The permanent displacement has been widely used for slope seismic stability in practical engineering; however, the effect of the dynamic pore water pressure on the saturated and unsaturated soil slopes could not be neglected. In this paper, we propose a calculation method of dynamic pore water pressure by the hollow cylinder apparatus (GCTS) which is the most advanced and complicated device in lab testing on soil dynamics. Then, based on the proposed calculation method of dynamic pore water pressure combined with the limit equilibrium and finite element methods, we introduce a simple calculation method of permanent displacement, which avoids solving complex nonlinear equations and greatly simplifies the computational effort. Shaking table test results demonstrate the effectiveness and efficiency of the simple calculation method of permanent displacement, which could rapidly assess the soil slope seismic stability considering the effect of dynamic pore water pressure.

The landslide induced by earthquake is a common geological disaster. According to preliminary statistics, more than 15,000 landslides were triggered by the Wenchuan earthquake [

Different soil slopes affected by different rainfall amounts are in different groundwater levels during the earthquake or aftershocks, and the slopes suffered from a combination of factors, including earthquake and groundwater. Seismic stability evaluation methods of slopes are the core of the slope seismic stability analysis. Therefore, it is especially important to use a reasonable safety evaluation method for slope seismic stability analysis. At present, the slope stability analysis methods mainly include the quasi-static method, Newmark sliding block method, and time-history method. The quasi-static method [

In recent years, a large number of landslide disaster cases especially the slope failure phenomena in the Wenchuan earthquake show that the current evaluation method of slope stability could not meet the safety performance evaluation of the slope. The design method based on deformation is one of the most important theories of seismic design [

An actual slope which is along the Zhunshuo railway in Inner Mongolia Autonomous Region in China is selected as the research object, as shown in Figure

Engineering field figure.

The slope model in reference [

Analysis model of the slope (reproduced from the study of Huang et al. [

The calculation parameters of the slope model are obtained by the indoor test and referenced in the

Calculation parameters of the model.

Soil type | Gravity (kN·m^{−3}) |
Poisson’s ratio | Elastic modulus (MPa) | Friction angle (°) | Cohesion (kPa) | Permeability coefficient (cm·s^{−1}) |
Saturated water content (%) |
---|---|---|---|---|---|---|---|

Sandy | 17.5 | 0.3 | 50.4 | 35.23 | 11.42 | 5e-5 | 30 |

By comparison of the slope codes of the earthquake-prone countries (China, Japan, European countries, and California in the United States), evaluation methods of the slope seismic stability in different specifications were determined at home and abroad, as shown in Table

Slope codes of the earthquake-prone countries.

Nation | Codes | Evaluation methods | Evaluation indictors |
---|---|---|---|

China | “Technical code for building slope engineering” (GB50330-2013) | Quasi-static method [ |
Safety factor |

“Design code for engineered slopes in water resources and hydropower projects” (SL386-2007) | Quasi-static method | Safety factor | |

“Specifications for design of highway Subgrades” (JTG D30-2004) | Quasi-static method | Safety factor | |

“Code for seismic design of railway engineering” (GB50111-2006) | Quasi-static method | Safety factor | |

“Code for design on subgrade of railway” (TB10001-2005) | Quasi-static method | Safety factor | |

“Code for design of high speed railway” (TB10621-2009) | Quasi-static method | Safety factor | |

Japan | “Design standards for railway structures” | Quasi-static method and Newmark method | Safety factor and permanent displacement |

European countries | Eurocode 7: geotechnical design | Quasi-static method | Safety factor |

California in the United States | California Geological Survey’s guidelines (2008) | Quasi-static method | Safety factor |

By comparing slope codes in different countries, we used the safety factor and permanent displacement to evaluate the slope stability, which are closer to the actuals.

Referring to Japanese

Parameters of the earthquake motions.

