually ranges from 1.1 to 1.6 in actual projects. Based on Equation (19), the additional stress and OCR at the center point of each sublayer are calculated and the values are taken as the average additional stress and OCR for each sublayer(d)
Calculate the postconstruction settlement under different OLRs. Based on the functional relationship betweenCαe and OCR, the creep coefficient of each layer is determined according to the average overconsolidation ratio for each sublayer. According to Equation (20), the settlement of each sublayer was calculated and the total postconstruction settlement of ground can be calculated as follows:(21)s=∑i=1nHi1+eoiCαeilgt1+Δtt1,where s is the total postconstruction settlement of ground, Hi is the thickness of each sublayer, Cαei is the creep coefficient of each sublayer, t1 is the preloading period, and △t is the service period which is usually taken as 15 years
(e)
Correct the settlement value with the safety factorμ and determine the overload ratio and the replacement capacity under the requirements of postconstruction settlement


### 4.2. Advantages of the New Method

On the one hand, the subgrade soils become overconsolidated soil after replacement with EPS, so the creep coefficient is greatly reduced. As a lightweight material, EPS itself has the characteristics of ultralightweight, compressibility resistance, self-reliance, water resistance, flame retardant, and so on. Therefore, this method can better control the postconstruction settlement.On the other hand, this method can be used for the quantitative design according to different requirements of postconstruction settlement of foundation. In the process of the engineering design, the calculation of postconstruction settlement is often calculated by empirical formula or correction coefficient. This is often unable to meet the strict requirements of some engineering. Using the creep coefficient, this method can realize the quantitative calculation of postconstruction settlement.Besides, this method can make the overloading ratio greater than 1.3 without the limitation of foundation stability. It is necessary to control the overloading ratio to ensure the stability of the foundation when using the overload preloading method for ground treatment. Thus, when the overloading is relatively small, a longer preloading time is needed to ensure the effect of controlling the postconstruction settlement, which would prolong the construction period. This method can make the overloading ratio greater than 1.3, which is like a strategy using space to exchange for time.


## 4.1. Procedures of Applying the Practical Design Method

The new method for controlling postconstruction settlement involves the following 5 steps:(a)
Determine the creep coefficient. Based on the Yin-Graham EVP model, the functional relationship between the creep coefficient and overconsolidation ratio is established by fitting the one-dimensional compression test data(b)
Divided the ground into a suitable number of sublayers. Each sublayer within a same soil layer should not be overly thick. The thickness of each sublayer should be controlled within 2 m-4 m. For each sublayer, it is assumed that pressure is uniformly distributed(c)
Select groups of different OLRs and calculate the average values of the additional stress and OCR for each sublayer under different OLRs. The OLR usually ranges from 1.1 to 1.6 in actual projects. Based on Equation (19), the additional stress and OCR at the center point of each sublayer are calculated and the values are taken as the average additional stress and OCR for each sublayer(d)
Calculate the postconstruction settlement under different OLRs. Based on the functional relationship betweenCαe and OCR, the creep coefficient of each layer is determined according to the average overconsolidation ratio for each sublayer. According to Equation (20), the settlement of each sublayer was calculated and the total postconstruction settlement of ground can be calculated as follows:(21)s=∑i=1nHi1+eoiCαeilgt1+Δtt1,where s is the total postconstruction settlement of ground, Hi is the thickness of each sublayer, Cαei is the creep coefficient of each sublayer, t1 is the preloading period, and △t is the service period which is usually taken as 15 years
(e)
Correct the settlement value with the safety factorμ and determine the overload ratio and the replacement capacity under the requirements of postconstruction settlement


## 4.2. Advantages of the New Method

On the one hand, the subgrade soils become overconsolidated soil after replacement with EPS, so the creep coefficient is greatly reduced. As a lightweight material, EPS itself has the characteristics of ultralightweight, compressibility resistance, self-reliance, water resistance, flame retardant, and so on. Therefore, this method can better control the postconstruction settlement.On the other hand, this method can be used for the quantitative design according to different requirements of postconstruction settlement of foundation. In the process of the engineering design, the calculation of postconstruction settlement is often calculated by empirical formula or correction coefficient. This is often unable to meet the strict requirements of some engineering. Using the creep coefficient, this method can realize the quantitative calculation of postconstruction settlement.Besides, this method can make the overloading ratio greater than 1.3 without the limitation of foundation stability. It is necessary to control the overloading ratio to ensure the stability of the foundation when using the overload preloading method for ground treatment. Thus, when the overloading is relatively small, a longer preloading time is needed to ensure the effect of controlling the postconstruction settlement, which would prolong the construction period. This method can make the overloading ratio greater than 1.3, which is like a strategy using space to exchange for time.


