Introduction
Significant seepage was observed downstream from an embankment dam founded on a clay layer underlain by sand. The presence of the reservoir generated pore pressures in the sand which created upward forces at the bottom of the overlying clay layer. These forces were expected to fissure clay causing seepage and erosion of sand. The assessment of long-term stability of the foundation regarding internal erosion was deemed necessary by determining the factor of safety against uplift at every point in the entire downstream area which covers more than 1 km2. These calculations also needed to be validated by comparing results with visual observations in the field.
This paper presents the modern technologies, namely electromagnetic and laser surveys as well as geostatistical tools, used for detection of seepage and determination of land surface elevations and foundation characteristics. This paper also shows how these results were used to compute factors of safety against uplift for the entire downstream area, delineate critical areas and how these technologies were instrumental in providing an optimal solution for the long-term stabilization of the foundation.
Description of embankment dam and foundation
The embankment dam is located in northern Québec, Canada. This structure is a 15.4 m high and 1190 m long embankment founded on marine clay underlain by a fine sand deposit of up to 70 m in thickness. This stratigraphy is observed for about 1 km downstream from the dam. A stream, located about 350 m downstream from the dam, flows in a parallel to the axis of the structure. Over time, this stream eroded 12 to 16 m of the clay deposit creating a 1.5 km long canyon covered by trees and a large lake. Most of the observed seepage phenomena are located along the stream and near the lake. Figure 1 shows an aerial view of the embankment dam and downstream area.
A cross section of the dam and foundation, in the upstream-downstream direction, is presented in Fig. 2.
Based on Fig. 2, the factor of safety against uplift is equal to the ratio of downward forces due to the weight of clay over upward forces due to pore pressures in sand. The calculation of factors of safety against uplift requires an estimation of clay thickness, Hs on Fig. 2, which is equal to the difference between land surface and clay-sand contact elevations, and an estimation of pore pressures (Hw on Fig. 2) for the entire study area. These factors of safety are adjusted to take into account the weight of water in the lake if necessary.
The area downstream from the dam is heavily forested and partially covered by a large lake. Detailed visual inspections are difficult, the direct observation of seepage is not always possible. Topography of land surface is only known to a limited extent. Subsurface conditions of the dam foundation are known only where boreholes and cone penetration tests were realized. The calculation of factors of safety against uplift for the entire downstream area is thus not possible using only available data which is representative of local conditions.
Insights into this problem were developed using modern technologies. First, a global electromagnetic survey over the entire downsteam area was realized to detect the main seepage phenomena through the clay layer. Second, a laser airborne survey (LIDAR: LIght Detection And Ranging) was made to determine the topography of land surface. Third, a geostatistical analysis of boreholes and cone penetration tests results allowed the estimation of subsurface characteristics of the foundation, including clay-sand contact elevations and distribution of pore pressures, over the entire downstream area. These results were used to compute factors of safety against uplift and delineate critical areas which were compared to the detected seepage.
Detection of seepage by global electromagnetic survey
A global electromagnetic survey of the downstream area was realized to detect the main sources, pathways and exits of seepage from the sand layer. This technology uses a low voltage, low amperage, audio-frequency electrical current to energize the groundwater in the seepage area by strategically placing a number of electrodes on the ground surface and in the reservoir.
Because water is a conductor, electrical current follows the path of groundwater between electrodes creating a magnetic field which can be surveyed from the surface using a highly sensitive and specially tuned magnetic receiver. This receiver also filters out interference and amplifies the signal. Repeated measurements are recorded over time to ensure consistent results. Equipment used to measure magnetic field includes three sensors oriented in orthogonal directions, a data logger used to collect, filter and process sensor data, a Global Positioning System (GPS) to locate and map field measurements, and a Windows-based hand-held computer to store GPS and magnetic field data. This equipment is mounted on a surveyor’s pole and can be hand-carried to each measuring station. More details are included in Smith et al.[
1].
The measured magnetic field data was processed, contoured and interpreted in conjunction with field data resulting in enhanced definition of the source and main pathways of seepage. Finally, a 3D theoretical electric current flow model of the site and flow paths was prepared to match theoretical magnetic field intensities with actual magnetic field measurements to establish credibility of data and to estimate the vertical position (depth) of water flow. The mapping of detected upward seepage exits is shown on Fig. 3.
