RELIEF WELL SYSTEM DESIGN APPROACH: HHD CASE STUDY

Erich D. Guy1, Ronald L. Nettles2, Jacob R. Davis3, Sean C. Carter4, Lucia A. Newberry5

Abstract

Seepage instability concerns exist at Herbert Hoover Dike (HHD) and project modification is required to reduce

associated risk. In the 4.9 mile long Reach 1A (R1A) of HHD, the preferred risk reduction alternative involves the construction of two primary components: a partially-penetrating seepage/piping barrier through the embankment and near-surface consolidated strata, and a landward seepage berm, which is coupled with a relief well system for blanket aquifer foundation condition regions. This paper provides an overview of the methodologies developed and employed for relief well system design work in R1A. Discussion regards a custom design computer program, the incorporation of variable well line position, well losses, and variable tail water position into solutions, an analytical approach which can account for partially-penetrating seepage/piping barrier affects and can allow estimation of effective seepage entrance or exit boundary conditions for cases that do not conform to established approaches, and the incorporation of reliability analysis into the design process. A comparison of a fully-penetrating system design solution with results from plan finite element modeling is also presented.

HHD Background Herbert Hoover Dike (HHD) encircles the 143 mile perimeter Lake Okeechobee in south central Florida (Figure 1). The project was originally authorized in response to 1926 and 1928 hurricanes which caused catastrophic damages and massive losses of life. It was constructed in two phases during the 1930’s and the 1960’s, and was generally carried out by a combination of dipper and hydraulic dredges which filled containment dikes built within the dike footprint. Outlet works having sufficient capacity to pass the Standard Project Flood (lake elevation of 25 feet NAVD88, and ~935-year return period) were not built during either phase of construction. The HHD embankment (Figure 2A) generally consists of a heterogeneous mixture of lightly compacted to dense, fine to medium carbonate, quartz, clayey, and silty sands, shells, and organic soils. Other embankment materials encountered include limestone and sandstone gravels, cobbles, and occasional small boulders. Typical embankment dimensions in HHD Reach 1A (R1A) are a crest width of 14 feet, a base width of 250 feet, a lakeside slope of 1V:6H, a landside slope of 1V:3H, and a crest height above ground of 25 feet (at elevation 36 feet). HHD Subsurface Conditions The HHD soils are highly variable in the vertical direction, generally consisting of foundation sands with variable silt content and several limestone and sandstone strata (having variable thicknesses and extents), which are overlain by an often-present continuous blanket of organic-rich materials (Figures 2B, 2C and 2D). Beneath this sequence is the Hawthorn Group (detrital clays, silts, and mudstones); it serves as the Intermediate Confining Unit that separates the surficial aquifer system from upper zones of the Floridan Aquifer System. Towards the southern end of R1A, the dike foundation (part of the surficial aquifer system) averages 180 feet thick, while the surficial blanket (absent in northern-most R1A) averages at least 10 feet thick. From a constant rate pumping test centrally located in R1A, the foundation average hydraulic conductivity was estimated at 42.5 ft per day (ft/d). This value is within a prior range estimated for the local surficial aquifer system (USGS, 1977), and it was adjusted for design analyses at R1A locations away from the pumping test (based on foundation stratigraphy variability) as described in Davis et al. (2009a). Where the continuous surficial blanket is present, conditions are generally referred to as a blanket aquifer foundation case. The densities of inorganic materials in R1A are similar to those at many other projects; however, the peat and organic silt comprising much of the blanket are much less dense than inorganic materials for which most seepage design guidance was written. Encountered peat when not completely saturated was frequently lighter than water, and the organic-rich blanket zones provide much less uplift pressure resistance than alluvial blankets found at many other projects. Such low tolerance for excess uplift pressure by organic blanket materials has been documented in two other known cases (Marsland, 1961; IPET, 2007). A general view of the R1A organic blanket materials is shown in Figure 2E, during the excavation of a test pit on the landward toe ditch slope. The pit was completed during a