## 5. Case Study

### 5.1. Project Background

The considered Huzhou Avenue is constructed on soft clay on the Huzhou plain, southeast of the city of Huzhou in China. As is shown in Figure5, the bridge approach is about 140 m long, which is divided into 5 transition sections (S1 to S5) and 1 general section (GS). The soft clay beneath it is about 13 m deep. In order to provide a smooth transition of vehicles from highway pavements to bridge structures, the design scheme is different for each section. Cement-soil mixed piles are used in S1 and S2. EPS lightweight materials are used in S3, S4, and S5. The plastic drainage plate is used in all sections.Figure 5
Profile of bridge approach.The soft clay has high water content, a high void ratio, high compressibility, low strength, and low permeability. The soil profile is depicted in Figure6, obtained from geological survey. The soil consists of 2 layers: (a) hard crust and (b) soft clay.Figure 6
Profile of soil.


### 5.2. One-Dimensional Compression Test

#### 5.2.1. Test Apparatus

As is shown in Figure7, the sixteen automatic pneumatic consolidation apparatus is adopted to carry out one-dimensional compression test. The ring knife is 2 cm high, and the base area is 45.6 cm2. Compared with traditional apparatus, the system has the advantage of automatic data acquisition during the test and overcomes the disadvantages of traditional manual recording. In order to ensure the reliability of the test results, the apparatus was proofread before the test.Figure 7
Automatic consolidation apparatus.


#### 5.2.2. Test Scheme and Description

In order to determine the stress history of the ground soils, the preconsolidation pressure should be first determined. Casagrande proposed an empirical graphical method using thee−lgp curve to obtain the maximum effective stress that had acted on the clay in the past. It is known through tests that the soft clay belongs to normally consolidated soil. The sample soils are taken from a depth of 5 m, and the preconsolidation pressure is about 110 kPa. In order to ensure that the maximum load is greater than the preconsolidation pressure, it is set as 150 kPa. The test loading path is divided into overloading, unloading, and reloading in order to simulate the actual construction condition. The soft clay is overconsolidated after reloading. For excluding the influence of the loading ratio factor, the loading ratio of each group is set as 1. Since the overconsolidation ratio is small and the creep coefficient changes greatly, the overconsolidation ratios are set as 1.1, 1.2, 1.4, and 1.8. It takes a long time for the creep coefficient to stabilize, so the duration of the last stage test should be at least 7 d. The specific scheme for one-dimensional compression tests is shown in Table 1.Table 1
Scheme for one-dimensional compression tests.
SampleOCRLoad path and duration11.037.5 kPa (1 d) ⟶75 kPa (1 d) ⟶150 kPa (7 d)21.137.5 kPa (1 d) ⟶75 kPa (1 d) ⟶150 kPa (1 d) ⟶60.6 kPa (1 d) ⟶90.9 kPa (1 d) ⟶136.4 kPa (7 d)31.237.5 kPa (1 d) ⟶75 kPa (1 d) ⟶150 kPa (1 d) ⟶55.5 kPa (1 d) ⟶83.33 kPa (1 d) ⟶125 kPa (7 d)41.437.5 kPa (1 d) ⟶75 kPa (1 d) ⟶150 kPa (1 d) ⟶47.5 kPa (1 d) ⟶71.3 kPa (1 d) ⟶107 kPa (7 d)51.837.5 kPa (1 d) ⟶75 kPa (1 d) ⟶150 kPa (1 d) ⟶37.0 kPa (1 d) ⟶55.5 kPa (1 d) ⟶ 83.3 kPa (7 d)Note: the arrow direction in the loading path represents the next level stress. The number before the brackets is the value of the load, and the number in the brackets is the duration of the load. For example, 37.5 kPa (1 d) represents that the load is 37.5 kPa (duration is 1 day).