The vertical magnetic fields map on Fig. 3 shows higher gradients bordering the southernmost part of the downstream lake where there are also sharp variations in the lake itself. This suggests the presence of vertical seepage exits around the perimeter and at the bottom of this part of the lake (see also arrows in Fig. 3). Most of this seepage is not surfacing in specific areas; rather, the groundwater is likely upwelling in several locations. No major seepage appears to occur in the north part of the lake and on the land surface toward the embankment dam.
Determination of land surface topography by LIDAR survey
LIDAR is an optical remote sensing technology that can measure the distance to a target using laser pulses to create point clouds of the earth ground for further processing. LIDAR is a technology capable of producing accurate digital elevation models using lasers, GPS and inertial navigation system. It allows the accurate positioning of the footprint of a laser beam as it hits land surface. The LIDAR system used in the presented case study was installed in a small aircraft. Corrections were made in results to account for the effects of vegetation. Resulting x,y,z coordinate data files were processed in specialized software to create the land surface model presesented in Fig. 4 which also shows the position of boreholes and cone penetration tests to be used for the geostatistical analysis presented in Section 6.
Figure 4 shows a shaded relief map which uses color variations to indicate the local orientation of the surface relative to a user-defined light source (upper left corner in case of Fig. 4). This can be thought of as the sun shining on the topographic surface. Portions of the surface that face away from the light source reflect less light toward the viewer and thus appear darker. The shaded relief digital elevation model on Fig. 4 allows numerical processing of land surface data including the determination of areas, volumes and cross sections such as presented in Fig. 2.
The LIDAR survey achieved an accuracy of about±15 cm based on comparisons with reference surface topographic measurements. LIDAR techniques are innovative, useful and widely applicable technologies for dam safety assessments such as the presented case study. However, they are not applicable for accurate acquisition of spatial data below free-water surfaces, such as the downstream lake, due to optical reflection, refraction and scattering of emitted light waves [
2]. Topography of the lake bottom was determined from bathymetric surveys realized over water. These results are shown in the downstream lake on Fig. 4 as elevation contours.
Overview of geostatistics
Geostatistics involves the analysis and prediction of spatial phenomena. The main objectives are to characterize and interpret the behavior of existing sample data and use that interpretation to estimate likely values at locations which have not yet been sampled. It is assumed that there is a relationship between values which depends on the location of the samples [
3]. Geostatistics assumes second order stationarity of the data. The mean has to exist and is constant and independent of location within the region of stationarity. No trends or ‘drifts’ in values should be present in the data over the area to be studied otherwise special techniques have to be used. Also, the covariance has to exist and is dependent on the distance between any two values and not on their location.
Univariate statistics do not take into account the fact that two values in space that are closer together tend to be more similar than two values farther apart. Study of the spatial correlation of data are usually called variogram modeling, it is the first part of a geostatistical analysis. It allows one to quantify the correlation between any two values separated by a specific distance. This information is used to make estimations at unsampled locations.
The estimations are made by kriging which is the second part of a geostatistical analysis. Kriging uses a linear combination of surrounding sampled values to make such estimations. Weights are applied to each sampled value resulting in optimal and unbiased estimates. Kriging allows to derive these weights by minimizing error variance and setting the mean of estimation errors to zero. Values at sampled and unsampled locations are related to one another in a way which is dependent on the distance between their locations. The variogram model is used to establish this relationship.
Generally, closer samples and a greater number of samples give more confidence in the estimates. However, using many samples close together is not necessarily better. Clustered samples do not give as much information about unsampled locations as sampling which is regularly spread out across the study area. The effect of clustering is taken into account by calculating how the samples are related to one another. Uncertainties in the results of a geostatistical analysis can be assessed by Gaussian simulation in which the estimation process is repeated to generate multiple realizations of kriged data.
Geostatistical analysis of pore pressures in sand and clay-sand contact elevations
A total of 78 boreholes and cone penetrations tests were realized to assess the stratigraphy of the foundation (see locations on Fig. 4). A number of investigations date back from the construction period while others are more recent. Clay-sand contact elevations identified during these investigations were used for the geostatistical analysis which allowed the estimation of contact elevations at every 50 cm for the entire downstream area. The quantity and quality of available sample data was sufficient to provide the required information for variogram analysis and kriging. The resulting spatial distribution of clay-sand contact elevation values, not shown here, is somewhat random considering the aleatory nature of the deposition and erosion mechanisms in effect during the formation of these soil deposits in the last Pleistocene glaciation [
4].
