Effects of compaction on soil undrained shear strength deteriorating during undrained cyclic loading and controlling seismic stability of embankment

Effects of compaction on the undrained shear strength of saturated earth-fill dam materials are presented. Poorly and well compacted saturated soils may exhibit undrained shear strengths, respectively, significantly lower and higher than corresponding drained shear strength and this trend is amplified as the undrained strength deteriorates by preceding undrained cyclic loading. These features are implemented in a new simplified seismic analysis to evaluate residual deformation of earth-fill dams. The analysis consists of: 1) a modified Newmark sliding block analysis; and 2) a pseudo-static non-linear FEM analysis, both formulated in a unified framework based on the cumulative damage concept, total stress earthquake response analysis and a direct total stress modelling of undrained monotonic and cyclic stress-strain behaviours obtained by triaxial tests. The analysis simulates very well the collapse of an earth-fill dam by the 2011 Off the Pacific Coast of Tohoku Earthquake, Japan, and indicates a substantially higher seismic stability under the same conditions of the newly restored dam completed in 2017. Paramount effects of soil compaction on the seismic stability of earth-filled dam are demonstrated.


Introduction
Around 2,000 of the 12,500 irrigation earth-fill dams in Iwate, Miyagi and Fukushima Prefectures in Japan were seriously damaged during the 2011 Off the Pacific Coast Tohoku Earthquake (magnitude M=9.0) [1]. The main and auxiliary dams of Fujinuma Reservoir, located on the branch of upper Sunoko River in Fukushima Prefecture ( Fig. 1), totally collapsed by the earthquake. The main dam breached resulting in a flood (indicated by a red arrow in Fig. 1a) that caused seven deaths and one missing [2].
As detailed later, the primary cause of the collapse was generally poor compaction of the dam body. In particular with the old main dam, the compaction of the sandy top fill was very poor, which resulted in a very low initial undrained shear strength that largely deteriorated by undrained cyclic loading (UCL) during a particularly long earthquake motion [2].
To reach these conclusions, dry densities of the fills remaining after the collapse were evaluated and laboratory compaction tests were performed on samples retrieved from the field. A series of undrained triaxial compression (TC) tests were also performed on specimens compacted to the field densities and those compacted looser or denser. Undrained shear strengths before and after undrained cyclic loading (UCL) histories causing different strains were also evaluated [4,5].
It is difficult to predict such collapse when based on the conventional design procedure for irrigation earth-fill a.
b. c. Fig. 1. a) Aerial picture of Fujinuma dams taken immediately after collapse; b) grading properties of fill materials; and c) central cross-section of main dam (height=18.5m) before and after collapse (after [2], [3]). dams in Japan, which is based on an allowable lower bound of the global safety factor by pseudo-static limit equilibrium method using the drained shear strength of soil. On the other hand, non-linear FEM effective stress analyses remain too sophisticated and too costly in engineering practice due to a number of highly complicated issues including: a) build-up/dissipation of excessive pore water pressure both globally and locally around and inside shear bands having a thickness controlled by particle size; b) effects of dilatancy characteristics under cyclic loading; c) proper undrained stress-strain modelling of well compacted soil. In view of the above, a pair of new simplified analysis methods was developed incorporating TC test results formulated in a unified and straightforward framework based on the cumulative damage concept combined with total stress earthquake response analysis [4,5]. By this method, the collapse of the old main dam was simulated very well, as shown below. The collapsed dams were restored to new modern earth-fill dams (Fig. 2) to be much more stable than the old ones. They were designed based on the seismic stability analysis explained in details below. The core and shelter were compacted following a new soil compaction procedure, which is presented in the companion paper [6]. Restoration was completed in January 2017. A set of laboratory stress-strain tests was then performed on the fill materials used to construct the dams precisely at field compacted states. The results of the seismic stability analysis of the new main dam evaluated by the same analysis method and under otherwise the same conditions as the analysis of the collapsed old main dam are reported below.

Old Fujinuma dam
A series of undrained TC tests were performed on specimens reconstituted using samples retrieved from the remaining part of the top fill (Fc=12%, NP, Uc=7.4), middle fill (Fc=57.8%, Ip=31.6) and bottom fill (Fc=35.5%, NP, Uc=156) of the old main dam (Fig. 1). Specimens were compacted closely to the measured field dry densities: (top fill) d (g/cm 3 b.