#### 5.2.3. Test Results

Figure8 shows the s−lgt curve of sample 1. Since the sample soil belongs to normally consolidated soil, it is obvious that the boundary between the primary and secondary consolidations is at about to=100 min. According to Equation (1),
(22)Cα=e0−e1lgt1−lgt0=1.469−1.437lg1440−lg100=0.0271.Figure 8
s−lgt curve.Figure9 shows the e−lgt curve of soil sample 2, sample 3, sample 4, and sample 5 under the last stage load. From Figure 9, we can learn that the lines of all samples are smooth after 100 min, so to is 100 min. And the duration should be reduced by 100 minutes, so △t=7d–100min=9980min. Since each stage of load, except the last stage, lasts for 1 day, the equivalent time should be taken as 1 day. According to Equation (8), the creep coefficient can be calculated.Figure 9
e−lgt curve of overconsolidated soil.Taking sample 2 as an example,te=1d=1440min, to=100min, △t=9980 min, e1=1.245, and e2=1.228. So, when OCR is 1.1, the creep coefficient.
(23)Cαe=e1−e2lg1+Δt/te1+to=1.245−1.228lg1+9980/1440+100≈0.0197.The creep coefficients under each overconsolidation ratio are calculated as shown in Table2.Table 2
Creep coefficient under different OCRs.
OCRCαe1.00.02711.10.01971.20.01561.40.01071.80.0019The relationship between the creep coefficient and OCR is depicted in Figure10.Figure 10
The relationship between the creep coefficient and OCR.It is found that the relationship between the creep coefficient and overconsolidation ratio can be fitted by an exponential function as follows, and the correlation coefficientR2 is 0.991.
(24)Cαe=−0.0031+0.2446e−2.1184OCR.


### 5.3. Calculate the Postconstruction Settlement

As is shown in Figure11, to facilitate the analysis, it is assumed that po is divided into 2 stages that are abruptly applied on the ground surface. When the final stage is applied up to t2, the additional surcharge is replaced with lightweight EPS, and the preload is reduced from po to pm. And then, the pavement is laid and the load is up to pf.Figure 11
Schematic diagram of load-time.As is shown in Figure6, the thickness of hard crust is approximate 1 m. Due to its low compressibility, the postconstruction settlement of this layer is negligible. The designed height of embankment fill H is 4.4 m. The unit weight of filling soil γ is taken as 20 kN/m3. According to Equation (13),
(25)po=γH=20×4.4=88kPa.The designed thickness of pavement structure layerhs is 0.9 m. And its unit weight γs is taken as 23 kN/m3. When the thickness of EPS △h is taken as 0.5 m, according to Equations (13) and (15), the final load pf and OLR are calculated below.
(26)pf=γh+γEΔh+γshs=20×3+0.2×0.5+23×0.9=80.47kPa,(27)OLR=popf=8880.47=1.093.For the first soil layer, the depth of the middle pointz=1 m. Having looking up the additional stress coefficient table, we obtain α=1.0. According to Equations (18), (19), and (21),
(28)βz=γizαγ−γEΔh+γ−γshs=16×11×20−0.3×0.5+20−23×0.9=1.838,(29)OCR=1+11/OLR−1+βz=1+11/1.093−1+1.838=1.077,(30)Cαe=−0.0031+0.2446e−2.1184OCR=0.0227.In this project, the timing of replacement is the timing of unloading. As the timing of unloading is mainly determined based on the degree of primary consolidation, the timing of replacement could be determined with traditional method. The preloading period lasts 1 year, sot1=1 year. The postconstruction settlement at the end of the service period can be calculated according to Equation (19).
(31)s1=H11+eoCαelgt1+Δtt1=21+1.574×0.0227lg1+151=0.021m.The postconstruction settlement of other soil layers is calculated in turn, and the calculation results are shown in Table3.Table 3
Settlement calculation results.
iHiαβOCRCαes12(1.0)14.9001.0620.02270.02123(4.5)17.3511.0540.02310.03232(7.0)0.9518.0541.0340.02420.02342(9.0)0.9323.7121.0280.02450.02352(11.0)0.8930.2841.0240.02480.02362(13.0)0.8637.0381.0200.02510.023Sum0.145Note: the number in parenthesis is the depth of the middle of each layer.Actually, the degree of consolidation cannot reach 100%, so the calculated postconstruction settlement should be corrected. The correction factorμ can be evaluated according to the degree of consolidation. The correction factor μ is an empirical coefficient. Here, according to existing engineering experience, as is shown in Table 4, we suggest the value of the correction factor should be determined based on the degree of consolidation after preloading. In this project, the degree of consolidation after preloading is about 80%, so the correction coefficient is 1.3.Table 4
Correction factor.
The degree of consolidationμ>95%1.185% ~ 95%1.275% ~ 85%1.3<75%1.4s=μ×s=1.3×145=188.5 mm.According to the above calculation process, the postconstruction settlement under different OLRs is calculated as Table5.Table 5
Postconstruction settlement under different OLRs.
△hOLRs (mm)s (mm)0.51.09145188.51.01.25126163.81.51.45109141.7The allowable postconstruction settlement of the general section is 30 cm, which is the requirement in the specification. The longitudinal grade allowable value is 4‰. As is shown in Figure5, the distance between the general section and Section 3 is 65 m. If the OLR of Section 3 is set as 1.09, the longitudinal grade is 300−141.7/65000=2.4‰<4‰.As is shown in Figure12, the settlement curve of the cross-section is distributed in parabolic shape roughly. However, the calculated overloading ratio above is that of the midpoint of each section. So, the cross-section can be optimized to get more economical. The specific optimization content will be introduced in another article.Figure 12
Settlement curve of cross-section of embankment.