1 Physical Scientist, USACE Huntington District, Email: Erich.D.Guy@usace.army.mil 2 Civil Engineer, USACE Mobile District, Email: Ronald.L.Nettles@usace.army.mil 3 Civil Engineer, USACE Jacksonville District, Email: Jacob.R.Davis@usace.army.mil 4 Civil Engineer, USACE Huntington District, Email: Sean.C.Carter@usace.army.mil 5 Civil Engineer, USACE Savannah District, Email: Lucia.A.Newberry@usace.army.mil

Figure 1. South central Florida (A), Lake Okeechobee showing the location of water control (gated inlets and outlets, culverts, navigation locks, pump stations) structures (B), and HHD project reaches (C). Reach 1A (4.9 miles long) is located between Port Mayaca and Sand Cut within the 22.5 mile long Reach 1.

Figure 2. Representative site conditions and geology for profile 1AG in Reach 1A of HHD: (A) and (B) Toe ditch in-filling performed as an interim risk reduction measure; (C) and (D) Forty feet of sonic core acquired at Station 1569+50 between elevations 15.7 and -24.3 feet (corresponding to depths of 20 to 60 feet), showing embankment fill from depths of 20 to 25 feet, blanket materials (inorganic clay, organic silt, peat, and inorganic silt with poorly graded sands) from depths of 25 to 35 feet, and foundation materials (sandstone, poorly graded sand, and silty sand) from depths of 35 to 60 feet; and (E) and (F) Exploratory test pit in organic blanket materials at Station 1567+00, completed five feet deep (from elevation 9.0 feet) on the toe ditch slope, at which point water began discharging at about 50 gallons per minute and the pit was back-filled with sand.

low lake period to an elevation of 4 feet, at which point heave of the pit floor (remaining blanket above the foundation) occurred and water began discharging while displacing small blocks of peat (Figure 2F). The general confining nature of the blanket was illustrated by this test pit; it was immediately back-filled with sand and the entire toe ditch in this region has since been in-filled as an interim risk reduction measure. During original HHD construction, continuous and relatively impervious blanket materials were excavated in borrow pits (parallel to dike alignment) exposing foundation materials in the lake bottom. Surveying and explorations indicated these pits have since filled in with various materials (sometimes being more pervious than the original blanket); thus original dredging decreased the effective seepage path distance beneath HHD. R1A Preferred Risk Reduction Alternative

The highly variable and relatively pervious embankment and foundation, low weight and relatively impervious landward surficial blanket, seepage entrance conditions, and lack of continuous control/cutoff features all contribute to seepage instability concerns at HHD. Concerns originated in the 1980’s and became more pronounced during the mid to late 1990’s when two high water events demonstrated the need for project modification. During these events, the lake crested around 17 feet (~30-year return period), and numerous sink holes, seeps, boils, and pipes were observed primarily along the 50 miles that comprise Reaches 1, 2, and 3; these were subsequently addressed with interim remedial measures. Due to its history of excessive seepage during frequent hydrologic events and potential for loss of life, HHD was ranked as an urgent and compelling project by the U.S. Army Corps of Engineers (USACE) Screening Portfolio Risk Assessment (SPRA) process (Halpin and Ferguson, 2007). In response to this ranking, numerous project modification alternatives to reduce risk were evaluated for the 4.9 mile long R1A of HHD (which is within the 22.5 mile long Reach 1 authorized for major rehabilitation); these evaluations and rationale for the preferred alternative are discussed in Davis et al. (2009a) and Davis et al. (2009b). The preferred risk reduction alternative requires the construction of two primary components: a partially-penetrating seepage/piping barrier (“cutoff wall”) through the embankment and near-surface consolidated strata, and a landward seepage berm, which is coupled with a relief well system for blanket aquifer foundation condition regions. The barrier will address embankment through seepage concerns and assist towards addressing under seepage concerns. The barrier depth (from the embankment crest) will range from 55 to 65 feet in R1A, and it will not restrict all groundwater flow, but is intended to cutoff pre-existing piping pathways and internally unstable materials within the embankment, as well as in near-surface consolidated and often quite pervious foundation strata. The landward seepage berm will have a width of 4 times the dike height (e.g. 100 feet where the dike is 25 feet tall), and will have thicknesses of 5 feet and 2 feet at the dike and berm toes, respectively. Where blanket aquifer foundation conditions exist (everywhere except northern-most R1A), the thickness and relatively impervious nature of the continuous blanket does not allow enough dissipation of foundation head with increasing distance downstream such that the relatively light weight of the blanket can provide adequate resistance to remaining uplift pressure beyond the berm toe. Required pressure relief will be achieved by fully-penetrating relief wells located at the seepage berm toe, with the well spacing varying across R1A depending on conditions in different sub-reaches.

