# A Prediction Method for Postconstruction Settlement of Pile-Soil Composite Subgrade Based on Fuzzy Comprehensive Evaluation

Authors: Hao Shan; Guanghui Jiang; Yajing Chang; Junli Cheng; Baoning Hong; Shengcheng Wang
Journal: Advances in Civil Engineering
 (2021)

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## Abstract

This paper presents a postconstruction settlement prediction method for pile-soil composite subgrade based on the multilevel fuzzy comprehensive evaluation principle. In this method, the variation range of postconstruction settlement can be obtained from a simple calculation based on the basic data of actual engineering. Firstly, according to the characteristics of influencing factors in the construction of soft soil subgrade, the evaluation index set and two-level factor index sets were selected. The grading standards of the evaluation index and factor index were determined according to the allowable value of the standard and the numerical simulation results. Secondly, each factor index was standardized, and the normal distribution function in the form of exponential was used to construct the standard membership function for the first and second factor indexes. Finally, the comprehensive evaluation matrix of postconstruction settlement of composite subgrade was constructed based on the entropy weight method. The variation range of postconstruction settlement was predicted by the principle of maximum membership. The example analysis shows that the predicted results of the prediction method and the field measurement method are in good agreement, indicating that the proposed method can realize the postconstruction settlement prediction of composite subgrade, and the results are more accurate and more instructive.


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## Body

## 1. Introduction

The postconstruction settlement of the composite subgrade of expressways has always been concerned by both academia and industry, especially in some special sections, such as bridge head transition sections and the sections containing structures [1, 2]. Higher requirements are put forward for the postconstruction settlement of subgrade in these sections. So people often adopt the foundation treatment method of pile-soil composite subgrade. Compared with other foundation treatment methods, pile-soil composite subgrade has certain advantages in improving the stability of subgrade and reducing settlement. However, there are still some large postconstruction settlements in the treatment section of pile-soil composite subgrade, such as car jump at the bridge head. Many scholars and engineers have carried out much useful work in the prediction of postconstruction settlements by means of theoretical analysis [3], numerical simulation [4], and on-site observation data fitting [5, 6]. Previous related works on postconstruction settlement prediction are discussed and tabulated in Table 1.Table 1
Previous related works on foundation settlement.
AuthorsData set sizeMethodReliable conditionOmar et al. [7]Footing width, effective unit weight, and SPT blow countArtificial neural networkShallow foundation on granular soilsWang et al. [8]Soil properties and parameters related to the pile, such as pile spacing, pile length, and cap widthA calculation model for predicting the additional stresses in the composite foundation soil and the layerwise summation methodComposite foundation with sparse prestressed tubular concrete (PTC) capped-piles under embankmentMeng et al. [9]The compression parameters of underlying soils related to soil disturbance degreeThe layerwise summation methodGround and tunnelEid et al. [3]Pile-subgrade stiffness ratios for piled foundations on nonhomogeneous mediaThree-dimensional finite-element (FE) analysisThe elastic settlement of piled foundations resting on rockHong et al. [2]The time-extended loading residual settlement and settlement rate calculated from the field test dataAn improved static loading test method, time-extended loading testPile-soil composite subgradeKermani et al. [10]Rockfill modulus and rock strengthA novel approach considering the dam’s deformation behavior during constructionConcrete face rockfill damsWang et al. [5]Three appropriate points for the measured settlement curve in the prediction samplesA three-point hyperbolic combination modelSubgrade filled with construction and demolition wasteCai et al. [11]The calculated dynamic stressesThe equivalent timeline model combined with the cyclic strain accumulation modelThe long-term settlements of roads on soft soil under cyclic traffic loadingsMohammed et al. [12]The width of footing, pressure of footing, geometry of footing, count of SPT blow, and ratio of footing embedmentMachine learning modelsSettlement of shallow foundation over cohesion soil propertiesTang et al. [13]The observation data of settlement during constructionThe Hushino model, hyperbolic curve method, and exponential curve methodFoundation after constructionDing [14] and Zhang et al. [15]The design parametersNumerical simulation approachPile-soil composite subgradeIn this paper, based on a large amount of postconstruction settlement field test data, a new prediction method of postconstruction settlement of composite subgrade is proposed using the multilevel fuzzy comprehensive evaluation method. This method calculates the variation interval of postconstruction settlement through a simple calculation by only considering the basic data from actual projects. The calculation results are beneficial to the optimization of design and improvement of construction quality. In the establishment process of this method, it is difficult to calculate weight and membership degree accurately, and there are many factors involved. Hence, the entropy weight method, standardized membership function, and two-level evaluation system are introduced. In this way, not only the calculation accuracy is improved but also the index of influencing factors involved in the comprehensive evaluation in each level is reduced, which is more convenient for practical applications.


## 2. Need for Research

In recent years, artificial intelligence technology has been developed rapidly, but at present, artificial intelligence technology still has some shortcomings and limitations [16–18]. Firstly, it needs more data and data support to build the model. When the data are insufficient, the error is often large. Secondly, sometimes, in the modeling process, some engineering features or states need to be represented by numbers, which will lead to the loss of information. Finally, the results obtained by the artificial intelligence technology model are usually qualitative indicators, while the quantitative indicators are relatively few and not rigorous enough. However, in addition to the aforementioned disadvantages, artificial intelligence technology also has obvious advantages [19–21]. First of all, it is an important tool for system analysis and will not cut the relationship between influencing factors and results. Secondly, it can solve complex relationships between multiple factors and predict unknown data. Finally, its analysis results are often more concise, easy-to-make decisions.Considering that the advantages of artificial intelligence technology have a great help to solve complex engineering problems, some artificial intelligence technologies have been widely used in civil engineering. To predict the settlement of rock-socketed piles, Danial et al. [22, 23] presented the development of a hybrid ANN-based model named PSO-ANN (or neuro-swarm) with detailed modeling process and a new model based on gene expression programming (GEP). Li et al. [16] use least squares support vector machines (LSSVMs) based on multipoint measurement to monitor and predict foundation pit displacement. In addition, fuzzy comprehensive evaluation (FCE) method is also a typical artificial intelligence technology; it can better solve the fuzzy but difficult to quantify the problem and is suitable for all kinds of nondeterministic problems. The FCE method has been widely used in mineral [24], environmental [25], slope [26] and other engineering areas [27]. However, its application in postconstruction settlement of composite subgrade has not been reported. As the postconstruction settlement of composite subgrade involves many factors and has obvious randomness, it is meaningful to explore the method of uncertainty and establish a prediction model and a calculation method.


## 3. Evaluation Index and Influencing Factors

As the postconstruction settlement of composite subgrade can be affected by many factors, a two-level fuzzy comprehensive evaluation system considering the main influencing factors is selected. The evaluation system can make up for the shortcomings of the existing single-level evaluation methods and make the evaluation results more accurate and more instructive [20]. In the two-level fuzzy comprehensive evaluation system, one of our key works is to determine the reasonable evaluation index set and the factor index set of each layer for improving the accuracy and practicability of the prediction method.