Fig. 4.
Typical undrained stress-strain behaviours and effective stress paths before and after applications of different UCL histories of middle fill [3] a. b.

Fig. 5.
Undrained shear strengths of specimens compacted to different dry densities: a) initial and damaged strengths converted to σ'c=70kPa; b) ratio of the damaged strength to the initial strength in a function of [Dc]1Ec [3] Fig. 5a shows the initial and deteriorated undrained shear strengths obtained from this and other similar series of undrained TC tests on specimens compacted to different dry densities, which are plotted in logarithmic scale against [Dc]1Ec. These undrained strengths have been converted to those at an effective consolidation pressure σ'c equal to 70 kPa by assuming that the undrained strength is proportional to σ'c. The initial undrained strength becomes much higher when compacted sufficiently denser than the respective field compacted states: i.e., [Dc]1Ec= 87.9 % (top fill); 84.5 % (middle fill); and 90.1 % (bottom fill). The deteriorated strengths are those observed until the axial strain became about 10 % in UML performed after applications of various UCL histories. As seen from Fig. 5b, for a same [Dc]1Ec, the decreasing rate of undrained strength is smaller with the middle fill material (having the largest fines content) than with the top fill material (non-plastic having the least fines contents) and the bottom fill material with an intermediate grading. Besides, with the respective fill materials, with an increase in [Dc]1Ec, the initial undrained strength increases while the decreasing rate of undrained strength decreases. As a result, the deteriorated strength increases significantly with [Dc]1Ec, particularly with the bottom fill material (Fig. 5a).  For the seismic stability analysis reported hereafter, the undrained shear strength was modelled by the socalled total stress method. That is, the initial undrained shear strength is represented by (fu)0= cu0+'n0.tanu0 and the deteriorated undrained strength after UCL by fu= cu+ 'n0.tanu, where 'n0 is the initial effective normal stress activated at respective places along the failure plane. It is assumed that, with an increase in the damage strain during precedent UCL, the linear strength envelop rotates about a fixed origin along the σ-axis in such that the strength Middle fill, old Fujinuma dam Undrained triaxial CL+ML tests Middle fill, old Fujinuma dam start of loading Undrained triaxial CL+ML tests ratio fu/(fu)0 is always kept equal to cu/cu0= tanu/tanu0. Fig. 6a shows the measured values of this ratio plotted against the respective damage strains. It may be seen that the deterioration rate is smallest with the middle fill and largest with the top fill showing that this rate increases with a decrease in the fines content. These relations were fitted by Eq. 1 to be used in the stability analysis: where A1, t1, d1, A2=1-A1, t2 and d2 are constants. Fig. 6b shows the relationships between the single amplitude cyclic shear stress ratio SR and the number of loading cycles Nc necessary to develop different maximum axial strains (i.e. fatigue curves). The SR value that is defined for a same strain and Nc is largest with the bottom fill (compacted relatively dense) and quite low with the top and middle fills (compacted loose).

Restored Fujinuma dam
A similar series of undrained TC tests were performed on reconstituted specimens of the fill materials used to construct the shell and core of the restored main dam ( Fig. 8 shows typical test results. Fig. 9a shows the ratios of the undrained strength that has deteriorated by various UCL histories to the initial value of core and shell materials, plotted against the maximum axial strain that developed during the respective UCL. Fig. 9b shows the fatigue curves obtained from the UCL phases. Compared to the fill materials of the old dam (Figs. 3, 4 & 6), the shell and core materials of the new dam exhibit: a) much higher initial undrained strengths (Fig. 8); b) much lower deterioration rates for a given damage strain (e.g., 10 %) (Fig. 9a); and c) noticeably higher SR values for the same strain and Nc (Fig. 9b). These trends are due to substantially higher [Dc]1Ec values achieved in the restored dams. These and other stress-strain properties were implemented in the seismic stability analyses described below.
a. b. Fig. 9. a) Ratio of deteriorated undrained strength to initial value; and b) fatigue curves obtained by UCL (new main dam).