Relief Well System Design Approach

The objective of this paper is to provide an overview of HHD seepage-related aspects while focusing some

discussion on the methodologies developed and employed for relief well system design work in R1A. To determine appropriate geometry for relief wells across the different sub-reaches of R1A, three-dimensional aspects relevant to (the laterally non-continuous) wells were considered utilizing a developed design program in conjunction with supporting two-dimensional SEEP/W (GEO-SLOPE International, 2004) finite element modeling. An “appropriate geometry” for this work is defined as a design which: satisfies HHD project-specific design criteria, satisfies engineering judgment, is demonstrated to be reliable, and is relatively economically efficient (optimized among different geometries which may meet requirements). The HHD remedial design criteria require for the Standard Project Flood (lake elevation of 25 feet), minimum steady-state seepage (effective stress uplift) factor of safety (FS) values of 3.0 at the dike toe, 1.6 at a distance 150 feet landward of the dike toe, and 1.1 at a distance 300 feet landward of the dike toe and beyond. Also required for the Maximum Surcharge Pool, are minimum transient seepage FS values of 1.5 at the dike toe and at a distance 150 feet landward of the dike toe, and 1.1 at a distance 300 feet landward of the dike toe and beyond. This event is simulated as a static lake elevation of 25 feet rising to an elevation of 30 feet (due to storm-related wind setup) over a 12 hour period; at a lake elevation of 30 feet overtopping would begin to occur on the western side of Lake Okeechobee. Analyses determined that subsurface head distributions would be similar for the Maximum Surcharge and Maximum (static elevation of 30 feet) Pools in blanket aquifer foundation condition regions (due to the general confining nature of the continuous surficial blanket). Therefore, steady-state seepage analyses for the Maximum Pool are deemed generally appropriate for approximating Maximum Surcharge Pool stability.

R1A Example Profile A representative (section) finite element seepage model for profile 1AG (a 3400 foot long sub-reach located in the

southern portion of R1A) is shown in Figure 3, and this profile will be used to illustrate the R1A relief well system design process. It is one of the 8 sub-reaches (i.e. profiles 1AA through 1AH) selected as representative of conditions across the R1A station ranges and analyzed. The subsurface in Figure 3 consists of idealized surficial blanket strata (brown regions), and the dike embankment, idealized foundation strata, and in-filled lake bottom borrow pits (yellow and gold regions; yellow have higher effective hydraulic conductivity than gold). Properties were assumed homogeneous within each idealized stratum and material zone, and composite property values were assigned to idealized strata based on the thicknesses, classifications, and properties of associated component layers (Davis et al., 2009a). With the lake at elevation 17 feet (highest historical level), base condition (i.e. no remedial features included) modeling yielded FS values against subsurface erosion initiation that were above unity at the dike toe and landward of the toe ditch, but approaching unity in the toe ditch. These results agreed with past event observations for R1A, in that seepage and related erosion initiation were not observed at the dike toe or landward of the toe ditch, but were periodically observed (where dense vegetation did not prevent observation) in the toe ditch. As shown in the section and conceptual aerial photograph overlay in Figure 3, subsequent remedial analyses (presented below) resulted in the designed rehabilitation components for this sub-reach which include a partially-penetrating seepage/piping barrier, a 100 foot long seepage berm, fully-penetrating relief wells at the seepage berm toe on 100 foot centers (represented by a laterally continuous well in the section model), and a drainage swale (which will be constructed to provide a filtered exit and adequate uplift resistance). This well system geometry satisfies design criteria and engineering judgement, is demonstrated as reliable, and is an optimized design. Utilizing the analysis procedures outlined below, it was separately determined that a system having an effective conductivity penetration of 75 percent would need to have wells on 50 foot centers (instead of 100 foot centers) to provide the same FS and reliability as the preferred fully-penetrating system. Design Program