### 3.1. Evaluation Index Set

In the two-level fuzzy comprehensive evaluation system, an evaluation indexv is constructed for describing the severity of the postconstruction settlement of the composite subgrade, and we have(1)V=v1,v2,…,vm,where V is a set that contains all the possible values of the evaluation index v. According to the requirements of the current specification in China, allowable values for the postconstruction settlements of high-quality highways at the bridgehead transition section, structural section, and general road section are 100, 200, and 300 mm, respectively. Therefore, the element vm in the evaluation index set V is obtained based on the postconstruction settlement value. The smaller the postconstruction settlement value, the better the construction quality. In this paper, the evaluation index set contains four values to represents four quality grades (see Table 2.Table 2
Classification standard for postconstruction settlement.
Evaluation indexPostconstruction settlement (mm)Standard classification intervalv1Excellent[0, 100)[0, 0.25)v2Good[100, 200)[0.25, 0.50)v3Moderate[200, 300)[0.50, 0.75)v4Poor[300, +∞)[0.75, 1)The space of the postconstruction settlement has been divided into four subsections, and the corresponding normalized classification intervals (w.r.t 400 mm) are also given in Table1. For the postconstruction settlement larger than 400 mm, 400 mm is applied to the normalization process. Hence, we have a closed range of the postconstruction settlement after the normalization process.


### 3.2. Influencing Factors Set

Since the postconstruction settlement of CFG pile composite subgrade-based road section involves many influencing factors, a two-level fuzzy comprehensive evaluation model is adopted to tackle the problem: 15 secondary influencing factors are constructed as the leaves of 4 primary influencing factors (geology, pile, cushion, and construction). Mathematically, we have(2)U=U1,U2,U3,U4,Ui=ui1,ui2,…uij,…,uini,i=1,2,3,4andj=1,2,…,ni,where Ui is the primary influencing factor, uij is the secondary influencing factor, and ni is the number of secondary influencing factors included in Ui.The factor values of the secondary influencing factors vary with the engineering characteristics. Taking CFG pile composite subgrade in Guangdong Province as an example, this paper discusses the method of determining the secondary influencing factors. According to the collected sample data of a large number of CFG pile composite subgrade engineering projects, existing specification requirements, and on-site survey results collected by the authors, the range of the factor for each secondary influencing factor is provided as follows.The influencing factors of the geologyU1 consist of compressed soil thickness u11, compression modulus u12, cohesion u13, and internal friction angle u14.In practical projects, the depth of CFG piles should not exceed 30 m. Otherwise, the quality of composite subgrade is not easy to control. Therefore, the range of compressed soil thicknessu11 should be 0 to 30 m. The cross-board shear strength of soft soil in Guangdong region is generally 4 to 12 kPa. In the shear strength index, the minimum cohesion c < 3.2 kPa, the minimum internal friction angle φ<2.1°, the porosity ratio is generally greater than 1.0, and the compression coefficient is within 0.5 to 1.0 MPa−1. Therefore, the range of the cohesive force u13 is 1 to 15 kPa, the range of the internal friction angle u14 is 1° to 15°, and the range of compression modulus u12 is 1 to 10 MPa.The influencing factors of the pileU2 consist of pile modulus u21, pile length u22, pile diameter u23, and pile spacing u24.Generally, CFG pile length rangeu22 is 0 to 30 m, the pile diameter u23 should be 0.35 to 0.60 m, and the pile spacing u24 should be 1.4 to 3.0 m. As the CFG pile design strength range is 5 to 20 MPa, the rounding range in CFG pile compression modulus u21 is ranging from 800 to 30,000 MPa.The influencing factors of the cushionU3 consist of cushion thickness u31, cushion modulus u32, and cushion internal friction angle u33.In practical projects, the general thickness of the CFG pile composite subgrade cushion is 0.3 to 0.6 m. Considering the action of the pile top support, the thickness of the cushionu31 is in the range of 0 to 0.8 m. As the cushion is mainly medium coarse sand and gravel, the cushion modulus u32 ranges from 50 to 250 MPa and the cushion internal friction angle u33 ranges from 15° to 60°.The influencing factors of the constructionU4 consist of filling height u41, filling rate u42, preloading height u43, and preloading time u44.The filling height of expressways is mainly affected by terrain and routes. Except for a few hill areas, the filling height usually does not exceed 20 m (including the converted thickness of the pavement structure layer). Therefore, the filling heightu41 ranges from 1 to 20 m. The embankment filling regular loading rate is 20 to 70 mm/d, the loading rate usually is less than 20 mm/d, and the loading rate is greater than 70 mm/d for fast loading. For the convenience of the analysis, the filling rate u42 ranges from 5 to 100 mm/d. Surcharge preloading mainly includes under-preloading, equal-preloading, and over-preloading. Under normal circumstances, the overloading height does not exceed 3.0 m, and the preloading time does not exceed 1 year. Therefore, the preloading height range is 0 to 3.0 m, and the preloading time range is 0 to 360 days.


## 3.1. Evaluation Index Set

In the two-level fuzzy comprehensive evaluation system, an evaluation indexv is constructed for describing the severity of the postconstruction settlement of the composite subgrade, and we have(1)V=v1,v2,…,vm,where V is a set that contains all the possible values of the evaluation index v. According to the requirements of the current specification in China, allowable values for the postconstruction settlements of high-quality highways at the bridgehead transition section, structural section, and general road section are 100, 200, and 300 mm, respectively. Therefore, the element vm in the evaluation index set V is obtained based on the postconstruction settlement value. The smaller the postconstruction settlement value, the better the construction quality. In this paper, the evaluation index set contains four values to represents four quality grades (see Table 2.Table 2
Classification standard for postconstruction settlement.
Evaluation indexPostconstruction settlement (mm)Standard classification intervalv1Excellent[0, 100)[0, 0.25)v2Good[100, 200)[0.25, 0.50)v3Moderate[200, 300)[0.50, 0.75)v4Poor[300, +∞)[0.75, 1)The space of the postconstruction settlement has been divided into four subsections, and the corresponding normalized classification intervals (w.r.t 400 mm) are also given in Table1. For the postconstruction settlement larger than 400 mm, 400 mm is applied to the normalization process. Hence, we have a closed range of the postconstruction settlement after the normalization process.