Simplified seismic stability analysis
The following numerical analyses were performed to evaluate the seismic-induced residual displacement and deformation of the old and new main dams [4,5]:

1) Plane strain 2D FEM equivalent-linear dynamic response analysis in the frequency domain to obtain the time histories of response acceleration and mobilized stresses:
It was confirmed that results are very similar to those obtained by a non-linear seismic response analysis in the time domain under otherwise the same conditions. Possible effects of degradation of non-linear stress-strain properties in the course of UCL were ignored. This method somehow over-estimates mobilized cyclic stresses therefore is on the safe side in usual design cases, where the natural frequency of fill dam decreases by the degradation of stress-strain properties from the initial value that is lower than predominant frequencies of major earthquakes usually considered in design.
2) Modified Newmark sliding block analysis taking into account the degradation of undrained shear strength by irregular UCL during seismic loading: For given cyclic undrained stress-strain properties (as described in Figs. 6b & 9b), the maximum strain (i.e., the damage strain) that has taken place by a given moment during a given time history of cyclic shear stress evaluated by analysis 1 above is obtained by the cumulative damage concept [7]. The instantaneous undrained shear strength is obtained by reducing the initial value by the degraded-toinitial strength ratio obtained by substituting the current damage strain into relevant relations, such as presented in Figs. 6a and 9a. Time histories of slip displacement for many relevant trial slip circles are obtained using the time histories of undrained shear strength of all saturated FEM elements. The critical slip plane is determined as the one that gives the maximum sliding displacement.
3) Plane strain 2D pseudo-static non-linear FEM analysis to evaluate the residual deformation by selfweight and seismic inertial forces obtained by analysis 1: The residual deformation at the end of seismic loading is assumed to be equal to the maximum deformation that has taken place by the end of seismic loading. The deformation excluding the one by slip failure at a given moment is computed by this FEM analysis, using instantaneous undrained pre-peak stress-strain relations of saturated FEM elements that have deteriorated as the damage strain increases, following a similar procedure as 2). Seismic inertia forces at this given moment are computed from node accelerations obtained in 1).
Assuming that the sliding body is rigid once the sliding starts, the total ultimate residual deformation is then obtained by combining the ultimate rotational rigid block displacement of the modified Newmark analysis with the ultimate residual displacement obtained by the pseudo-static non-linear FEM analysis.   Fig. 11. a) Slip planes inferred by field investigations (after [2]); and b) critical slip circles obtained by modified Newmark analysis (old main dam) Fig. 11b shows the critical slip circles obtained by the modified Newmark analysis, which are remarkably consistent with the actual ones inferred by field investigation after the collapse (Fig. 11a). As indicated in Fig. 11b, the yield horizontal seismic coefficient, khy, along these critical slip circles becomes very low by the end of seismic loading, which results in significant sliding displacements. Fig. 12 shows the ultimate residual deformation obtained by combining those by the two analysis methods when slips C1, C2 and C4b take place separately. Large residual deformation at crest obtained by summing up these results is consistent with the overtopping flow that actually took place and resulted in the breaching of the old main dam. Fig. 13 shows the ultimate residual deformation of the restored main dam under the same conditions and obtained by the same analysis method. No rigid slip displacement takes place due to high initial yield seismic coefficients along the critical slip circles, khy= 1.068 (upstream slope) and 0.696 (downstream slope), which only slightly decreases by seismic loading. Besides, the   Significant effects of compaction may be seen in Fig.14. That is, the initial undrained strengths of the poorly compacted materials of the old main dam and the well compacted materials of the new main dam are respectively noticeably lower and significantly higher than their corresponding initial drained strength and this trend is amplified after having been deteriorated by UCL.

Conclusions
Series of undrained monotonic triaxial compression tests were performed before and after applying undrained cyclic loading histories developing different strains on saturated poorly compacted specimens of the fill materials retrieved from of a 18.5 m-high Fujinuma main dam that collapsed by the 2011 Off the Pacific Coast of Tohoku Earthquake. Similar tests were performed on much better compacted shell and core materials of the restored main dam. "Rigid slip analysis by the modified Newmark method" combined with "residual deformation analysis by a pseudo-static non-linear FEM" using these laboratory test data modelled in a single framework simulates very well the collapse of the old main dam and indicates a high seismic stability of the new dams showing paramount importance of good soil compaction for a high seismic stability of fill dam.