Open-tube piezometers were installed in some boreholes for long-term monitoring of pore pressures in sand. Cone penetration tests allowed continuous pore pressure measurements in sand during these investigations. A total of 30 data values were considered for the geostatistical analysis of pore pressures in sand. The reservoir level is almost constant and is not a significant cause of localized pore pressure variations. However, measured pore pressure values in sand gradually decrease from upstream to downstream due to head losses related to the horizontal flow of water, originating from the reservoir, in the sand layer. This global trend in data values was taken into account in the geostatistical analysis by modifying the linear constraint and hence the method for calculating the weights in each estimation. Figure 5 shows the distribution of estimated pore pressures in sand, converted in piezometric levels, for the entire downstream area.
Higher piezometric levels (>130 m), and thus higher upward forces, are present in a section of the dam toe but clay thickness in this area is significant and thus downward forces are also higher. Pore pressures decrease near the stream and lake but clay thickness is lower in this area due to its erosion by the stream (see also an example cross section in Fig. 2). The ratio of downward forces to upward forces in the stream and lake area may therefore be lower.
Factors of safety against uplift and rehabilitation measures
A factor of safety against uplift was computed at every 50 cm of the entire downstream area by considering the results from the LIDAR and bathymetric surveys (see Fig. 4) where the land surface was determined and also by considering results of the geostatistical analyses where clay-sand contact elevations and pore pressures in sand were estimated (see Fig. 5). Computation of Hs and Hw values (see also Fig. 2) allowed the determination of the spatial distribution of factors of safety represented on Fig. 6 in which the shaded relief model (see Fig. 4) is replaced by land surface elevation contours for more clarity.
Minimal factors of safety against uplift (less than 1.1) are shown on Fig. 6 by shaded areas in the southermost part of the lake. These critical areas also correspond to minimal clay thickness (Hs) in the foundation due to the greatest effect of erosion by the stream. They also correspond to vertical seepage exits detected around the perimeter and at the bottom of this part of the lake by the electromagnetic survey (see also Fig. 3).
The risk of internal erosion of the sand layer through the overlying clay is increased where the factor of safety against uplift is lower. However, a pore pressure drawdown, due to drainage effects, can be expected at the location of existing seepage exits which can locally increase the factor of safety against uplift. The computed factors of safety do not take into account this stabilizing effect since the exact location and shape of every seepage exit is not known. Also, the electromagnetic survey has shown that most of the seepage is not surfacing in specific areas; rather, the groundwater is likely upwelling in several locations.
The design of stabilizing measures was specifically targeted at the critical areas delineated by the geostatistical analyses where factors of safety were minimal (see Fig. 6). The reduction of internal erosion risk in this case study could be achieved by increasing the factor of safety against uplift by increasing downward forces or by decreasing upward forces. Globally, the latter approach was deemed more feasible, economical and, above all, more effective.
Based on factor of safety calculations (see Fig. 6) and seepage detection results (see Section 3), a total of 18 relief wells were installed mostly along the upstream edge of the southernmost part of the lake (see Fig. 7).
The drainage effect of the relief wells caused a decrease of piezometric levels in the sand layer of more than 2.5 m in the lake area. This decrease of pore pressures increased the factor of safety against uplift to acceptable values and decreased the likelihood of internal erosion.
Conclusions
Significant seepage was observed downstream from an embankment dam founded on a clay layer underlain by sand. Rehabilitation measures were considered to decrease the risk of internal erosion of sand through the overlying clay. Zones where thickness of foundation clay layer is minimal, pore pressures are higher and thus where the factor of safety against uplift is lower, needed to be identified. Considering the large extent of the downstream area and the scarcity of available data, the delineation of critical areas was difficult. The implementation of optimized rehabilitation measures was thus not possible.
A global electromagnetic survey of the downstream area was realized to detect the main sources, pathways and exits of seepage from the sand layer. The land surface elevation was determined by an airborne LIDAR survey which was used to produce a digital elevation model. Geostatistical analyses of boreholes and cone penetration tests data allowed the estimation of overall subsurface characteristics of the foundation such as clay-sand contact elevations and pore pressure distribution in sand. These results were used to compute factors of safety against uplift at every 50 cm of the downstream area and delineate critical zones where internal erosion is more likely to occur.
The use of modern technologies, namely electromagnetic and laser surveys as well as geostatistical tools, was instrumental in defining the limits of an otherwise spread-out problem and to provide an optimal solution, in terms of costs, feasibility and effectiveness, for the long-term stabilization of the foundation.
Higher Education Press and Springer-Verlag Berlin Heidelberg
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