Fiber-reinforced soils have been of great interest to experimenters for building foundations’ strength performance, time, and economy. This paper investigates the effects of water content and polypropylene fiber dosage and length on loess’s unconfined compressive strength (UCS) according to the central composite response surface design test procedure. The water content is 11%–25%, the mass ratio of fiber to soil is 0.1%–0.9%, and the fiber length ranges from 6–18 mm. The response surface method (RSM) developed full quadratic models of different variables with response values. After analysis of variance (ANOVA), the mathematical model developed in this study was statistically significant (

Collapsible loess is a typical structural soil with strong water sensitivity [

Because traditional stabilizers such as lime and cement have good pozzolanic properties with soil particles, they are often used to improve the engineering properties of soil [_{2} emissions, and resource depletion, e.g., approximately one ton of CO_{2} is released into the environment for each ton of cement produced [

Several scholars have conducted experiments on the mechanical properties of reinforced soils [

This paper uses polypropylene fiber as an additive material to develop the unconfined compressive strength of loess with different water content. This study applied the surface response method to fiber-strengthened loess and developed a quadratic model between the independent variables and response values. Finally, the mechanism of the influence of polypropylene fibers on the strength of loess was analyzed by scanning electron microscopy. The results of the study can provide theoretical guidance for the use of polypropylene fibers for reinforcing loess.

The loess specimens used in this paper were taken from Guyuan City, Ningxia Hui Autonomous Region, with a sampling depth of 3–3.2 m. The soil sample was Malan loess, and a Bettersize2000 laser particle size distribution instrument tested the particle size distribution. The results showed that the loess sample consisted mainly of silt particles (about 83.54%), with approximately the same sand and clay particle content of 8.18% and 8.28%, respectively (

Property | Value |
---|---|

Maximum dry density ^{3}) |
1.72 |

Optimal water content |
16.21 |

Specific gravity Gs | 2.69 |

Liquid limit _{L} |
26.6 |

Plastic limit _{P} |
17.4 |

Particle size distribution | |

Sand 0.075–2 mm (%) | 8.18 |

Silt 0.002–0.075 mm (%) | 83.54 |

Clay < 0.002 mm (%) | 8.28 |

Type | Color | Density/(g/cm^{3}) |
Melting point/°C | Diameter/μm | Tensile strength/MPa | Stretch limit/% | Elastic modulus/GPa |
---|---|---|---|---|---|---|---|

Bunched monofilament | White | 0.91 | >165 | 18 | >458 | >150 | >3.5 |

The test results were closely related to the specimen preparation method, so mixing the fibers with the soil was a major consideration in the specimen preparation process. The specific test steps were as follows: The soil obtained in the field was dried, crushed, and passed through a 2 mm sieve. The water mass of the soil humidified to the target water content is calculated, and then the water is added uniformly to the dry soil. After mixing, the soil was sealed and left to stand for 24 h to ensure uniform distribution of water in the soil. Since the fibers are bundles, they are first dispersed in water. The dispersed fibers were air-dried after being removed from the water and mixed into the soil. The dispersed fibers and soil were mixed well and put into the compactor for compaction, and the compaction work per unit volume of the control specimen was 592.2 kJ/m^{3}. Finally, the compacted soil sample was chipped to the specimen size required for the unconfined compressive strength test. The specimen used for the unconfined compressive strength test is cylindrical with a diameter of 39.1 mm and a height of 80 mm. After the samples were prepared, they were placed in a constant temperature and humidity chamber for 7 days at 20°C and 70% humidity. The specimens’ unconfined compressive strength (UCS) was tested by a YSH-2 type unconfined pressure instrument produced by Nanjing Soil Instrument Factory, and the strain rate was controlled as 1 mm/min. Three parallel tests were conducted for each test condition to eliminate errors in test results and take the average value. After the unconfined compression test, representative soil samples were selected for electron microscopy scanning analysis to observe fibers’ distribution characteristics and interface morphology in the soil.

The response surface method (RSM) is a collection of statistical and mathematical techniques that can be used to develop, improve, and optimize the input terms in a manufacturing process [_{PF}

Variable | Level | ||
---|---|---|---|

−1 | 0 | 1 | |

11 | 18 | 25 | |

PFC (%) | 0.1 | 0.5 | 0.9 |

PFL (mm) | 6 | 12 | 18 |

This study used a face-central composite design (FCCCD) for the experimental design, which is essential for developing response surface models. The three-way experimental design using FCCCD contains eight factorial points, six vertices, and six central points. The number of center points was determined according to the design matrix that can be orthogonalized. The center point provides information about curvature in the constructed system. The purely quadratic term can be efficiently estimated by adding axis points if the curvature is available.