The computer program developed and utilized for relief well system design work is presented in Figure 4, with expected input values (red text) and results shown for the profile 1AG preferred remedial alternative (Figure 3). The Excel program was developed in accordance with USACE (1992) design guidance, and to date has been validated against hand calculations and finite element plan modeling for fully-penetrating wells. It is applicable for blanket aquifer foundation conditions with an infinite line of wells parallel to an infinite line source, and can be employed for new system design or existing system back-analysis. The program was developed based upon methods presented in USACE (1956) and USACE (1992), and development benefitted from discussions in Mansur and Kaufman (1962) and U.S. Army (1983). Certain modifications and advancements beyond existing design approaches were incorporated to the program as discussed below.

In the Load and Underseepage Geometric Parameters section of Figure 4, pool, tail water, and top of ground elevations are input, as are embankment width and well line position. Effective seepage entrance and exit conditions are directly specified (user-estimated from available piezometric data or a separate approach), or the program calculates them based on other input (geometry, blanket, and foundation) parameters using “blanket theory” equations (USACE, 1956). For this example, the steady-state Maximum Pool was modeled (to approximate Maximum Surcharge Pool stability), the well line was located downstream of the embankment toe as discussed below, the effective seepage entrance was estimated using a separate approach as discussed below, and the effective seepage exit was calculated by the program based on other input parameters. For profile 1AG (and other R1A profiles analyzed), the Maximum Surcharge Pool loading governed design geometry; designs determined appropriate for this case were also appropriate for the Standard Project Flood loading. In the Blanket Strata Parameters and Aquifer Foundation Strata Parameters sections, relevant thicknesses, hydraulic conductivities, and weights of blanket and foundation strata are input; the program accommodates up to 5 blanket strata and 10 foundation strata (when all possible strata input cells are not utilized, the cells can be hidden by the user, as was done for the case in Figure 4). From these values, the program calculates effective vertical hydraulic conductivities and constants for poolside and landside blankets, an effective buoyant unit weight for the landside blanket, effective horizontal and vertical hydraulic conductivities for the foundation, and a transformed (homogeneous, isotropic) foundation thickness and effective hydraulic conductivity. For this example, expected property values of the idealized blanket and foundation strata (Davis et al., 2009a) shown in Figure 3 were modeled. In the Well Parameters section of Figure 4, screen diameter and filter pack thickness are input and the program calculates an effective well radius. The relief well riser elevation and efficiency are input such that well losses can be considered by the program as discussed below, and the effective well screen penetration percentage is also input (the program currently accommodates values in increments of 25 percent). For this example, fully-penetrating wells with 10 inch screens and 7 inches of filter pack were modeled, the top of riser elevation was specified as 0.25 ft above the ground surface, and the design well efficiency (for projected well discharge) was estimated at 75 percent. In the Input Parameters Conceptual Diagram section, a figure summarizing the above-described inputs is created with program calculation results shown; the figure is not to scale, and the plotted head curves are intended for illustration purpose.

