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The knowledge of the internal stability of granular soils is a key factor for the design of granular and filter for the geotechnical infrastructures such as dykes, barrages, weirs and roads embankment. To evaluate the internal instability of granular soils different criteria are generally used in the practice. However, the results of these criteria on the same soil may lead to different evaluations of the internal instability. In this paper the common criteria used for the internal instability have been presented and compared as far as possible. It was found that the most internal instability criteria define a limit value for the secant slope of the grain size distribution curve of the granular soils. Based on this finding an own criterion for the evaluation of the internal instability of granular soil has been developed and compared to the common criteria. A very good agreement between some criteria was found. Furthermore, a site specific assessment for the evaluation of the internal instability of granular soil has been proposed in order to get more confidence in this evaluation.

Internal instability or suffusion is a failure mode of the soil subjected to seepage. This failure mode is characterized by the wash out of the fine fraction through the pore matrix of the coarse fraction of the soil. The results are segregation in soil, a modification of the drainage properties, possible increase of the soil permeability of the porosity of the bulk density, and of the pore pressure. As consequence the resistance of the soil against external load decreases and the settlement increases.

Likewise, all drainage solutions become inefficient with the time due to migration of fine grains also internal instability or piping, Chapuis (1992) [

To assess whether internal instability or suffusion is possible, two criteria i.e. the geometric criterion and the hydraulic criterion have to be fulfilled. For the geometric criterion, the proof consists to check whether it is possible that fine grains are able to pass through the smallest constrictions along the relevant pore path of coarse soil fraction without clogging. For that, the geometry of the pore channels has to be considered. Since the pore channel geometry cannot be exactly measured, the assessment is generally based on the curve of the grain size distribution, which is related to the pore channel geometry.

When the geometric criterion shows that the migration of fine fraction of the soil is possible, it has to be checked whether the hydrodynamic load in the pore structure provides a critical energy to mobilize and to transport fines grains (hydraulic criteria). Only the geometric criteria have been dealt in this paper, for the hydraulic criteria reference is made to Ahlinhan (2011) [

The geometric criteria for the internal instability can be classified in three categories as follows:

the geometric criteria based on the pore constriction size

the geometric criteria based on filter rules, and

the geometric criteria based on comparison between the curve of the grain size distribution of the soil concerned and the curves of the grain size distribution of theoretical stable soils.

The above mentioned criteria are presented (Section 2 to Section 4) and compared (Section 5). Then, a resultant geometric criterion is developed in Section 6. Moreover a site specific assessment for the internal instability is proposed in Section 7.

A simple geometric criterion for the internal stability of granular soils is the requirement that the pore diameter d_{p} shall be smaller than the smallest grain diameter d_{min}.

Kovacs (1981) [

or

Here, n is the porosity, d_{h} is the effective grain diameter, α is the shape factor and d_{0} is the mean diameter of the channels. Equations (2) and (3) show that the quotient of two grains diameters arbitrary of a grain size distribution curve e.g. d_{h}/d_{min} shall be smaller than a value depending on the porosity of the soil concerned.

Based on this approach, Istomina (1957)―cited in Busch et al. (1993) [

The internal instability criteria based on the filter rules compare the ratio of mass percent for two grain diameters with a constant value. As explained above, internal stability is the detachment, and the transport of the fine grains of a soil through the grain skeleton formed by the coarse parts. It can be considered as a contact erosion process (i.e. the wash-out of a fine soil through the pores of an adjacent coarse soil layer) between the fine and coarse parts of the soil. Based on this consideration, Kezdi (1979) [

Here, d_{15F} is grain diameter for which 15% of the grains by weight of the coarse soil are smaller and d_{85b} is grain diameter for which 85% of the grains by weight of the fine soil are smaller.

The filter rule according to Sherard (1979) [

However, the Terzaghi criterion is valid only for poorly graded soil. To avoid this limitation, in the German guideline BAW (1989) [

Burenkova (1993) [_{15}, d_{60} and d_{90}, the internal stability of the soil was described by two ratios called conditional factors of uniformity d_{90}/d_{60} and d_{90}/d_{15}. With these two factors of uniformity, Burenkova (1993) [

In addition to the criterion for suffusion, an approximate diameter d_{d} dividing the suffusive and non-suffusive portion is also defined as follows:

Wan and Fell (2008) [

Lubochkov (1965)―cited in Kovacs (1981) [

Based on the laboratory tests Lubochkov (1965)―cited in Kenney and Lau (1985) [

Here, d_{60} is the particle size for 60% mass percent, d is an arbitrary particle size between d_{0} and d_{100}, and F is the masse percent of particles smaller than d.

Kenney and Lau (1985) [

Here, H is the masse fraction between d and 4d.

There was a particular reason for choosing the interval between d and 4d. The size of the relevant constriction in a void network of a filter is approximately equal to one quarter of the size of particles for the filter, Kenney et al. (1985) [

The results of the laboratory tests performed by Kenney and Lau (1985) [

Chapuis (1992) [

Let us call I the point at which the grain size distribution curve is divided in fine and coarse fraction (

The mass percentage for particle size smaller than the size d_{I} is called y_{I}. In the fine portion, the abscise of the point J is x_{J} = logd_{85b} and its masse percentage is y_{J} = 0.85y_{I}. In the coarse portion, the abscise of the point K is to x_{K} = logd_{15F} and its mass percentage is:

The secant slope s_{JK} between the points J and K can be expressed as:

Equation (4) in Equation (12) can be expressed as follows:

In a similar way the Kenney and Lau (1985) [

Therefore, the Kezdi (1979) [_{y} (y ≤ 20%), the slope per cycle of the grain size distribution curve must be larger than 1.66∙H to have internal stability.