Experimental design | Experimental program | UCS (kPa) | |||||
---|---|---|---|---|---|---|---|

PFL | PFC | PFL (mm) | PFC (%) | Actual | RSM | ||

−1 | −1 | −1 | 11 | 6 | 0.1 | 110.02 | 127.89 |

1 | −1 | −1 | 25 | 6 | 0.1 | 62.24 | 65.59 |

−1 | 1 | −1 | 11 | 18 | 0.1 | 138.03 | 124.27 |

1 | 1 | −1 | 25 | 18 | 0.1 | 78.09 | 82.57 |

−1 | −1 | 1 | 11 | 6 | 0.9 | 117.56 | 145.13 |

1 | −1 | 1 | 25 | 6 | 0.9 | 66.51 | 52.03 |

−1 | 1 | 1 | 11 | 18 | 0.9 | 186.75 | 152.35 |

1 | 1 | 1 | 25 | 18 | 0.9 | 105.66 | 97.24 |

−1 | 0 | 0 | 11 | 12 | 0.5 | 215.41 | 249.52 |

1 | 0 | 0 | 25 | 12 | 0.5 | 121.86 | 104.19 |

0 | −1 | 0 | 18 | 6 | 0.5 | 222.25 | 187.93 |

0 | 1 | 0 | 18 | 18 | 0.5 | 297.71 | 416.60 |

0 | 0 | −1 | 18 | 12 | 0.1 | 222.55 | 190.90 |

0 | 0 | 1 | 18 | 12 | 0.9 | 277.04 | 382.20 |

0 | 0 | 0 | 18 | 12 | 0.5 | 317.33 | 309.06 |

0 | 0 | 0 | 18 | 12 | 0.5 | 317.33 | 309.06 |

0 | 0 | 0 | 18 | 12 | 0.5 | 317.33 | 309.06 |

0 | 0 | 0 | 18 | 12 | 0.5 | 317.33 | 309.06 |

0 | 0 | 0 | 18 | 12 | 0.5 | 317.33 | 309.06 |

0 | 0 | 0 | 18 | 12 | 0.5 | 317.33 | 309.06 |

The unconfined compressive strength tests were performed on each group of specimens as described in

In controlled variable methods, it is challenging to examine the interaction of independent variables on the change of the dependent variable, so ANOVA can be helpful for describing the relationship between variables. The independent factor and interaction effects on the dependent variable (UCS) are examined via ANOVA. For RSM methods and ANOVA analysis, Stat-Ease Inc.’s free evaluation statistics package Design-Expert was used. With a 95% confidence level,

Source | Sum of |
Degree of |
Mean square | ||
---|---|---|---|---|---|

Model | 6.24 | 9 | 0.69 | 4230.52 | <0.0001 |

0.81 | 1 | 0.81 | 4952.61 | <0.0001 | |

PFL | 0.28 | 1 | 0.28 | 1706.23 | <0.0001 |

PFC | 0.091 | 1 | 0.091 | 558.38 | <0.0001 |

w * PFL | 1.44E-009 | 1 | 1.44E-009 | 8.793E-006 | 0.9977 |

w * PFC | 2.19E-009 | 1 | 2.19E-009 | 1.337E-005 | 0.9972 |

PFC * PFL | 0.028 | 1 | 0.028 | 170.05 | <0.0001 |

w * w | 1.26 | 1 | 1.26 | 7678.37 | <0.0001 |

PFL * PFL | 0.13 | 1 | 0.13 | 768.87 | <0.0001 |

PFC * PFC | 0.17 | 1 | 0.17 | 1043.50 | <0.0001 |

Residual | 1.638E-003 | 10 | 1.638E-004 | ||

Lack of Fit | 1.638E-003 | 5 | 3.276E-004 | ||

Pure Error | 0.00 | 5 | 0.000 | ||

Cor Total | 6.24 | 19 | |||

R^{2} |
0.9997 | Pred R^{2} |
0.9980 | ||

Adj R^{2} |
0.9995 | Std. Dev. | 0.013 |

The determination coefficient (R^{2}) describes how much variation there is around the mean defined by the fitted model. ^{2} is 0.9997, which is close to 1. Although the R^{2} value of a model is high, it does not necessarily mean the model is great because any additional variable, regardless of its statistical significance, increases the R^{2} value [^{2} (Adj R^{2}) will not always increase when variables are added to a built model, since it measures the variation in the mean explained by the model, adjusted for the number of terms. In addition, Adj R^{2} values typically decrease as unnecessary terms are added to the model. The value of Adj R^{2} is 0.9995. R^{2} and Adj R^{2} are similar, indicating a good agreement between predicted and measured UCS values. In addition, predicted R^{2} (Pred R^{2}) is another assessment criterion used in this study to measure the change in new data, which is explained by the built-in RSM model. In ^{2} of the RSM model is found to be 0.9980, which indicates that the RSM model can explain approximately 99.80% of the variability in new response values, in contrast to approximately 99.97% in the original data. Additionally, since the difference between Pred R^{2} and Adj R^{2} is less than 0.20, it can be said that these statistics fit very well in the developed model [

