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.
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 [
Previous related works on foundation settlement.
Authors | Data set size | Method | Reliable condition |
---|---|---|---|
Omar et al. [ | Footing width, effective unit weight, and SPT blow count | Artificial neural network | Shallow foundation on granular soils |
Wang et al. [ | Soil properties and parameters related to the pile, such as pile spacing, pile length, and cap width | A calculation model for predicting the additional stresses in the composite foundation soil and the layerwise summation method | Composite foundation with sparse prestressed tubular concrete (PTC) capped-piles under embankment |
Meng et al. [ | The compression parameters of underlying soils related to soil disturbance degree | The layerwise summation method | Ground and tunnel |
Eid et al. [ | Pile-subgrade stiffness ratios for piled foundations on nonhomogeneous media | Three-dimensional finite-element (FE) analysis | The elastic settlement of piled foundations resting on rock |
Hong et al. [ | The time-extended loading residual settlement and settlement rate calculated from the field test data | An improved static loading test method, time-extended loading test | Pile-soil composite subgrade |
Kermani et al. [ | Rockfill modulus and rock strength | A novel approach considering the dam’s deformation behavior during construction | Concrete face rockfill dams |
Wang et al. [ | Three appropriate points for the measured settlement curve in the prediction samples | A three-point hyperbolic combination model | Subgrade filled with construction and demolition waste |
Cai et al. [ | The calculated dynamic stresses | The equivalent timeline model combined with the cyclic strain accumulation model | The long-term settlements of roads on soft soil under cyclic traffic loadings |
Mohammed et al. [ | The width of footing, pressure of footing, geometry of footing, count of SPT blow, and ratio of footing embedment | Machine learning models | Settlement of shallow foundation over cohesion soil properties |
Tang et al. [ | The observation data of settlement during construction | The Hushino model, hyperbolic curve method, and exponential curve method | Foundation after construction |
Ding [ | The design parameters | Numerical simulation approach | Pile-soil composite subgrade |
In 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.
In recent years, artificial intelligence technology has been developed rapidly, but at present, artificial intelligence technology still has some shortcomings and limitations [
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. [
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 [
In the two-level fuzzy comprehensive evaluation system, an evaluation index
Classification standard for postconstruction settlement.
Evaluation index | Postconstruction settlement (mm) | Standard classification interval | |
---|---|---|---|
Excellent | [0, 100) | [0, 0.25) | |
Good | [100, 200) | [0.25, 0.50) | |
Moderate | [200, 300) | [0.50, 0.75) | |
Poor | [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 Table
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
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 geology
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 thickness
The influencing factors of the pile
Generally, CFG pile length range
The influencing factors of the cushion
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 cushion
The influencing factors of the construction
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 height
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.
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 factor
The second category is named as negative attribute factor
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 soil
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:
According to formula (
The relationships between the postconstruction settlements and the normalized values of the influencing factors are concluded and shown in Figures
Effects of geological factors on postconstruction settlement.
Effects of piles geological factors on postconstruction settlement.
Effects of cushion factors on postconstruction settlement.
Effects of construction factors on postconstruction settlement.
According to Figures
Based on Figure
Among the influencing factors of the pile, the postconstruction settlement is sensitive to the pile modulus
In Figure
Among the construction-influencing factors, the preloading height
According to the simulation and analysis results shown in Figures
The change of friction angle in the subgrade soil does not affect the postconstruction settlement
Classification standard of all the secondary influencing factors is shown in Tables
Initial conditions and classification standard of geological and pile secondary influencing factors.
Index | Geological influencing factors | Pile influencing factors | ||||||
---|---|---|---|---|---|---|---|---|
Initial condition | 18 | 6 | 6 | 2 × 104 | 15 | 0.5 | 2.0 | |
Classification standard | 0∼18.94 | 5.52∼10.00 | 3.87∼15.00 | 17,288.90∼30,000 | 13.99∼30.00 | 0.48∼0.60 | 1.40∼2.09 | |
18.94∼24.84 | 2.24∼5.52 | 2.43∼3.86 | 9543.25∼17,288.90 | 8.99∼13.99 | 0.39∼0.48 | 2.09∼2.55 | ||
24.84∼27.42 | 1.62∼2.24 | 1.71∼2.43 | 5649.22∼9543.25 | 6.01∼8.99 | 0.34∼0.39 | 2.55∼2.82 | ||
27.42∼30.00 | 1.00∼1.62 | 1.00∼1.71 | 800.00∼5649.22 | 0∼6.01 | 0.30∼0.34 | 2.82∼3.00 |
Initial conditions and classification standard of cushion and construction secondary influencing factors.