The criteria based on the filter rules compare the slope of the grain size distribution curve with a constant value 24.91% by the Kezdi (1979) [

Theoretical considerations were made in order to define the point at which the split-up of the curve of the grain size distribution should be carried out. In general, the grain size distribution might be split at several points. For the illustration of the splitting up approach in _{1} and T_{2} have been exemplary considered. The steeper the grading curve, the smaller is the distance b between fine and coarse fraction obtained from the splitting up of the grain size distribution curve at a point T (

Here, d is the particle diameter at the split-off point T, F the mass fraction of particles smaller than d and H the mass fraction of particles between d and 4d. If b is maximal, β is minimal, and then H also becomes minimal. Therefore, it is proposed to split the grading curve at (H/F)_{min}. The associated filter quotient is denoted as a modified filter or instability index (d_{15f}/d_{85b})_{mod}. The point (H/F)_{min} represents a “weak point” for the soils and is therefore relevant for the assessment of its geometric stability. For internal stable soil the instability index (d_{15f}/d_{85b})_{mod} shall be smaller than 4, Ahlinhan [

The above mentioned criteria for the internal stability cannot generally be compared with each other except the criteria based on filter rules and the Kenney and Lau (1986) criterion [_{x}_{%} can be derived from the grain size distribution curves.

The geometric criteria after Kezdi (1979) [

Parameters/criteria | Reference soils | ||||
---|---|---|---|---|---|

A1 | A2 | E1 | E2 | E5 | |

Coefficient of uniformity U | 2.10 | 3.00 | 6.80 | 13.50 | 23.40 |

Ratio (H/F)_{min} | 2.92 | 3.23 | 1.10 | 0.20 | 0.03 |

(d_{15F}/d_{85b})_{mod} | 1.21 | 1.41 | 3.80 | 7.20 | 13.84 |

Istomina (1957) | S | S | S | S/U | U |

Cistin (1965) | S | S | S | U | U |

Lubochkov (1965) | S | S | U | U | U |

Kezdi (1979) @ (H/F)_{min} | S | S | S | U | U |

Sherard (1979) @ (H/F)_{min} | S | S | S | U | U |

De Mello (1975) @ (H/F)_{min} | S | S | S | U | U |

Kenney et Lau (1986) | S | S | S | U | U |

BAW MSD (1989) @ (H/F)_{min} | S | S | U | U | U |

Proposed method | S | S | S/U | U | U |

Legend: S for geometric Stable; U for geometric Unstable; S/U geometric Stable or Unstable (transition zone).

A site specific assessment regarding internal stability is recommended for the construction or the rehabilitation of dykes, barrages, weirs, road embankment, etc. To carry the site specific assessment the environmental data such as water depth, seepage condition, seepage velocity, hydraulic gradient are required. These environmental data are the effect of action. Moreover the site specific geotechnical data, which are the resistance, must be considered. The type and amount of the geotechnical data required will depend on the particular circumstances such as the type of the geotechnical infrastructure (dykes, barrages, weirs, road embankment, etc.) and previous experience of the site, or nearby or similar sites, for which the assessment is being performed. Such geotechnical information includes shallow seismic survey, coring data, cone penetrometer tests, side-scan sonar, magnetometer survey and diver’s survey. The environmental and geotechnical data have to be considered for the evaluation of the internal stability of the soil as follows:

1) Carry out analysis regarding the susceptibility to internal stability by applying relevant criteria, e.g. Ahlinhan et al. (2011) [

2) Take reasonably into account the complex soil structure, its variability its non-homogeneity (layered soils, soils variability, etc.) for some laboratory tests regarding the internal instability.

3) Compare the results from (1) and (2) in order to get more confidence for the assessment of the internal stability.

For economic reason the unstable soils may be used in the practice. For that, it has to be proved that hydrodynamic energy i.e. the hydraulic gradient and the velocity of the seepage will not reach the critical one.

The main criteria for the internal instability of the granular soil subjected to seepage have been presented and compared. These main criteria can be classified in three categories, i.e. the criteria based on the pore distribution or constriction size, the criteria based on filter rules, and the criteria based on the comparison of the grain size distribution curve with the grain size distribution curve of a theoretical stable soil. The comparison shows that the criteria based of filter rules (e.g. Sherard (1979) [_{min}. It should be noted that these geometric criteria are based on the resistance that means the pore distribution or the constriction size or the grain size distribution curve of the soil, but not the effect of action or the loading that means the seepage velocity, the hydraulic gradient. Therefore, combined geometric and hydraulic criteria will be an economical design approach, since unstable soils are often used in the practice, when the hydrodynamic energy, the hydraulic gradient, and the seepage velocity are lower than the critical one.

Moreover, a site specific assessment regarding the internal stability has been proposed for engineering practice. Hence, this paper presents a practical approach to analyze the geometric internal instability. However, a development of a software tool which would consider the grain size distribution curve (resistance) and the hydrodynamic energy (effect of action), would be very helpful for the design and analysis with respect to the internal instability.

This research was partially supported by the Germany Ministry of Education and Research through IPSWaT (International Postgraduate Studies in Water Technologies). This support is gratefully acknowledged.

Marx Ferdinand Ahlinhan,Marius Bocco Koube,Codjo Edmond Adjovi, (2016) Assessment of the Internal Instability for Granular Soils Subjected to Seepage. Journal of Geoscience and Environment Protection,04,46-55. doi: 10.4236/gep.2016.46004