## 3.2. Influencing Factors Set

Since the postconstruction settlement of CFG pile composite subgrade-based road section involves many influencing factors, a two-level fuzzy comprehensive evaluation model is adopted to tackle the problem: 15 secondary influencing factors are constructed as the leaves of 4 primary influencing factors (geology, pile, cushion, and construction). Mathematically, we have(2)U=U1,U2,U3,U4,Ui=ui1,ui2,…uij,…,uini,i=1,2,3,4andj=1,2,…,ni,where Ui is the primary influencing factor, uij is the secondary influencing factor, and ni is the number of secondary influencing factors included in Ui.The factor values of the secondary influencing factors vary with the engineering characteristics. Taking CFG pile composite subgrade in Guangdong Province as an example, this paper discusses the method of determining the secondary influencing factors. According to the collected sample data of a large number of CFG pile composite subgrade engineering projects, existing specification requirements, and on-site survey results collected by the authors, the range of the factor for each secondary influencing factor is provided as follows.The influencing factors of the geologyU1 consist of compressed soil thickness u11, compression modulus u12, cohesion u13, and internal friction angle u14.In practical projects, the depth of CFG piles should not exceed 30 m. Otherwise, the quality of composite subgrade is not easy to control. Therefore, the range of compressed soil thicknessu11 should be 0 to 30 m. The cross-board shear strength of soft soil in Guangdong region is generally 4 to 12 kPa. In the shear strength index, the minimum cohesion c < 3.2 kPa, the minimum internal friction angle φ<2.1°, the porosity ratio is generally greater than 1.0, and the compression coefficient is within 0.5 to 1.0 MPa−1. Therefore, the range of the cohesive force u13 is 1 to 15 kPa, the range of the internal friction angle u14 is 1° to 15°, and the range of compression modulus u12 is 1 to 10 MPa.The influencing factors of the pileU2 consist of pile modulus u21, pile length u22, pile diameter u23, and pile spacing u24.Generally, CFG pile length rangeu22 is 0 to 30 m, the pile diameter u23 should be 0.35 to 0.60 m, and the pile spacing u24 should be 1.4 to 3.0 m. As the CFG pile design strength range is 5 to 20 MPa, the rounding range in CFG pile compression modulus u21 is ranging from 800 to 30,000 MPa.The influencing factors of the cushionU3 consist of cushion thickness u31, cushion modulus u32, and cushion internal friction angle u33.In practical projects, the general thickness of the CFG pile composite subgrade cushion is 0.3 to 0.6 m. Considering the action of the pile top support, the thickness of the cushionu31 is in the range of 0 to 0.8 m. As the cushion is mainly medium coarse sand and gravel, the cushion modulus u32 ranges from 50 to 250 MPa and the cushion internal friction angle u33 ranges from 15° to 60°.The influencing factors of the constructionU4 consist of filling height u41, filling rate u42, preloading height u43, and preloading time u44.The filling height of expressways is mainly affected by terrain and routes. Except for a few hill areas, the filling height usually does not exceed 20 m (including the converted thickness of the pavement structure layer). Therefore, the filling heightu41 ranges from 1 to 20 m. The embankment filling regular loading rate is 20 to 70 mm/d, the loading rate usually is less than 20 mm/d, and the loading rate is greater than 70 mm/d for fast loading. For the convenience of the analysis, the filling rate u42 ranges from 5 to 100 mm/d. Surcharge preloading mainly includes under-preloading, equal-preloading, and over-preloading. Under normal circumstances, the overloading height does not exceed 3.0 m, and the preloading time does not exceed 1 year. Therefore, the preloading height range is 0 to 3.0 m, and the preloading time range is 0 to 360 days.


## 4. Factor Grading Standard of Secondary Influencing Factors

By analysing a large number of engineering samples, the finite-element numerical software can be used to calculate the single-factor influence of the representative engineering example of composite subgrade. To determine the factor grading standard of all the secondary influencing factors, the influence of the individual factor was analysed separately by taking five to six values within its range. Taking CFG pile composite subgrade as an example, Plaxis finite-element numerical software can be used to analyse the law of single-factor influence. The detailed simplified processing, calculation method, and calculation process, as well as reliability demonstration will not be discussed due to the limitation of space. The specific method to determine the grading standard of the secondary influencing factors is as follows.


### 4.1. Quantification of Influence of Individual Factors

According to the FEM simulation results, three categories can be concluded to describe the relationship between the postconstruction settlement changes and the secondary influencing factors.This first category is named as positive attribute factoruij+. As the factor uij+ increases, the postconstruction settlement value increases and the evaluation grade decreases. According to the simulation studies, compressed soil thickness u11, pile spacing u24, filling height u41, and filling rate u42 belong to this category.The second category is named as negative attribute factoruij−. As the factor value increases, the postconstruction settlement value decreases and the evaluation grade increases. Compression modulus u12, cohesion u13, pile modulus u21, pile length u22, pile diameter u23, cushion thickness u31, cushion modulus u32, internal friction angle of cushion u33, preloading height u32, and preloading time u33 belong to this category.The third category is named as zero attribute factor. As the factor value increases, the postconstruction settlement value does not change or changes little. The internal friction angle of subgrade soilu14 belongs to this category.For analysing the physical quantities with different units, a normalization process is implemented to both positive and negative attribute factors (zero-attribute factor is considered as the positive attribute factor in this paper). The normalization formulas for both positive and negative attribute factors are as follows:(3)qij=maxuij+−uij+maxuij+−minuij+.(4)qij=uij−−minuij−maxuij−−minuij−.According to formula (3), the normalized positive attribute factors have a negative correlation with the postconstruction settlement and a positive correlation with the evaluation grade.The relationships between the postconstruction settlements and the normalized values of the influencing factors are concluded and shown in Figures1 to 4.Figure 1
Effects of geological factors on postconstruction settlement.Figure 2
Effects of piles geological factors on postconstruction settlement.Figure 3
Effects of cushion factors on postconstruction settlement.Figure 4
Effects of construction factors on postconstruction settlement.According to Figures1 to 4, the contribution of each secondary influencing factor can be obtained, which can be used as the reference for weight distribution in the fuzzy comprehensive evaluation process.Based on Figure1, the postconstruction settlement is very sensitive to the compressed soil thickness q11 and the compression modulus q12. Compared with q11 and q12, the changes of the cohesion q13 have a small effect on the postconstruction settlement. The changes of the internal friction angle of subgrade soil do not influence the postconstruction settlement.Among the influencing factors of the pile, the postconstruction settlement is sensitive to the pile modulusq21 and pile length q22. The pile diameter q23 has the smallest influence on the postconstruction settlement in Figure 2.In Figure3, the changes of the internal friction angle q33 and the thickness of the cushion q31 have major effects on the postconstruction settlement. In comparison, the influence of the cushion modulus q32 is relatively small.Among the construction-influencing factors, the preloading heightq43 and preloading time q44 have a major effect on the postconstruction settlement, and the effects of the filling height q41 and filling rate q42 are relatively small.


### 4.2. Grading Standard

According to the simulation and analysis results shown in Figures1 to 4, the linear interpolation method is used to determine the relationships between the normalized factors qij and the postconstruction settlement and we have qij=fijSp. Where Sp is the postconstruction settlement, fij ( ) is the linear mapping from postconstruction settlement to normalized influencing factor qij. Based on the derived linear relationships fij ( ), the values of the normalized factors qij can be calculated when Sp equals 100, 200, and 300 mm. As a result, the corresponding uij can be obtained, and the grading standard can be determined. For particular influencing factors, the postconstruction settlement is smaller than 300 mm when qij = 0. At the same time, we need to consider all the situations when Sp > 100 mm. Hence, additional grading procedures are added as follows:(a)
Sp∈200,300: the linear interpolation method is used to determine the qij values when the settlement equals to 100 and 200 mm. The qij value for Sp = 300 mm is equal to 0.5fij (200). With the qij for Sp = 100, 200, and 300 mm, the corresponding uij can be determined, and grading standard can be obtained.(b)
Sp∈100,200: the linear interpolation method is used to determine the qij value when the settlement is 100 mm. The qij value for Sp = 200 mm is equal to 0.5fij (100) and the qij value for Sp = 300 mm is equal to 0.25fij (100). With qij for Sp = 100, 200, and 300 mm, the corresponding uij can be determined, and grading standard can be obtained.The change of friction angle in the subgrade soil does not affect the postconstruction settlementSp. Therefore, the entire range of internal friction angle belongs to the grade v1.Classification standard of all the secondary influencing factors is shown in Tables3 and 4.Table 3
Initial conditions and classification standard of geological and pile secondary influencing factors.
IndexGeological influencing factorsU1Pile influencing factorsU2u11 (m)u12 (MPa)u13 (kPa)u21 (MPa)u22 (m)u23 (m)u24 (m)Initial condition18662 × 104150.52.0Classification standardv10∼18.945.52∼10.003.87∼15.0017,288.90∼30,00013.99∼30.000.48∼0.601.40∼2.09v218.94∼24.842.24∼5.522.43∼3.869543.25∼17,288.908.99∼13.990.39∼0.482.09∼2.55v324.84∼27.421.62∼2.241.71∼2.435649.22∼9543.256.01∼8.990.34∼0.392.55∼2.82v427.42∼30.001.00∼1.621.00∼1.71800.00∼5649.220∼6.010.30∼0.342.82∼3.00Table 4
Initial conditions and classification standard of cushion and construction secondary influencing factors.
IndexCushion influencing factorsU3Construction influencing factorsU4u31 (m)u32 (MPa)u33 (°)u41 (m)u42 (mm/d)u43 (m)u44 (d)Initial condition0.6150406502.0180Classification standardv10.40∼0.80128.81∼25032.89∼60.001.00∼11.615.00∼85.761.48∼3.00108.30∼360v20.14∼0.4089.41∼128.8121.85∼32.8911.61∼15.8085.76∼92.880.49∼1.4824.10∼108.30v30.07∼0.1469.70∼89.4118.42∼21.8515.80∼17.9092.88∼96.440.15∼0.497.32∼24.10v40∼0.0750.00∼69.7015.00∼18.4217.90∼20.0096.44∼100.000∼0.150∼7.32