Generally, the smaller the

The water content, the fiber length, and the fiber content are the three parameters that have the greatest influence, as shown by the contribution values in

The developed RSM model is shown in

On the other hand, the conversion of the response (dependent variable) is frequently done once the graph demonstrates that the normalcy assumption is broken.

By showing the connection between the t-student internal residuals and the predicted response variable, the assumption of equal variances (UCS) is examined. The graph will frequently display a funnel-shaped pattern if the response variance is dependent on the average of the measured responses, suggesting that the response variable has to be shifted. The internal t-student residuals are randomly distributed in the plot, as shown in the overall representation of

Expert software was designed to determine the reinforced soil’s maximum unconfined compressive strength. The optimum ratio is 16.41% water content, 0.579% polypropylene fiber content, and 14.90 mm polypropylene fiber length. The unconfined compressive strength of reinforced soil is 342.757 kPa at the optimum ratio, and the unconfined compressive strength of plain soil is 54.74 kPa. Compared with the unconfined compressive strength of plain soil, the unconfined compressive strength is increased by 288.017 kPa at the optimum ratio.

During the unconfined compression strength test, the inconsistent modulus of elasticity of the fiber and soil must cause the fiber and soil surfaces to misalign with each other and generate interfacial forces. Interfacial forces depend mainly on friction and cohesion [

The polypropylene fibers incorporated in the soil are randomly distributed, and the fibers do not form a good linkage when the fiber content is small and are mainly single fibers under tension (

The fiber surface of the specimen with 18% water content clearly showed scratches along the longitudinal direction of the fiber (

The SEM images of the specimens with 11% and 18% water content are shown in

The mean area of the particle aggregates _{i}

The surface porosity of the specimens with 11% and 18% water content was 18.33% and 11.35%, respectively, indicating that the 18% water content specimens were denser. The average particle areas of the specimens with 11% and 18% water content were 1434.27 μm^{2} and 3292.52 μm^{2}, respectively, indicating that the water film bonded the soil particles together, increasing the area of the particles. Therefore, the unconfined compressive strength of the sample with 18% water content is increased compared with the 11% sample due to the following reasons: i) The water film thickness of the sample with 18% water content is moderate compared with the 11% sample. Because the water film is too thin, it will affect the compaction of the sample, resulting in large pores in the sample; The increase in water content makes the soil more compact, thereby increasing the effective contact area between the fiber and the soil; ii) An appropriate amount of water film binds the soil particles together, and the aggregate volume of the particles increases, thereby restricting the rearrangement of the soil particles on the interface; iii) The increase in sample density creates an interlocking force, making it more difficult to pull out the fiber. For the 25% water content sample, due to the large water film thickness inside the sample, it plays a role in lubrication, and the strength is reduced to a certain extent. Therefore, the specimens’ unconfined compressive strength increased with the water content, but when the water content exceeded 16.41%, the high-water content caused the unconfined compressive strength to decrease.

About one-third of the geological disasters in China occur on the Loess Plateau [

This paper investigates the optimization problem of loess improvement based on the performance of UCS using response surface methodology. Based on the UCS values, an RSM model was developed to study the input variables’ optimal ratios (w, PFC, PFL). The following main conclusions were obtained:

Water content, polypropylene fiber length, and polypropylene fiber content significantly affect the fiber reinforced loess strength. The unconfined compressive strength shows an increasing trend and then decreases with the abovementioned factors.

Water content is the most important factor influencing the strength of fiber-reinforced loess, followed by the fiber length and content.

There is an optimal ratio to maximize the unconfined compressive strength, which is 16.41% water content, 0.579% polypropylene fiber content, and 14.90 mm polypropylene fiber length. The unconfined compressive strength of reinforced soil under the optimal ratio is 342.757 kPa. The unconfined compressive strength under the optimal ratio is increased by 288.017 kPa.

As a result of mathematical modeling of the experimental design of the RSM method, the formula for the RSM model used to predict the response variable (UCS) was constructed, and the established model was determined to be statistically significant by analysis of variance.

This study was financially supported by the National Nature Science Foundation of China (Grant No. 1931285) and the Key Research and Development Program of Shaanxi Province (Grant No. 2020SF-436).