Seismic wave | Recorded location | Earthquake name | Magnitude | Epicentral distance (km) |
---|---|---|---|---|

T1-II-1 | Foundation of Itajima bridge | Hyūganada earthquake (1968) | 7.5 | 100 |

El Centro | El Centro | Emperor Valley earthquake (1940) | 7.7 | 12 |

T2-II-1 | JR Takatori station | Kobe (1995) | 7.2 | 16 |

Time-history of earthquakes (reproduced from the study of Huang et al. [

Different factors are changed, respectively, on the basis of the original slope. Effects of various factors including slope rates, slope heights, groundwater levels, peak accelerations, and earthquake types on the safety factor and the permanent displacement of the slope are studied, as shown in Table

Numerical procedure.

Slope rate | Slope height (m) | Underground water level |
Peak acceleration (m·s^{−2}) |
Seismic waves |
---|---|---|---|---|

1 : 1.5 | 12 | 5 | 2, 3, 4, 5, 6, 7, 8, 9, 10 | El Centro |

1 : 1.4 | 12 | 5 | 4, 5, 6 | El Centro |

1 : 1.5 | 12 | 5 | 4, 5, 6 | |

1 : 1.6 | 12 | 5 | 4, 5, 6 | |

1 : 1.5 | 12 | 6 | 4, 5, 6 | El Centro |

7 | 4, 5, 6 | |||

8 | 4, 5, 6 | |||

1 : 1.5 | 12 | 5 | 4, 5, 6 | El Centro |

24 | 10 | 4, 5, 6 | El Centro | |

36 | 15 | 4, 5,6 | El Centro | |

1 : 1.5 | 12 | 5 | 4, 5, 6 | El Centro, T1-II-1, T2-II-1 |

The permanent displacement is calculated by the finite element method at a certain groundwater level considering the effect of the large deformation nonlinearity. And we calculated the permanent displacement of the slope under El Centro (2 m/s^{2}) at the groundwater level 5 m, as shown in Figure

Permanent displacement calculated by the finite element method.

As shown in Figure

Generation of the dynamic pore water pressure is mainly caused by the changes in the deviatoric stress and the average effective stress. Thus, the maximum dynamic pore water pressure could be calculated by the deviatoric stress and the average effective stress of the soil, as shown in Table

Test results under earthquakes and sine waves.

Soil compaction | Working condition | Cycle times | ||||||
---|---|---|---|---|---|---|---|---|

Vertical stress (kPa) | Horizontal stress (kPa) | Average effective stress (kPa) | Initial deviatoric stress (kPa) | Seismic waves | Maximum deviatoric stress (kPa) | Stress ratio | Dynamic pore water pressure (kPa) | |

300 | 150 | 200 | 150 | T1-II-1 | 56.02 | 0.09 | 24 | 2 |

255 | 170 | 198 | 85 | El Centro | 51.56 | 0.26 | 25 | 2 |

300 | 150 | 200 | 150 | 62.36 | 0.10 | 29 | 2 | |

255 | 170 | 198 | 85 | T2-II-1 | 40.01 | 0.20 | 16 | 2 |

300 | 150 | 200 | 150 | 57.96 | 0.10 | 26 | 2 | |

255 | 170 | 198 | 85 | Sine wave 1 Hz | 48.27 | 0.24 | 23 | 2 |

300 | 150 | 200 | 150 | 70.73 | 0.12 | 35 | 2 | |

255 | 170 | 198 | 85 | Sine wave 2 Hz | 59.21 | 0.30 | 30 | 2 |

300 | 150 | 200 | 150 | 57.5 | 0.095 | 25 | 2 | |

255 | 170 | 198 | 85 | Sine wave 3 Hz | 40.51 | 0.20 | 17 | 2 |

300 | 150 | 200 | 150 | 58.60 | 0.098 | 26 | 2 | |

255 | 170 | 198 | 85 | Sine wave 4 Hz | 50.90 | 0.26 | 24 | 2 |

300 | 150 | 200 | 150 | 66.42 | 0.098 | 32 | 2 | |

255 | 170 | 198 | 85 | Sine wave 5 Hz | 52.70 | 0.27 | 26 | 2 |

300 | 150 | 200 | 150 | 57.47 | 0.096 | 25 | 2 | |

255 | 170 | 198 | 85 | Sine wave 6 Hz | 48.87 | 0.25 | 23 | 2 |

300 | 150 | 200 | 150 | 52.47 | 0.13 | 28 | 2 |

Relationship curve of the maximum dynamic pore water pressure and the maximum deviatoric stress.