## 4.1. Quantification of Influence of Individual Factors

According to the FEM simulation results, three categories can be concluded to describe the relationship between the postconstruction settlement changes and the secondary influencing factors.This first category is named as positive attribute factoruij+. As the factor uij+ increases, the postconstruction settlement value increases and the evaluation grade decreases. According to the simulation studies, compressed soil thickness u11, pile spacing u24, filling height u41, and filling rate u42 belong to this category.The second category is named as negative attribute factoruij−. As the factor value increases, the postconstruction settlement value decreases and the evaluation grade increases. Compression modulus u12, cohesion u13, pile modulus u21, pile length u22, pile diameter u23, cushion thickness u31, cushion modulus u32, internal friction angle of cushion u33, preloading height u32, and preloading time u33 belong to this category.The third category is named as zero attribute factor. As the factor value increases, the postconstruction settlement value does not change or changes little. The internal friction angle of subgrade soilu14 belongs to this category.For analysing the physical quantities with different units, a normalization process is implemented to both positive and negative attribute factors (zero-attribute factor is considered as the positive attribute factor in this paper). The normalization formulas for both positive and negative attribute factors are as follows:(3)qij=maxuij+−uij+maxuij+−minuij+.(4)qij=uij−−minuij−maxuij−−minuij−.According to formula (3), the normalized positive attribute factors have a negative correlation with the postconstruction settlement and a positive correlation with the evaluation grade.The relationships between the postconstruction settlements and the normalized values of the influencing factors are concluded and shown in Figures1 to 4.Figure 1
Effects of geological factors on postconstruction settlement.Figure 2
Effects of piles geological factors on postconstruction settlement.Figure 3
Effects of cushion factors on postconstruction settlement.Figure 4
Effects of construction factors on postconstruction settlement.According to Figures1 to 4, the contribution of each secondary influencing factor can be obtained, which can be used as the reference for weight distribution in the fuzzy comprehensive evaluation process.Based on Figure1, the postconstruction settlement is very sensitive to the compressed soil thickness q11 and the compression modulus q12. Compared with q11 and q12, the changes of the cohesion q13 have a small effect on the postconstruction settlement. The changes of the internal friction angle of subgrade soil do not influence the postconstruction settlement.Among the influencing factors of the pile, the postconstruction settlement is sensitive to the pile modulusq21 and pile length q22. The pile diameter q23 has the smallest influence on the postconstruction settlement in Figure 2.In Figure3, the changes of the internal friction angle q33 and the thickness of the cushion q31 have major effects on the postconstruction settlement. In comparison, the influence of the cushion modulus q32 is relatively small.Among the construction-influencing factors, the preloading heightq43 and preloading time q44 have a major effect on the postconstruction settlement, and the effects of the filling height q41 and filling rate q42 are relatively small.


## 4.2. Grading Standard

According to the simulation and analysis results shown in Figures1 to 4, the linear interpolation method is used to determine the relationships between the normalized factors qij and the postconstruction settlement and we have qij=fijSp. Where Sp is the postconstruction settlement, fij ( ) is the linear mapping from postconstruction settlement to normalized influencing factor qij. Based on the derived linear relationships fij ( ), the values of the normalized factors qij can be calculated when Sp equals 100, 200, and 300 mm. As a result, the corresponding uij can be obtained, and the grading standard can be determined. For particular influencing factors, the postconstruction settlement is smaller than 300 mm when qij = 0. At the same time, we need to consider all the situations when Sp > 100 mm. Hence, additional grading procedures are added as follows:(a)
Sp∈200,300: the linear interpolation method is used to determine the qij values when the settlement equals to 100 and 200 mm. The qij value for Sp = 300 mm is equal to 0.5fij (200). With the qij for Sp = 100, 200, and 300 mm, the corresponding uij can be determined, and grading standard can be obtained.(b)
Sp∈100,200: the linear interpolation method is used to determine the qij value when the settlement is 100 mm. The qij value for Sp = 200 mm is equal to 0.5fij (100) and the qij value for Sp = 300 mm is equal to 0.25fij (100). With qij for Sp = 100, 200, and 300 mm, the corresponding uij can be determined, and grading standard can be obtained.The change of friction angle in the subgrade soil does not affect the postconstruction settlementSp. Therefore, the entire range of internal friction angle belongs to the grade v1.Classification standard of all the secondary influencing factors is shown in Tables3 and 4.Table 3
Initial conditions and classification standard of geological and pile secondary influencing factors.
IndexGeological influencing factorsU1Pile influencing factorsU2u11 (m)u12 (MPa)u13 (kPa)u21 (MPa)u22 (m)u23 (m)u24 (m)Initial condition18662 × 104150.52.0Classification standardv10∼18.945.52∼10.003.87∼15.0017,288.90∼30,00013.99∼30.000.48∼0.601.40∼2.09v218.94∼24.842.24∼5.522.43∼3.869543.25∼17,288.908.99∼13.990.39∼0.482.09∼2.55v324.84∼27.421.62∼2.241.71∼2.435649.22∼9543.256.01∼8.990.34∼0.392.55∼2.82v427.42∼30.001.00∼1.621.00∼1.71800.00∼5649.220∼6.010.30∼0.342.82∼3.00Table 4
Initial conditions and classification standard of cushion and construction secondary influencing factors.
IndexCushion influencing factorsU3Construction influencing factorsU4u31 (m)u32 (MPa)u33 (°)u41 (m)u42 (mm/d)u43 (m)u44 (d)Initial condition0.6150406502.0180Classification standardv10.40∼0.80128.81∼25032.89∼60.001.00∼11.615.00∼85.761.48∼3.00108.30∼360v20.14∼0.4089.41∼128.8121.85∼32.8911.61∼15.8085.76∼92.880.49∼1.4824.10∼108.30v30.07∼0.1469.70∼89.4118.42∼21.8515.80∼17.9092.88∼96.440.15∼0.497.32∼24.10v40∼0.0750.00∼69.7015.00∼18.4217.90∼20.0096.44∼100.000∼0.150∼7.32


## 5. Membership Functions and Weights

Based on the sensitivity analysis in the previous section and the classification standard of influencing factors in Tables2 and 3, the membership functions and weights in the fuzzy comprehensive evaluation can be determined. As many factors are affecting the postconstruction settlement of CFG pile composite subgrade, a standardized membership function is used to describe the influence of each secondary influencing factor. The entropy weight method is used to determine the weights of the primary and secondary influencing factors.