Figure 3. Finite element (section) seepage model (top) for Station 1568+00 of HHD. The model includes designed rehabilitation components for the 3400 feet long profile 1AG (Stations 1547+00 to 1581+00) of Reach 1A: partially-penetrating seepage/piping barrier, 100 foot long seepage berm, fully-penetrating relief wells at the berm toe on 100 foot centers (represented by laterally continuous well in section model), and a drainage swale (having a filtered exit and adequate uplift resistance). A conceptual view of the remedial features is shown on an aerial photograph which was taken during normal lake stage (bottom).

Figure 4. Relief well system design program user inputs (red text) and results for profile 1AG (Figure 3); the program also includes a reliability analysis module (Figure 5). Deterministic analysis and uncertainty consideration result in design geometry for this profile of fully-penetrating wells on 100 foot centers. Figure continues on following pages.

Figure 4 (continued). Refer to prior page for figure caption; user inputs are in red text.

Figure 4 (continued). Refer to prior page for figure caption; user inputs are in red text.

In the Deterministic Design Requirements section of Figure 4, the required (effective stress) FS against uplift (heave) at the well line is input, and the corresponding value of allowable excess head at the well line is calculated by the program based on input blanket properties. The base condition (without well system) FS at the embankment toe is also calculated for reference. For this example, the well line was located downstream of the dike toe, and the required FS was specified as 1.5 (required at this location for the Maximum Surcharge Pool). In the Well Spacing Parameters section, the design well spacing (a) which provides adequate FS and reliability is input after its value is user-determined (e.g. after different effective well penetrations and reliability have been evaluated as discussed below). To assist the user in determining appropriate design spacing, the program provides a spacing value (aapproximate) which satisfies the FS requirement alone (without reliability consideration). Using the input design spacing (along with other prior inputs and calculated values, such as well losses as discussed below), the program determines through iteration the resulting average net head in the plane of wells (Hav) and the resulting net head midway between the wells (Hm) which ultimately influence system design. These heads are a function of the theoretical well factors (average uplift and midwell uplift) solutions developed by Barron (1982) and presented in Table 5-1 of USACE (1992); note the ∆ө value of 1.00 in Table 5-1 is incorrect and it should instead read 0.3665. For this example, appropriate design well spacing (at 100 percent effective penetration) was determined as 100 feet.

In the Deterministic Design Results section of Figure 4, the single well discharge, and the excess head and FS against uplift at the well line, which result from the design well system geometry, are calculated as discussed below. A plot illustrating the resulting net heads as a function of distance is also created; the “at well” curve is approximated, and the “midway and average” curves are assumed to converge upstream and downstream from the well line at a distance equal to one well spacing. Further, resulting head values at the downstream embankment toe and at a user-specified distance landward of the well line are calculated; this provides a basis for additional recommended hand calculations to ensure adequate FS values at locations away from the well line (e.g. where uplift resistance may differ due to blanket or topography variation). For this example, the resulting single well discharge was 90.5 gallons per minute (gpm), and the resulting FS of 2.38 at the well line exceeded the design requirement of 1.5 due to uncertainty consideration as discussed below. In the Theoretical Uplift Parameters Check section, an interactive nomograph based on approximate well factors solutions developed by Bennett and Barron (1957) and presented in Figure 60 of USACE (1956) is provided; note a similar nomograph presented in Figure 5-8 of USACE (1992) does not include the required “pole” point (on the D/a line for өav). The interactive nomograph allows comparison between the uplift parameters automatically determined and utilized by the program (based on theoretical solutions) and those determined manually (based on approximate solutions). For this example, and other separate analyses performed to date, good agreement between the two uplift parameters determination approaches was found to exist.