## 5.1. Project Background

The considered Huzhou Avenue is constructed on soft clay on the Huzhou plain, southeast of the city of Huzhou in China. As is shown in Figure5, the bridge approach is about 140 m long, which is divided into 5 transition sections (S1 to S5) and 1 general section (GS). The soft clay beneath it is about 13 m deep. In order to provide a smooth transition of vehicles from highway pavements to bridge structures, the design scheme is different for each section. Cement-soil mixed piles are used in S1 and S2. EPS lightweight materials are used in S3, S4, and S5. The plastic drainage plate is used in all sections.Figure 5
Profile of bridge approach.The soft clay has high water content, a high void ratio, high compressibility, low strength, and low permeability. The soil profile is depicted in Figure6, obtained from geological survey. The soil consists of 2 layers: (a) hard crust and (b) soft clay.Figure 6
Profile of soil.


## 5.2. One-Dimensional Compression Test

### 5.2.1. Test Apparatus

As is shown in Figure7, the sixteen automatic pneumatic consolidation apparatus is adopted to carry out one-dimensional compression test. The ring knife is 2 cm high, and the base area is 45.6 cm2. Compared with traditional apparatus, the system has the advantage of automatic data acquisition during the test and overcomes the disadvantages of traditional manual recording. In order to ensure the reliability of the test results, the apparatus was proofread before the test.Figure 7
Automatic consolidation apparatus.