### 5.1. Standardized Membership Functions

Normal membership function: the commonly used membership functions in geotechnical engineering area are normal-type functions, triangular fuzzy functions, trapezoidal functions, and ridge-type functions [28]. The parameter membership function that in geotechnical engineering should adopt an exponential normal distribution function was suggested [29]. Therefore, the membership function [30] of the structural influencing factor uij on the evaluation index is as follows:(5)fkuij=exp−uij−aijkcijk2,where k is the evaluation index of uij and aijk and cijk are constants, satisfying aijk>0 and cijk>0.Standardization of membership functions: to give a standardized membership function, the classification interval of the secondary influencing factor is linearly converted into a classification standard interval with the same size as the evaluation index. According to the levelk to which uij belongs, the positive and negative attribute factors have been normalized separately. After standardized treatment of influencing factors, the classification standards of each factor are consistent with the classification ranges of the postconstruction settlement classification standards in Table 1. aijk and cijk can be calculated using the upper and lower boundaries of the classification intervals of each factor classification standard. For the evaluation index level v1∼v4, the normal distribution membership function in the form of the normalized index is(6)rij1=1yij<0.125exp−yij−0.1250.1501420.125≤yij<0.251−exp−yij−0.3750.1501420.25≤yij<0.37500.375≤yij<1,(7)rij2=0yij<0.125∨yij≥0.6251−exp−yij−0.1250.1501420.125≤yij<0.25exp−yij−0.3750.1501420.25≤yij<0.501−exp−yij−0.6250.1501420.50≤yij<0.625,(8)rij3=0yij<0.375∨yij≥0.8751−exp−yij−0.3750.1501420.375≤yij<0.50exp−yij−0.6250.1501420.50≤yij<0.751−exp−yij−0.8750.1501420.75≤yij<0.875,(9)rij4=0yij<0.6251−exp−yij−0.6250.1501420.625≤yij<0.75exp−yij−0.8750.1501420.75≤yij<0.8751yij≥0.875,where yij is the normalized value of the influencing factor; rijk is the standard membership value of each influencing factor, and k = 1, 2, 3, and 4. The membership of each secondary influencing factor can be obtained using formulas (6) to (9). After obtaining the membership value of each secondary influencing factor, a matrix Ri can be constructed:(10)Ri=ri11ri12ri13ri14ri21ri22ri23ri24⋮⋮⋮⋮rini1rini2rini3rini4.


### 5.2. Weights of Influencing Factors

In the fuzzy comprehensive evaluation of multiple influencing factors, the weight is a measure of the influence of each influencing factor on the evaluation index. The method of determining the weight can generally be divided into subjective empowerment and objective weighting methods. Common subjective empowerment methods have Delphi method, analytic hierarchy process, and statistical method. Common objective weighting methods include entropy weight method, principal component analysis method, and mean square error method. As the subjective empowerment method relies on human factors, such as expert experience which may cause bias on the evaluation results, the entropy weight method in the objective weighting method is used to determine the weight of the influencing factors.Entropy is a physical quantity that reflects the randomness and disorder of subjects. The weight of each influencing factor can be constructed based on the entropy of each influencing factor [31]. The steps for determining the weights of influencing factors by the entropy weight method are provided as follows [32]:(1)
Collect the influencing factor samples fromT projects. The projects are ordered and t is the index of the project.(2)
Calculate the normalization valueyij,t of the secondary influencing factors.(3)
Calculate the ratiopij,t by(11)pij,t=yij,t∑t=1Tyij,t.(4)
Calculate the entropyEij of the secondary influencing factor uij with(12)Eij=−ξ∑t=1Tpij,tlnpij,t,whereξ=1/lnT is a constant related to the number of samples. pij,t has three requirements:(13)pij,t∈0,1,∑t=1Tpij,t=1,pij,tlnpij,t=0|pij,t=0.The largerEij is, the smaller the information of Ui contained in uij is and vice versa.(5)
Calculate the difference coefficientdij of each secondary influencing factor Eij by(14)dij=1−Eij.And then calculate the weightwij of uij w.r.t. Ui. The expression of wij is(15)wij=dij∑j=1nidij=1−Eij∑j=1ni1−Eij=1−Eijni−∑j=1niEij.According to formula (15), a weight vector for the secondary influencing factors can be obtained, we have(16)Wi=wi1,wi2,…,wini,where all weight factors satisfy∑j=1niwij=1 naturally.(6)
Use formula (16) to calculate the normalized value Yi,t of the primary influencing factor Ui,t for project t, and we have(17)Yi,t=∑j=1niwijyij,t.(7)
Use the entropy weight method similar to the process from Steps 2 to 5, the weight of the primary influencing factors can be calculated. According to formula (11), the ratio Pi,t and entropy Ei of the primary influencing factor Ui,t are computed by(18)Pi,t=Yi,t∑t=1TYi,t,Ei=−ξ∑t=1TPi,tlnPi,t,when Pi,t=0, Pi,tlnPi,t=0. The difference coefficient that defines for the primary influencing factor Ui is(19)Di=1−Ei.The weight of the primary influencing factors on the evaluation indicators is(20)wi=Di∑i=14Dij=1−Ei∑i=141−Ei=1−Ei4−∑i=14Ei.A weight vector of the primary influencing factors can be obtained:(21)W=w1,w2,w3,w4,where all weight factors satisfy ∑i=14wi=1.


## 5.1. Standardized Membership Functions

Normal membership function: the commonly used membership functions in geotechnical engineering area are normal-type functions, triangular fuzzy functions, trapezoidal functions, and ridge-type functions [28]. The parameter membership function that in geotechnical engineering should adopt an exponential normal distribution function was suggested [29]. Therefore, the membership function [30] of the structural influencing factor uij on the evaluation index is as follows:(5)fkuij=exp−uij−aijkcijk2,where k is the evaluation index of uij and aijk and cijk are constants, satisfying aijk>0 and cijk>0.Standardization of membership functions: to give a standardized membership function, the classification interval of the secondary influencing factor is linearly converted into a classification standard interval with the same size as the evaluation index. According to the levelk to which uij belongs, the positive and negative attribute factors have been normalized separately. After standardized treatment of influencing factors, the classification standards of each factor are consistent with the classification ranges of the postconstruction settlement classification standards in Table 1. aijk and cijk can be calculated using the upper and lower boundaries of the classification intervals of each factor classification standard. For the evaluation index level v1∼v4, the normal distribution membership function in the form of the normalized index is(6)rij1=1yij<0.125exp−yij−0.1250.1501420.125≤yij<0.251−exp−yij−0.3750.1501420.25≤yij<0.37500.375≤yij<1,(7)rij2=0yij<0.125∨yij≥0.6251−exp−yij−0.1250.1501420.125≤yij<0.25exp−yij−0.3750.1501420.25≤yij<0.501−exp−yij−0.6250.1501420.50≤yij<0.625,(8)rij3=0yij<0.375∨yij≥0.8751−exp−yij−0.3750.1501420.375≤yij<0.50exp−yij−0.6250.1501420.50≤yij<0.751−exp−yij−0.8750.1501420.75≤yij<0.875,(9)rij4=0yij<0.6251−exp−yij−0.6250.1501420.625≤yij<0.75exp−yij−0.8750.1501420.75≤yij<0.8751yij≥0.875,where yij is the normalized value of the influencing factor; rijk is the standard membership value of each influencing factor, and k = 1, 2, 3, and 4. The membership of each secondary influencing factor can be obtained using formulas (6) to (9). After obtaining the membership value of each secondary influencing factor, a matrix Ri can be constructed:(10)Ri=ri11ri12ri13ri14ri21ri22ri23ri24⋮⋮⋮⋮rini1rini2rini3rini4.