The relations of the maximum dynamic pore water pressure and the maximum deviatoric stress and the average effective stress under different earthquakes and sine waves are analyzed, as shown in Figures

Relationship curve of the maximum dynamic pore water pressure and the average effective stress.

As shown in Figures

Through the nonlinear regression analysis, the simple calculation method of the maximum dynamic pore water pressure could be obtained, as shown in the following equation:

The simple calculation method of the maximum dynamic pore pressure is plugged into the limit equilibrium equation, and the safety factor which could consider the effect of the dynamic pore pressure is obtained, as shown in Figure

Stress state of a free body in the slope.

By analyzing the stress state of the isolator in the slope, the limit equilibrium method is shown as follows:

By using balance equation (

By using equations (

Equations (

Fitting relationship of the permanent displacement and safety factor is shown in Figure

(a) Relationship of the safety factor and the peak acceleration. (b) Fitting relationship of the permanent displacement and safety factor.

As shown in Figure

Thus, fitting relationship of the permanent displacement and the safety factor could be obtained, as shown in the following equation:

Equation (

In order to determine the accuracy of the proposed simple calculation method, a shaking table test of a small soil slope is carried out, as shown in Figure

The small slope model (reproduced from the study of Huang et al. [

In this study, a one-way shaking table (ES-15/KE-2000) is used for testing. There are four technical indicators in this equipment. The maximum test load and acceleration are 5000 kg and 20 m/s^{2}, respectively. The rated speed is 0.5 m/s. And the equipment is shown in Figure

Vibration equipment (reproduced from the study of Huang et al. [

The permanent displacements are obtained from the shaking table test under T1-II-1 when the peak acceleration value is 0.4 g, as shown in Figure

Permanent displacements during the test. (a) _{w} = 0 m. (b) _{w} = 0.6 m. (c) _{w} = 0.7 m. (d) _{w} = 0.8 m.

As shown in Figure

The permanent displacement obtained from the shaking table test is compared with that calculated by the simple calculation method, as shown in Figure

Permanent displacements of different methods.

As shown in Figure

The aim of this research is to lay a foundation for the stability evaluation of the saturated and unsaturated soil slopes using permanent displacement. A series of dynamic hollow cylinder torsional shear tests were conducted under different confining and deviatoric stresses, and a calculation method of dynamic pore water pressure associated with deviatoric and average effective stresses is proposed. The calculation method avoids the solution of complex nonlinear equations and greatly simplifies the computational effort.

Based on the proposed calculation method of dynamic pore water pressure combined with the limit equilibrium and finite element methods, we introduced a simple calculation method of permanent displacement, which could provide a reference to the slope seismic reinforcement for engineering designers and be used as a rapid assessment method to the slope seismic stability. Unlike traditional calculation methods of permanent displacement, the proposed calculation method considered the effect of the dynamic pore water pressure.

The superior performance of the simple calculation method of the permanent displacement was demonstrated based on the shaking table test. The shaking table test results indicated that the calculation method could rapidly assess the seismic stability of the soil slope considering the effect of dynamic pore water pressure. The permanent displacement values obtained from the simple calculation method were greater than the permanent displacement values obtained from the shaking table test; however, the maximum deviation was within 18%, which verified the simple calculation method is feasible.

The data used to support the findings of this study are included within the article.

There are no conflicts of interest regarding the publication of this paper.

This work was financially supported by the Beijing Natural Science Foundation (Grant No. 8174078), National Natural Science Foundation of China (Grant No. 51708516), and National Key R&D Program of China (2017YFC1500404) and the research grant from Institute of Crustal Dynamics, China Earthquake Administration (No. ZDJ2016-12).