### 5.2.2. Test Scheme and Description

In order to determine the stress history of the ground soils, the preconsolidation pressure should be first determined. Casagrande proposed an empirical graphical method using thee−lgp curve to obtain the maximum effective stress that had acted on the clay in the past. It is known through tests that the soft clay belongs to normally consolidated soil. The sample soils are taken from a depth of 5 m, and the preconsolidation pressure is about 110 kPa. In order to ensure that the maximum load is greater than the preconsolidation pressure, it is set as 150 kPa. The test loading path is divided into overloading, unloading, and reloading in order to simulate the actual construction condition. The soft clay is overconsolidated after reloading. For excluding the influence of the loading ratio factor, the loading ratio of each group is set as 1. Since the overconsolidation ratio is small and the creep coefficient changes greatly, the overconsolidation ratios are set as 1.1, 1.2, 1.4, and 1.8. It takes a long time for the creep coefficient to stabilize, so the duration of the last stage test should be at least 7 d. The specific scheme for one-dimensional compression tests is shown in Table 1.Table 1
Scheme for one-dimensional compression tests.
SampleOCRLoad path and duration11.037.5 kPa (1 d) ⟶75 kPa (1 d) ⟶150 kPa (7 d)21.137.5 kPa (1 d) ⟶75 kPa (1 d) ⟶150 kPa (1 d) ⟶60.6 kPa (1 d) ⟶90.9 kPa (1 d) ⟶136.4 kPa (7 d)31.237.5 kPa (1 d) ⟶75 kPa (1 d) ⟶150 kPa (1 d) ⟶55.5 kPa (1 d) ⟶83.33 kPa (1 d) ⟶125 kPa (7 d)41.437.5 kPa (1 d) ⟶75 kPa (1 d) ⟶150 kPa (1 d) ⟶47.5 kPa (1 d) ⟶71.3 kPa (1 d) ⟶107 kPa (7 d)51.837.5 kPa (1 d) ⟶75 kPa (1 d) ⟶150 kPa (1 d) ⟶37.0 kPa (1 d) ⟶55.5 kPa (1 d) ⟶ 83.3 kPa (7 d)Note: the arrow direction in the loading path represents the next level stress. The number before the brackets is the value of the load, and the number in the brackets is the duration of the load. For example, 37.5 kPa (1 d) represents that the load is 37.5 kPa (duration is 1 day).


### 5.2.3. Test Results

Figure8 shows the s−lgt curve of sample 1. Since the sample soil belongs to normally consolidated soil, it is obvious that the boundary between the primary and secondary consolidations is at about to=100 min. According to Equation (1),
(22)Cα=e0−e1lgt1−lgt0=1.469−1.437lg1440−lg100=0.0271.Figure 8
s−lgt curve.Figure9 shows the e−lgt curve of soil sample 2, sample 3, sample 4, and sample 5 under the last stage load. From Figure 9, we can learn that the lines of all samples are smooth after 100 min, so to is 100 min. And the duration should be reduced by 100 minutes, so △t=7d–100min=9980min. Since each stage of load, except the last stage, lasts for 1 day, the equivalent time should be taken as 1 day. According to Equation (8), the creep coefficient can be calculated.Figure 9
e−lgt curve of overconsolidated soil.Taking sample 2 as an example,te=1d=1440min, to=100min, △t=9980 min, e1=1.245, and e2=1.228. So, when OCR is 1.1, the creep coefficient.
(23)Cαe=e1−e2lg1+Δt/te1+to=1.245−1.228lg1+9980/1440+100≈0.0197.The creep coefficients under each overconsolidation ratio are calculated as shown in Table2.Table 2
Creep coefficient under different OCRs.
OCRCαe1.00.02711.10.01971.20.01561.40.01071.80.0019The relationship between the creep coefficient and OCR is depicted in Figure10.Figure 10
The relationship between the creep coefficient and OCR.It is found that the relationship between the creep coefficient and overconsolidation ratio can be fitted by an exponential function as follows, and the correlation coefficientR2 is 0.991.
(24)Cαe=−0.0031+0.2446e−2.1184OCR.


## 5.2.1. Test Apparatus

As is shown in Figure7, the sixteen automatic pneumatic consolidation apparatus is adopted to carry out one-dimensional compression test. The ring knife is 2 cm high, and the base area is 45.6 cm2. Compared with traditional apparatus, the system has the advantage of automatic data acquisition during the test and overcomes the disadvantages of traditional manual recording. In order to ensure the reliability of the test results, the apparatus was proofread before the test.Figure 7
Automatic consolidation apparatus.