## 5.2. Weights of Influencing Factors

In the fuzzy comprehensive evaluation of multiple influencing factors, the weight is a measure of the influence of each influencing factor on the evaluation index. The method of determining the weight can generally be divided into subjective empowerment and objective weighting methods. Common subjective empowerment methods have Delphi method, analytic hierarchy process, and statistical method. Common objective weighting methods include entropy weight method, principal component analysis method, and mean square error method. As the subjective empowerment method relies on human factors, such as expert experience which may cause bias on the evaluation results, the entropy weight method in the objective weighting method is used to determine the weight of the influencing factors.Entropy is a physical quantity that reflects the randomness and disorder of subjects. The weight of each influencing factor can be constructed based on the entropy of each influencing factor [31]. The steps for determining the weights of influencing factors by the entropy weight method are provided as follows [32]:(1)
Collect the influencing factor samples fromT projects. The projects are ordered and t is the index of the project.(2)
Calculate the normalization valueyij,t of the secondary influencing factors.(3)
Calculate the ratiopij,t by(11)pij,t=yij,t∑t=1Tyij,t.(4)
Calculate the entropyEij of the secondary influencing factor uij with(12)Eij=−ξ∑t=1Tpij,tlnpij,t,whereξ=1/lnT is a constant related to the number of samples. pij,t has three requirements:(13)pij,t∈0,1,∑t=1Tpij,t=1,pij,tlnpij,t=0|pij,t=0.The largerEij is, the smaller the information of Ui contained in uij is and vice versa.(5)
Calculate the difference coefficientdij of each secondary influencing factor Eij by(14)dij=1−Eij.And then calculate the weightwij of uij w.r.t. Ui. The expression of wij is(15)wij=dij∑j=1nidij=1−Eij∑j=1ni1−Eij=1−Eijni−∑j=1niEij.According to formula (15), a weight vector for the secondary influencing factors can be obtained, we have(16)Wi=wi1,wi2,…,wini,where all weight factors satisfy∑j=1niwij=1 naturally.(6)
Use formula (16) to calculate the normalized value Yi,t of the primary influencing factor Ui,t for project t, and we have(17)Yi,t=∑j=1niwijyij,t.(7)
Use the entropy weight method similar to the process from Steps 2 to 5, the weight of the primary influencing factors can be calculated. According to formula (11), the ratio Pi,t and entropy Ei of the primary influencing factor Ui,t are computed by(18)Pi,t=Yi,t∑t=1TYi,t,Ei=−ξ∑t=1TPi,tlnPi,t,when Pi,t=0, Pi,tlnPi,t=0. The difference coefficient that defines for the primary influencing factor Ui is(19)Di=1−Ei.The weight of the primary influencing factors on the evaluation indicators is(20)wi=Di∑i=14Dij=1−Ei∑i=141−Ei=1−Ei4−∑i=14Ei.A weight vector of the primary influencing factors can be obtained:(21)W=w1,w2,w3,w4,where all weight factors satisfy ∑i=14wi=1.


## 6. Postconstruction Settlement Assessment Method for Two-Level Fuzzy Comprehensive Evaluation

After introducing the evaluation index, the influencing factor grading standard, the standardized membership function, the weight of the influencing factors, and a two-level fuzzy comprehensive evaluation method of the postconstruction settlement of the CFG pile composite subgrade are proposed in this section.


### 6.1. Evaluation Procedure

(1)
According to the postconstruction settlement requirements of the CFG pile composite subgrade in different road sections and the factors affecting the postconstruction settlement, the evaluation index evaluation setV, the primary influencing factor set U, and the secondary influencing factor set Ui are determined. The secondary influencing factors are the inputs of this model.(2)
Derive the relationship matrixRi for each primary influencing factors based on formula (10).(3)
Based on formula (16), determine the comprehensive evaluation vector Bi for the primary influencing factor Ui using(22)Bi=Wi∘Ri=bi1,bi2,bi3,bi4,where “∘” is the sign of the composition operator; this paper takes the composition operator as the addition and multiplication operator M (g+), namely,(23)bik=∑j=1niwijrijk.(4)
Construct the relationship matrixR for the primary influencing factors:(24)R=B1B2B3B4=b11b12b13b14b21b22b23b24b31b32b33b34b41b42b43b44.(5)
Calculate the evaluation vectorB for the evaluation index by using(25)B=W∘R=b1,b2,b3,b4,where(26)bk=∑i=14wibik.(6)
Determine the evaluation results of the postconstruction settlement based on the value of the element in the evaluation vectorB.


### 6.2. Weights of Factors Affecting Postconstruction Settlement of CFG Pile Composite Subgrade

Taking CFG pile composite subgrade in Guangdong Province as an example, the calculation process and analysis method of the index weight of each layer are described. With the support from the Guangdong Province Transportation Engineering Quality Supervision Station, the authors have collected the design and construction data from 71 different CFG pile composite subgrade road sections in Guangdong Province area. All the CFG pile composite subgrade road sections have operated for 2 to 5 years. Based on the entropy weight method mentioned in the previous section, the weights of the secondary influencing factors are calculated and given in Tables5 and 6.Table 5
Weights of geological and pile secondary influencing factors.
IndexGeological influencing factorU1Pile influencing factorU2u11u12u13u14u21u22u23u24Weights (%)39.135.922.52.527.424.326.921.4Table 6
Weights of cushion and construction secondary influencing factors.
IndexCushion influencing factorU3Construction influencing factorU4u31u32u33u41u42u43u44Weights (%)41.121.737.222.39.337.431.0According to the secondary weight factor values shown in Tables5 and 6, the weights of the internal friction angle (2.5%) of the subgrade soil and the filling rate (9.3%) are relatively small, and they have little effect on their corresponding primary influencing factors. The weights of all other secondary influencing factors exceed 20% and smaller than 50%, which is satisfied with our claim that the postconstruction settlement of CFG pile composite subgrade depends on many factors. The weights of all the secondary influencing factors are in consistent with the sensitivity analysis results discussed in the previous section.Similarly, the weights of the primary influencing factors can be computed. The results are shown in Table7.Table 7
Weights of primary factor index.
IndexWeights (%)Geological influencing factorU115.7Pile influencing factorU229.4Cushion influencing factorU334.8Construction influencing factorU420.1The data in Table7 show that the weights of the influencing factors of cushion, pile, construction, and geology are reduced in descending order, meaning their influences on the postconstruction settlement are reduced in turn. For composite subgrade, the cushion plays a role in adjusting the stress ratio of the pile and soil and determines the structural form of the bearing system. The pile is the main bearing part for undertaking the weight of the composite subgrade. Hence, the weight of the geological influencing factor is the smallest (15.7%) among all the primary influencing factors. However, none of the primary influencing factors can be neglected. The calculated weights of the primary influencing factors also indicate that the proposed entropy weight method can be used for analysing the relationships between the primary influencing factors and the postconstruction settlements.