Index | Cushion influencing factors | Construction influencing factors | ||||||
---|---|---|---|---|---|---|---|---|
Initial condition | 0.6 | 150 | 40 | 6 | 50 | 2.0 | 180 | |
Classification standard | 0.40∼0.80 | 128.81∼250 | 32.89∼60.00 | 1.00∼11.61 | 5.00∼85.76 | 1.48∼3.00 | 108.30∼360 | |
0.14∼0.40 | 89.41∼128.81 | 21.85∼32.89 | 11.61∼15.80 | 85.76∼92.88 | 0.49∼1.48 | 24.10∼108.30 | ||
0.07∼0.14 | 69.70∼89.41 | 18.42∼21.85 | 15.80∼17.90 | 92.88∼96.44 | 0.15∼0.49 | 7.32∼24.10 | ||
0∼0.07 | 50.00∼69.70 | 15.00∼18.42 | 17.90∼20.00 | 96.44∼100.00 | 0∼0.15 | 0∼7.32 |
Based on the sensitivity analysis in the previous section and the classification standard of influencing factors in Tables
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 [
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 level
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 [ Collect the influencing factor samples from Calculate the normalization value Calculate the ratio Calculate the entropy where The larger Calculate the difference coefficient And then calculate the weight According to formula ( where all weight factors satisfy Use formula ( 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 (
when
The weight of the primary influencing factors on the evaluation indicators is
A weight vector of the primary influencing factors can be obtained:
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.
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 set
Derive the relationship matrix
Based on formula (
where “
Construct the relationship matrix
Calculate the evaluation vector
where
Determine the evaluation results of the postconstruction settlement based on the value of the element in the evaluation vector
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 Tables
Weights of geological and pile secondary influencing factors.
Index | Geological influencing factor | Pile influencing factor | ||||||
---|---|---|---|---|---|---|---|---|
Weights (%) | 39.1 | 35.9 | 22.5 | 2.5 | 27.4 | 24.3 | 26.9 | 21.4 |
Weights of cushion and construction secondary influencing factors.
Index | Cushion influencing factor | Construction influencing factor | |||||
---|---|---|---|---|---|---|---|
Weights (%) | 41.1 | 21.7 | 37.2 | 22.3 | 9.3 | 37.4 | 31.0 |
According to the secondary weight factor values shown in Tables
Similarly, the weights of the primary influencing factors can be computed. The results are shown in Table
Weights of primary factor index.
Index | Weights (%) |
---|---|
Geological influencing factor | 15.7 |
Pile influencing factor | 29.4 |
Cushion influencing factor | 34.8 |
Construction influencing factor | 20.1 |
The data in Table
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 thickness
Index value and normalized value of geological and pile secondary influencing factors.
Index | Geological influencing factors | Pile influencing factors | |||||
---|---|---|---|---|---|---|---|
Index value | 22.6 | 6.45 | 9.5 | 8.0 × 103 | 25.0 | 0.4 | 2.2 |
Normalized value | 0.405 | 0.198 | 0.124 | 0.599 | 0.078 | 0.472 | 0.310 |
Index value and normalized value of cushion and construction secondary influencing factors.
Index | Cushion influencing factors | Construction influencing factors | |||||
---|---|---|---|---|---|---|---|
Index value | 0.3 | 100.0 | 35.0 | 5.3 | 80.0 | 0.0 | 0.0 |
Normalized value | 0.346 | 0.433 | 0.231 | 0.101 | 0.232 | 1.000 | 1.000 |
Based on the information of the target road section, the relationship matrix
According to the principle of the maximum membership, it can be seen from the matrix
According to equation (
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 Table
Postconstruction settlement monitoring data.
Monitoring frequency of postconstruction settlement.
Period | 0∼6 months | 7∼18 months | 18∼30 months |
---|---|---|---|
Frequency | 2 times/month | 1 time/month | 1 time/2 months |
According 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.
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.
The data used to support the findings of this study are presented in the tables and figures.
This work is an original one conducted at Xuzhou University of Technology. The work described has not been submitted elsewhere for publication, in whole or in part.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
All the authors have contributed to and approved this paper.
This work was supported by the National Science Foundation for Young Scientists of China (grant no. 51904270).