## 5.2.2. Test Scheme and Description

In order to determine the stress history of the ground soils, the preconsolidation pressure should be first determined. Casagrande proposed an empirical graphical method using thee−lgp curve to obtain the maximum effective stress that had acted on the clay in the past. It is known through tests that the soft clay belongs to normally consolidated soil. The sample soils are taken from a depth of 5 m, and the preconsolidation pressure is about 110 kPa. In order to ensure that the maximum load is greater than the preconsolidation pressure, it is set as 150 kPa. The test loading path is divided into overloading, unloading, and reloading in order to simulate the actual construction condition. The soft clay is overconsolidated after reloading. For excluding the influence of the loading ratio factor, the loading ratio of each group is set as 1. Since the overconsolidation ratio is small and the creep coefficient changes greatly, the overconsolidation ratios are set as 1.1, 1.2, 1.4, and 1.8. It takes a long time for the creep coefficient to stabilize, so the duration of the last stage test should be at least 7 d. The specific scheme for one-dimensional compression tests is shown in Table 1.Table 1
Scheme for one-dimensional compression tests.
SampleOCRLoad path and duration11.037.5 kPa (1 d) ⟶75 kPa (1 d) ⟶150 kPa (7 d)21.137.5 kPa (1 d) ⟶75 kPa (1 d) ⟶150 kPa (1 d) ⟶60.6 kPa (1 d) ⟶90.9 kPa (1 d) ⟶136.4 kPa (7 d)31.237.5 kPa (1 d) ⟶75 kPa (1 d) ⟶150 kPa (1 d) ⟶55.5 kPa (1 d) ⟶83.33 kPa (1 d) ⟶125 kPa (7 d)41.437.5 kPa (1 d) ⟶75 kPa (1 d) ⟶150 kPa (1 d) ⟶47.5 kPa (1 d) ⟶71.3 kPa (1 d) ⟶107 kPa (7 d)51.837.5 kPa (1 d) ⟶75 kPa (1 d) ⟶150 kPa (1 d) ⟶37.0 kPa (1 d) ⟶55.5 kPa (1 d) ⟶ 83.3 kPa (7 d)Note: the arrow direction in the loading path represents the next level stress. The number before the brackets is the value of the load, and the number in the brackets is the duration of the load. For example, 37.5 kPa (1 d) represents that the load is 37.5 kPa (duration is 1 day).


## 5.2.3. Test Results

Figure8 shows the s−lgt curve of sample 1. Since the sample soil belongs to normally consolidated soil, it is obvious that the boundary between the primary and secondary consolidations is at about to=100 min. According to Equation (1),
(22)Cα=e0−e1lgt1−lgt0=1.469−1.437lg1440−lg100=0.0271.Figure 8
s−lgt curve.Figure9 shows the e−lgt curve of soil sample 2, sample 3, sample 4, and sample 5 under the last stage load. From Figure 9, we can learn that the lines of all samples are smooth after 100 min, so to is 100 min. And the duration should be reduced by 100 minutes, so △t=7d–100min=9980min. Since each stage of load, except the last stage, lasts for 1 day, the equivalent time should be taken as 1 day. According to Equation (8), the creep coefficient can be calculated.Figure 9
e−lgt curve of overconsolidated soil.Taking sample 2 as an example,te=1d=1440min, to=100min, △t=9980 min, e1=1.245, and e2=1.228. So, when OCR is 1.1, the creep coefficient.
(23)Cαe=e1−e2lg1+Δt/te1+to=1.245−1.228lg1+9980/1440+100≈0.0197.The creep coefficients under each overconsolidation ratio are calculated as shown in Table2.Table 2
Creep coefficient under different OCRs.
OCRCαe1.00.02711.10.01971.20.01561.40.01071.80.0019The relationship between the creep coefficient and OCR is depicted in Figure10.Figure 10
The relationship between the creep coefficient and OCR.It is found that the relationship between the creep coefficient and overconsolidation ratio can be fitted by an exponential function as follows, and the correlation coefficientR2 is 0.991.
(24)Cαe=−0.0031+0.2446e−2.1184OCR.