### 6.3. Example Analysis

#### 6.3.1. Model Inputs

A bridge transition section in Guangdong Province has been selected to validate the proposed evaluation method. The target bridge transition section has CFG pile composite subgrade. The geological conditions and construction information are concluded as follows. The compressed soil thicknessu11 is 22.6 m, the averaged compression modulus u12 is 6450 kPa, the averaged cohesion u13 is 9.5 kPa, and the internal friction angle u14 is 6.7°. The pile diameter u23 is 0.4 m, the pile length u22 is 25 m, the pile spacing u24 is 2.2 m, and the pile modulus u21 is 8.0 GPa. The piles have a plum-type arrangement. The gravel cushion thickness u31 is 30 cm, the cushion modulus u32 is 100 MPa, and the cushion internal friction angle u33 is 35°. The filling height u41 is 5.3 m, and the filling rate u42 is 80 mm/d. Due to the tight schedule, the preloading process has not been applied in this road section. In this case, the preloading height u43 and preloading time u44 are 0. The index value and normalized value of secondary influencing factors are shown in Tables 8 and 9.Table 8
Index value and normalized value of geological and pile secondary influencing factors.
IndexGeological influencing factorsU1Pile influencing factorsU2u11 (m)u12 (MPa)u13 (kPa)u21 (MPa)u22 (m)u23 (m)u24 (m)Index valueuij22.66.459.58.0 × 10325.00.42.2Normalized valueyij0.4050.1980.1240.5990.0780.4720.310Table 9
Index value and normalized value of cushion and construction secondary influencing factors.
IndexCushion influencing factorsU3Construction influencing factorsU4u31 (m)u32 (MPa)u33 (°)u41 (m)u42 (mm/d)u43 (m)u44 (d)Index valueuij0.3100.035.05.380.00.00.0Normalized valueyij0.3460.4330.2310.1010.2321.0001.000


#### 6.3.2. Postconstruction Settlement Prediction

Based on the information of the target road section, the relationship matrixRi of each secondary influencing factors can be obtained. Following the process mentioned in the previous section, the relationship matrix R can be computed and we have(27)R=B1B2⋮Bs=W1R1W2R2W3R3W4R4=0.5330.4510.01500.2800.3620.35800.2420.7280.03000.2790.03700.684.According to the principle of the maximum membership, it can be seen from the matrixR that the level of geological influencing factors is excellent, the level of pile-influencing factors and cushion-influencing factors are good, and the level of construction-influencing factors is bad. The analysis conclusion is consistent with the reality that no preloading was performed to the target road section.According to equation (25), the comprehensive evaluation vector for the postconstruction settlement of CFG pile composite subgrade can be obtained as(28)B=W∘R=0.2220.2750.2620.192.According to the principle of maximum membership, the evaluation result of the postconstruction settlement is good. Namely, the range of the postconstruction settlement is [100 mm, 200 mm).The construction of the target road section was completed and opened to traffic in July 2015. The observation frequency of the postconstruction settlement is shown in Table10 and the collected postconstruction settlement data are shown in Figure 5.Figure 5
Postconstruction settlement monitoring data.Table 10
Monitoring frequency of postconstruction settlement.
Period0∼6 months7∼18 months18∼30 monthsFrequency2 times/month1 time/month1 time/2 monthsAccording to the field observation data, the current settlement is 88.7 mm. Using the hyperbolic method, the final postconstruction settlement of the CFG pile composite subgrade after 15 years operation is 164.23 mm, which satisfies the calculation and evaluation results. Since the road section is a transitional section at the bridgehead, the allowable value of its postconstruction settlement should be less than 100 mm. Hence, certain remedial measures, such as grouting, are necessary for this road section so as to meet the regulations.


## 6.1. Evaluation Procedure

(1)
According to the postconstruction settlement requirements of the CFG pile composite subgrade in different road sections and the factors affecting the postconstruction settlement, the evaluation index evaluation setV, the primary influencing factor set U, and the secondary influencing factor set Ui are determined. The secondary influencing factors are the inputs of this model.(2)
Derive the relationship matrixRi for each primary influencing factors based on formula (10).(3)
Based on formula (16), determine the comprehensive evaluation vector Bi for the primary influencing factor Ui using(22)Bi=Wi∘Ri=bi1,bi2,bi3,bi4,where “∘” is the sign of the composition operator; this paper takes the composition operator as the addition and multiplication operator M (g+), namely,(23)bik=∑j=1niwijrijk.(4)
Construct the relationship matrixR for the primary influencing factors:(24)R=B1B2B3B4=b11b12b13b14b21b22b23b24b31b32b33b34b41b42b43b44.(5)
Calculate the evaluation vectorB for the evaluation index by using(25)B=W∘R=b1,b2,b3,b4,where(26)bk=∑i=14wibik.(6)
Determine the evaluation results of the postconstruction settlement based on the value of the element in the evaluation vectorB.


## 6.2. Weights of Factors Affecting Postconstruction Settlement of CFG Pile Composite Subgrade

Taking CFG pile composite subgrade in Guangdong Province as an example, the calculation process and analysis method of the index weight of each layer are described. With the support from the Guangdong Province Transportation Engineering Quality Supervision Station, the authors have collected the design and construction data from 71 different CFG pile composite subgrade road sections in Guangdong Province area. All the CFG pile composite subgrade road sections have operated for 2 to 5 years. Based on the entropy weight method mentioned in the previous section, the weights of the secondary influencing factors are calculated and given in Tables5 and 6.Table 5
Weights of geological and pile secondary influencing factors.
IndexGeological influencing factorU1Pile influencing factorU2u11u12u13u14u21u22u23u24Weights (%)39.135.922.52.527.424.326.921.4Table 6
Weights of cushion and construction secondary influencing factors.
IndexCushion influencing factorU3Construction influencing factorU4u31u32u33u41u42u43u44Weights (%)41.121.737.222.39.337.431.0According to the secondary weight factor values shown in Tables5 and 6, the weights of the internal friction angle (2.5%) of the subgrade soil and the filling rate (9.3%) are relatively small, and they have little effect on their corresponding primary influencing factors. The weights of all other secondary influencing factors exceed 20% and smaller than 50%, which is satisfied with our claim that the postconstruction settlement of CFG pile composite subgrade depends on many factors. The weights of all the secondary influencing factors are in consistent with the sensitivity analysis results discussed in the previous section.Similarly, the weights of the primary influencing factors can be computed. The results are shown in Table7.Table 7
Weights of primary factor index.
IndexWeights (%)Geological influencing factorU115.7Pile influencing factorU229.4Cushion influencing factorU334.8Construction influencing factorU420.1The data in Table7 show that the weights of the influencing factors of cushion, pile, construction, and geology are reduced in descending order, meaning their influences on the postconstruction settlement are reduced in turn. For composite subgrade, the cushion plays a role in adjusting the stress ratio of the pile and soil and determines the structural form of the bearing system. The pile is the main bearing part for undertaking the weight of the composite subgrade. Hence, the weight of the geological influencing factor is the smallest (15.7%) among all the primary influencing factors. However, none of the primary influencing factors can be neglected. The calculated weights of the primary influencing factors also indicate that the proposed entropy weight method can be used for analysing the relationships between the primary influencing factors and the postconstruction settlements.