Variable Well Line Position

Existing methodology (USACE, 1992) is applicable for an infinite well line (parallel to an infinite line source) located at the landside embankment toe. For R1A design work, it was desirable to locate the well line landward of the embankment toe at the seepage berm toe (still parallel to the infinite line source), as this allows more efficient well system discharge conveyance. For the profile 1AG preferred remedial alternative (Figure 3), the seepage berm top width is 100 feet and its toe is located 78 feet downstream of the embankment toe; as discussed above, the design spacing for the preferred well line location is 100 feet in profile 1AG. By locating the well line at the berm toe, discharge will drain immediately into a swale rather than having to be conveyed through a collector system installed through the berm. To incorporate the variable well line position into the design program, the variable xw was introduced in the Load and Underseepage Geometric Parameters section of Figure 4, and defined as the line of wells distance downstream of the landside embankment toe. Net head on the well system corrected for total well losses (h) is then expressed in the Well Spacing Parameters section as:

w

w xx

xLxHHh

3

321

where H is the net head (pool - tail water) on the well system, Hw is total well losses as discussed below, x1 is the distance from poolside embankment toe to effective seepage entry, L2 is the embankment base width, and x3 is the distance from landside embankment toe to effective seepage exit. Also directly considering xw, the average net head in the plane of wells corrected for well losses (hav), and the net head midway between the wells corrected for well losses (hm), are expressed as:

wav

w

avav

xx

xLx

a

xLx

hh

3

32121

wav

w

mm

xx

xLx

a

xLx

hh

3

32121

where өav is the average uplift parameter, a is the design well spacing, and өm is the midwell uplift parameter. As discussed below, the resulting net seepage gradient towards the well line is additionally determined by direct consideration of xw. Well Losses

The USACE (1992) relief well design guidance presents equations formulated with the assumption that well losses are zero, and recommends that losses be estimated for projected well discharge and added to the maximum computed landside head. Total well losses are comprised of elevation and hydraulic head loss components, and in practice the latter has been estimated during system design by calculating expected entrance, friction, and velocity losses for the proposed screen, filter, riser, and connections. As a conservative measure, loss values utilized for design have often been further increased, since upon and following installation losses generally increase above theoretical estimates due to a variety of reasons (e.g. drilling activities, insufficient development, mechanical clogging, and/or chemical and biological incrustations). Following installation, subsequent well performance and the need for any maintenance, rehabilitation, or well replacement, has typically been assessed based on visual observations, and measurements made over time such as specific capacity or well discharge normalized to net head. Although such observations and data can provide a good basis for identifying decreased well efficiency which may be problematic, the approaches do not yield measured quantities that can be directly compared to loss values assumed at the time of system design, and therefore the affect of actual well condition on stability is not calculable. For the R1A relief well system design work, it was desirable to consider total well losses in a manner that in theory will allow actual post-installation measurements of well performance to be related to original design assumptions and project stability. An additional benefit is that the approach provides the potential for a much improved/more efficient maintenance program.

In the Well Parameters section of the design program (Figure 4), elevation head loss (Hel) is determined based on user-inputs regarding tail water and top of ground elevations, the greater of the riser elevation and the elevation of backed-up well discharge water in the well housing (RWTOR/TOW) as could be expected if discharge conduit is undersized, and whether or not effective well riser elevation will remain constant for all tail water elevations below the top of ground (e.g. via pumping of a housing discharge conduit located below the top of ground and isolated from tail water). It was assumed that if the tail water elevation is above the top of ground, the well housing would flood, the riser would submerge, and no benefit would be realized from a pumping a discharge conduit below ground elevation. Specifically, when RWTOR/TOW is less than or equal to tail water elevation, the design program computes as Hel as zero, and when RWTOR/TOW is greater than tail water elevation, Hel is computed as RWTOR/TOW minus tail water elevation. For the special case when RWTOR/TOW is less than tail water elevation, tail water elevation is less than or equal to the top of ground, and RWTOR/TOW remains constant via isolated housing discharge conduit pumping, Hel is computed as RWTOR/TOW minus tail water elevation; note computed Hel will be negative in this case. A well efficiency value, used to incorporate the hydraulic head loss component of total well losses, is user-specified in the Well Parameters section of the design program (Figure 4). Well efficiency (Ew) is generally the ratio of theoretical (aquifer) head loss or drawdown to actual (total) head losses or drawdown, and can be expressed as (Delleur, 1999):

