A commonly used approach to evaluating the potential for internal instability in soils is that of Kenney and Lau. This method involves a shape analysis of the grain size curve over a length of the soil’s finer part. A soil that is internally unstable has a particle size distribution with a finer fraction less than the coarser fraction; therefore, the coarser fraction makes up the primary fabric of the material. Thus, the fine-grained particles are loose (non-structural) in between fixed (structural) coarser grains, and these loose fine particles are permitted to migrate through the constrictions of the fabric of the coarser fraction. This paper discusses the evolution of the Kenney-Lau method and its boundary relations, and furthermore, a discussion on adaptations of the method, which touches on field experience and engineering practice, is given.
Normally, a soil comprises particles of different sizes. The relative amount by mass contributed by these particles defines the grain size distribution (i.e., grading) of the soil. A soil spread over a wide range of particle sizes is considered widely graded, whereas a grading containing few fractions is uniform. In a soil with stable grading, all particles contribute to the skeletal structure of the soil. In the case of unstable grading, there is an imbalance that creates a coarser fraction that is structural (with few highly stressed particle contacts) and a finer fraction, which is non-structural with moveable fine-grained particles (with no effective stress transfer between grains). Depending on the severity of seepage and the geometrical constraints of the coarser fraction of a grading, the finer fraction of the internally unstable soil can be washed out due to erosion by suffusion. Suffusion is a mechanism of internal erosion, which involves a “selective erosion of finer particles from the matrix of coarser particles (…) leaving behind a soil skeleton formed by the coarser particles” [
Stemming back to the filter rules of Terzaghi [
Herein, the Kenney-Lau approach to the internal stability evaluation of soils is discussed. The tested gradings, the evolution of the boundary relation between internal stability and instability, and the laboratory results, which determine this boundary, are studied in detail in this paper. Furthermore, the Kenney-Lau approach has been adapted by others, and these extensions and potential improvements are discussed in addition to field experience comparisons from the application of the method in engineering practice.
To Kenney and Lau [
Thus, internal instability indicates on one aspect of internal erosion susceptibility of a soil, i.e., the geometrical constraints. The other aspect concerns hydraulic loading, i.e., the velocity of flow (i.e., critical gradient) through the soil matrix to cause movement of the finer fraction, and these criteria combined, i.e., internal instability and critical seepage velocity, may cause internal erosion by suffusion [
The Kenney-Lau approach involves a shape analysis of the grain size curve over a length of its finer part. The predominant filter constriction is one-quarter the size of the small particles making up the filter (i.e., D’c ≤ D5/4); thus, size D particles can pass through constrictions of filters composed of particles of size 4D and coarser [
The following rendition of the Kenney-Lau method reflects on the approach to internal stability evaluation of soils, and special emphasis is placed on the boundary relations between stable and unstable soils found by [
Kenney and Lau tested soil samples in permeameters with diameters of 245 and 580 mm and with a downward flow (
A drainage layer, sufficiently coarse to allow for an open system, was placed on the bottom of the cell against the samples. All samples were created from 10 to 20 individually mixed batches to ensure an overall grading uniformity. The test duration was at least 30 hours and until particles were no longer flushed out. In a companion study on controlling the constriction sizes of filters by Kenney et al. [
Vibration was added during testing by tapping the seepage cells with a rubber hammer. Subsequent to equilibrium, which was reached when insignificant amounts of solids were discharged [
Kenney and Lau [
The unstable soils usually exhibited three zones: a top transition zone with a coarse top surface, a central homogenous zone, and a bottom transition zone [
The homogenous central zone exhibited, in some cases, no net change from the initial grading (i.e., no loss of particles, or the same amount was lost as was gained during the test), and conversely, in other tests, this central zone had become coarser grained compared to the initial grading (i.e., a loss of particles throughout the sample).
Material A ranges from 0.2 to 40 mm (
The grading As had become stabilized in the test of grading A (i.e., part of the homogenous zone), and complementing tests were carried out on As, which revealed that the bottom layers (i.e., layers 5, 6 and 7) lost 9% of their mass and that the topmost layer 1 had become slightly coarser, indicating lost fines (
from these layers). However, Sherard and Dunnigan [
Kenney and Lau [
Furthermore, Kenny and Lau [
Given that the constrictions of a filter are one-quarter the size of the small particles making up the filter [
The methodology of generating the H:F-shape curve and the extraction of the stability index (H/F)min (i.e., the smallest value along the H:F curve within the evaluation range, as first introduced by Skempton and Brogan [
The H:F-shape curves of the specimens tested by Kenney and Lau are shown in
Initially, a tentative boundary relation between stable and unstable gradings that equaled the H:F-shape curves of specimens tested as borderline stable, e.g., material Ys.s and As.s (particle size distributions in
However, the boundary was modified after studying the limiting grading curve of Loebotsjkov given in Equation (4) [
Adapting the Loebotsjkov curve to the H: F space, a logical linear relation of H/F = 1.3 is found (
However, the H = 1.3F boundary was closely scrutinized [
Although Kenney and Lau [
Possibly the most influential work on the elaboration of the Kenney-Lau method is the research of Skempton and Brogan [
Li [
The Kenney-Lau method has been validated against tests of others in the literature, and adaptions have been made to potentially improve its predictive capacity [
The comparative analysis of Li and Fannin [
Wan and Fell [
luating the slope finer end of the grading (i.e., the Kenney-Lau approach) with the slope of the coarser fraction and the complete grain size curve (i.e., the Burenkova approach), improved the estimation of the internal stability of silt, sand and gravel mixtures.
Validity on Widely Graded Soils with FinesThe Kenney-Lau method is, strictly speaking, intended for granular non-cohesive materials, and widely graded soils with fines is outside of its scope. However, studies have been performed on its validity for widely graded soils with some fines [
In some cases, the Kenney-Lau method has been found to be conservative (i.e., over-predicting instability) (e.g., [
The basis of the Kenney-Lau method is the evaluation of the finer end in increments of four, namely, the amount between D and 4D (i.e., denoted by H) in relation to the amount of mass passing at D (i.e., denoted by F). This is based on Kenney et al. [
Empirical methods developed from laboratory studies may, in practice, have little systematic comparison to field experience, however, in terms of the Kenney-Lau method, comparison to engineering practice and the field has been done by e.g., Li et al. [
Li et al. [
On the large scale, Rönnqvist [
The Kenney-Lau method determines the potential for internal instability in cohesion less granular soils. Relatively severe loading conditions were applied to the granular filter samples to promote the movement of the largest possible non-structural particles. Although there are reports that the method’s predictions may be overly conservative [
The validity of the Kenney-Lau method for widely graded soils with some fines content needs further attention. Although it appears to have merit for coarse-grained soils containing some fines, especially in its Li-Fannin adaptation [
The research presented was carried out as part of the “Swedish Hydropower Centre-SVC”. SVC has been established by the Swedish Energy Agency, Elforsk and Svenska Kraftnät together with Luleå University of Technology, the Royal Institute of Technology, Chalmers University of Technology and Uppsala University.
The authors wish to acknowledge that financial support has also been received from WSP Sweden.
D, grain size (mm);
F, amount of mass passing at grain size D (%);
H, mass increment between D and 4D (%);
(H/F)min, stability index, defined by the smallest value of H/F, for 0% < F ≤ 20% in soil with a widely graded coarse fraction and 0% < F ≤ 30% in soils that are narrowly graded.