## 6.3. Example Analysis

### 6.3.1. Model Inputs

A bridge transition section in Guangdong Province has been selected to validate the proposed evaluation method. The target bridge transition section has CFG pile composite subgrade. The geological conditions and construction information are concluded as follows. The compressed soil thicknessu11 is 22.6 m, the averaged compression modulus u12 is 6450 kPa, the averaged cohesion u13 is 9.5 kPa, and the internal friction angle u14 is 6.7°. The pile diameter u23 is 0.4 m, the pile length u22 is 25 m, the pile spacing u24 is 2.2 m, and the pile modulus u21 is 8.0 GPa. The piles have a plum-type arrangement. The gravel cushion thickness u31 is 30 cm, the cushion modulus u32 is 100 MPa, and the cushion internal friction angle u33 is 35°. The filling height u41 is 5.3 m, and the filling rate u42 is 80 mm/d. Due to the tight schedule, the preloading process has not been applied in this road section. In this case, the preloading height u43 and preloading time u44 are 0. The index value and normalized value of secondary influencing factors are shown in Tables 8 and 9.Table 8
Index value and normalized value of geological and pile secondary influencing factors.
IndexGeological influencing factorsU1Pile influencing factorsU2u11 (m)u12 (MPa)u13 (kPa)u21 (MPa)u22 (m)u23 (m)u24 (m)Index valueuij22.66.459.58.0 × 10325.00.42.2Normalized valueyij0.4050.1980.1240.5990.0780.4720.310Table 9
Index value and normalized value of cushion and construction secondary influencing factors.
IndexCushion influencing factorsU3Construction influencing factorsU4u31 (m)u32 (MPa)u33 (°)u41 (m)u42 (mm/d)u43 (m)u44 (d)Index valueuij0.3100.035.05.380.00.00.0Normalized valueyij0.3460.4330.2310.1010.2321.0001.000


### 6.3.2. Postconstruction Settlement Prediction

Based on the information of the target road section, the relationship matrixRi of each secondary influencing factors can be obtained. Following the process mentioned in the previous section, the relationship matrix R can be computed and we have(27)R=B1B2⋮Bs=W1R1W2R2W3R3W4R4=0.5330.4510.01500.2800.3620.35800.2420.7280.03000.2790.03700.684.According to the principle of the maximum membership, it can be seen from the matrixR that the level of geological influencing factors is excellent, the level of pile-influencing factors and cushion-influencing factors are good, and the level of construction-influencing factors is bad. The analysis conclusion is consistent with the reality that no preloading was performed to the target road section.According to equation (25), the comprehensive evaluation vector for the postconstruction settlement of CFG pile composite subgrade can be obtained as(28)B=W∘R=0.2220.2750.2620.192.According to the principle of maximum membership, the evaluation result of the postconstruction settlement is good. Namely, the range of the postconstruction settlement is [100 mm, 200 mm).The construction of the target road section was completed and opened to traffic in July 2015. The observation frequency of the postconstruction settlement is shown in Table10 and the collected postconstruction settlement data are shown in Figure 5.Figure 5
Postconstruction settlement monitoring data.Table 10
Monitoring frequency of postconstruction settlement.
Period0∼6 months7∼18 months18∼30 monthsFrequency2 times/month1 time/month1 time/2 monthsAccording to the field observation data, the current settlement is 88.7 mm. Using the hyperbolic method, the final postconstruction settlement of the CFG pile composite subgrade after 15 years operation is 164.23 mm, which satisfies the calculation and evaluation results. Since the road section is a transitional section at the bridgehead, the allowable value of its postconstruction settlement should be less than 100 mm. Hence, certain remedial measures, such as grouting, are necessary for this road section so as to meet the regulations.


## 6.3.1. Model Inputs

A bridge transition section in Guangdong Province has been selected to validate the proposed evaluation method. The target bridge transition section has CFG pile composite subgrade. The geological conditions and construction information are concluded as follows. The compressed soil thicknessu11 is 22.6 m, the averaged compression modulus u12 is 6450 kPa, the averaged cohesion u13 is 9.5 kPa, and the internal friction angle u14 is 6.7°. The pile diameter u23 is 0.4 m, the pile length u22 is 25 m, the pile spacing u24 is 2.2 m, and the pile modulus u21 is 8.0 GPa. The piles have a plum-type arrangement. The gravel cushion thickness u31 is 30 cm, the cushion modulus u32 is 100 MPa, and the cushion internal friction angle u33 is 35°. The filling height u41 is 5.3 m, and the filling rate u42 is 80 mm/d. Due to the tight schedule, the preloading process has not been applied in this road section. In this case, the preloading height u43 and preloading time u44 are 0. The index value and normalized value of secondary influencing factors are shown in Tables 8 and 9.Table 8
Index value and normalized value of geological and pile secondary influencing factors.
IndexGeological influencing factorsU1Pile influencing factorsU2u11 (m)u12 (MPa)u13 (kPa)u21 (MPa)u22 (m)u23 (m)u24 (m)Index valueuij22.66.459.58.0 × 10325.00.42.2Normalized valueyij0.4050.1980.1240.5990.0780.4720.310Table 9
Index value and normalized value of cushion and construction secondary influencing factors.
IndexCushion influencing factorsU3Construction influencing factorsU4u31 (m)u32 (MPa)u33 (°)u41 (m)u42 (mm/d)u43 (m)u44 (d)Index valueuij0.3100.035.05.380.00.00.0Normalized valueyij0.3460.4330.2310.1010.2321.0001.000


## 6.3.2. Postconstruction Settlement Prediction

Based on the information of the target road section, the relationship matrixRi of each secondary influencing factors can be obtained. Following the process mentioned in the previous section, the relationship matrix R can be computed and we have(27)R=B1B2⋮Bs=W1R1W2R2W3R3W4R4=0.5330.4510.01500.2800.3620.35800.2420.7280.03000.2790.03700.684.According to the principle of the maximum membership, it can be seen from the matrixR that the level of geological influencing factors is excellent, the level of pile-influencing factors and cushion-influencing factors are good, and the level of construction-influencing factors is bad. The analysis conclusion is consistent with the reality that no preloading was performed to the target road section.According to equation (25), the comprehensive evaluation vector for the postconstruction settlement of CFG pile composite subgrade can be obtained as(28)B=W∘R=0.2220.2750.2620.192.According to the principle of maximum membership, the evaluation result of the postconstruction settlement is good. Namely, the range of the postconstruction settlement is [100 mm, 200 mm).The construction of the target road section was completed and opened to traffic in July 2015. The observation frequency of the postconstruction settlement is shown in Table10 and the collected postconstruction settlement data are shown in Figure 5.Figure 5
Postconstruction settlement monitoring data.Table 10
Monitoring frequency of postconstruction settlement.
Period0∼6 months7∼18 months18∼30 monthsFrequency2 times/month1 time/month1 time/2 monthsAccording to the field observation data, the current settlement is 88.7 mm. Using the hyperbolic method, the final postconstruction settlement of the CFG pile composite subgrade after 15 years operation is 164.23 mm, which satisfies the calculation and evaluation results. Since the road section is a transitional section at the bridgehead, the allowable value of its postconstruction settlement should be less than 100 mm. Hence, certain remedial measures, such as grouting, are necessary for this road section so as to meet the regulations.


## 7. Conclusion

In this paper, a two-level fuzzy comprehensive evaluation method is proposed for evaluating the postconstruction settlement of the CFG pile composite subgrade. Four primary influencing factors and 15 secondary factors are selected as the indexes to build the two-level evaluation system.The entropy weight method and normal membership function with the normalization process are used to describe the fuzzy relationship between the evaluation results and the influencing factors.A real bridgehead road section example in Guangdong Province has been selected to validate the proposed fuzzy comprehensive evaluation method. The evaluation results of the proposed method are in consistent with the field test results. Hence, the proposed fuzzy comprehensive evaluation method can be used to evaluate the construction quality of the CFG pile composite subgrade.The FCE method requires a large amount of data and is complicated to calculate. Moreover, the samples used in this paper to calculate the weight of influencing factors are mainly from Guangdong Province, China, which has certain limitations. Moving forward, efforts will be made to explore how to reduce the subjectivity in the determination of evaluation factors and weights and therefore to construct a more rational and adaptive FCE method.



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*Source: 8894942-2021-09-14.xml*