## 5.3. Calculate the Postconstruction Settlement

As is shown in Figure11, to facilitate the analysis, it is assumed that po is divided into 2 stages that are abruptly applied on the ground surface. When the final stage is applied up to t2, the additional surcharge is replaced with lightweight EPS, and the preload is reduced from po to pm. And then, the pavement is laid and the load is up to pf.Figure 11
Schematic diagram of load-time.As is shown in Figure6, the thickness of hard crust is approximate 1 m. Due to its low compressibility, the postconstruction settlement of this layer is negligible. The designed height of embankment fill H is 4.4 m. The unit weight of filling soil γ is taken as 20 kN/m3. According to Equation (13),
(25)po=γH=20×4.4=88kPa.The designed thickness of pavement structure layerhs is 0.9 m. And its unit weight γs is taken as 23 kN/m3. When the thickness of EPS △h is taken as 0.5 m, according to Equations (13) and (15), the final load pf and OLR are calculated below.
(26)pf=γh+γEΔh+γshs=20×3+0.2×0.5+23×0.9=80.47kPa,(27)OLR=popf=8880.47=1.093.For the first soil layer, the depth of the middle pointz=1 m. Having looking up the additional stress coefficient table, we obtain α=1.0. According to Equations (18), (19), and (21),
(28)βz=γizαγ−γEΔh+γ−γshs=16×11×20−0.3×0.5+20−23×0.9=1.838,(29)OCR=1+11/OLR−1+βz=1+11/1.093−1+1.838=1.077,(30)Cαe=−0.0031+0.2446e−2.1184OCR=0.0227.In this project, the timing of replacement is the timing of unloading. As the timing of unloading is mainly determined based on the degree of primary consolidation, the timing of replacement could be determined with traditional method. The preloading period lasts 1 year, sot1=1 year. The postconstruction settlement at the end of the service period can be calculated according to Equation (19).
(31)s1=H11+eoCαelgt1+Δtt1=21+1.574×0.0227lg1+151=0.021m.The postconstruction settlement of other soil layers is calculated in turn, and the calculation results are shown in Table3.Table 3
Settlement calculation results.
iHiαβOCRCαes12(1.0)14.9001.0620.02270.02123(4.5)17.3511.0540.02310.03232(7.0)0.9518.0541.0340.02420.02342(9.0)0.9323.7121.0280.02450.02352(11.0)0.8930.2841.0240.02480.02362(13.0)0.8637.0381.0200.02510.023Sum0.145Note: the number in parenthesis is the depth of the middle of each layer.Actually, the degree of consolidation cannot reach 100%, so the calculated postconstruction settlement should be corrected. The correction factorμ can be evaluated according to the degree of consolidation. The correction factor μ is an empirical coefficient. Here, according to existing engineering experience, as is shown in Table 4, we suggest the value of the correction factor should be determined based on the degree of consolidation after preloading. In this project, the degree of consolidation after preloading is about 80%, so the correction coefficient is 1.3.Table 4
Correction factor.
The degree of consolidationμ>95%1.185% ~ 95%1.275% ~ 85%1.3<75%1.4s=μ×s=1.3×145=188.5 mm.According to the above calculation process, the postconstruction settlement under different OLRs is calculated as Table5.Table 5
Postconstruction settlement under different OLRs.
△hOLRs (mm)s (mm)0.51.09145188.51.01.25126163.81.51.45109141.7The allowable postconstruction settlement of the general section is 30 cm, which is the requirement in the specification. The longitudinal grade allowable value is 4‰. As is shown in Figure5, the distance between the general section and Section 3 is 65 m. If the OLR of Section 3 is set as 1.09, the longitudinal grade is 300−141.7/65000=2.4‰<4‰.As is shown in Figure12, the settlement curve of the cross-section is distributed in parabolic shape roughly. However, the calculated overloading ratio above is that of the midpoint of each section. So, the cross-section can be optimized to get more economical. The specific optimization content will be introduced in another article.Figure 12
Settlement curve of cross-section of embankment.


## 6. Conclusions

Based on practical engineering, a new design method for controlling postconstruction settlement is proposed in this paper. Main conclusions are drawn as follows:(a)
Based on the1D EVP model and the concept of equivalent time, the functional relationship between the creep coefficient and overconsolidation ratio can be established by fitting one-dimensional compression test data. It is found that the creep coefficient decreases with the overconsolidation ratio increasing(b)
The relationship between the overloading ratio and overconsolidation ratio is deduced. In practical engineering, the overconsolidation ratio can be changed by adjusting the overloading ratio, and then, the creep coefficient can be changed to control the postconstruction settlement(c)
The new method can be used for the quantitative design according to different requirements of postconstruction settlement of foundation. The case study shows that the method is operable in engineering



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