%100

21

1

P

ww

ww

CQQBB

QBE

where B1 is the linear aquifer loss coefficient, Qw is well discharge, B2 is the linear well loss coefficient, C is the nonlinear well loss coefficient, and P is an exponent. This equation applies for a fully-penetrating well (relevant to designed R1A system), whereas for a partially-penetrating well, additional linear loss related to partial penetration should be determined and considered to compute Ew. Generally stated, from constant rate pump testing (providing transmissivity and storage coefficient values) B1 can be calculated, and from step-drawdown testing B1+B2, C, and P can be calculated. The user-specified Ew in the design program (Figure 4) represents the value which should be confirmed to exist upon and following well installation (via post-installation and maintenance program field testing) for the projected Qw in order for the system to provide the design level of stability. The specified value of Ew should ideally be based on experience with wells at the project site and engineering judgment, but alternatively, the design program provides an equivalent value of hydraulic well losses (Hh) corresponding to Ew if the user chooses to estimate losses using a different approach, such as that mentioned above and discussed in USACE (1992). For R1A, Ew was selected based on regional knowledge and judgment, and Ew was used a random variable in the design program reliability module (as discussed below). As discussed above, the design

spacing for the preferred fully-penetrating wells alternative (design Ew = 75% with corresponding Hh = 0.29 feet) is 100 feet in profile 1AG. Separate analysis indicates a 120 foot spacing would be required without hydraulic head losses assumed (Ew = 100%) to achieve the same FS and reliability; it is noted this would be an unrealistic and unconservative design approach. Since total well losses (Hw) affect the net head on the well system (h) as defined above, and vice versa, the design program uses an iterative approach to determine best estimates for both in the Well Spacing Parameters section (Figure 4). Initially, h is computed by assuming that Hw is equivalent to Hel, and the resulting average net head in the plane of wells corrected for well losses (hav), as defined above is computed. From initially computed hav , Hw is then initially computed as:

elhelavw

avw HHHh

E

hH

The program performs three such iterations, at which point the values of hav and Hw usually stabilize. The value of hm (as defined above) is then computed using the h value determined in the final iteration, and best estimates of hav, Hw, and hm are utilized to compute the resulting average net head in the plane of wells (Hav) and net head midway between the wells (Hm) as:

wavav HhH

wmm HhH

As discussed below, the computed Hav and Hm are used in factor of safety calculation and ultimately influence system design. Uplift Factor of Safety and Variable Tail Water Elevation As mentioned above, relief well system designs for blanket aquifer foundation condition regions were required to satisfy HHD project-specific (effective stress uplift) factor of safety (FS) criteria. Project criteria also required remedial designs to satisfy gradient-based FS criteria where emerging embankment through seepage was predicted or emerging under seepage was predicted in (northern-most R1A) non-blanket regions (Davis et al., 2009a). For blanket aquifer regions relevant to the R1A profile 1AG work being discussed, the FS against uplift (FSuplift) can generally be expressed as:

wexcess

n

iiwblsati

uplift h

zFS

1

)(

where i is idealized landside blanket stratum, zi is thickness of idealized landside blanket stratum, sat-bl is saturated unit weight of idealized landside blanket stratum, w is unit weight of water, and hexcess is excess head above top of ground elevation (or excess head above tail water elevation if it is above the top of ground). A distinction between previously published equations and this one is that prior equations have been expressed only for the case of tail water at the ground surface, whereas this equation is also expressed for cases when tail water exceeds the ground surface. The above equation could be modified to incorporate fractions of moist and buoyant unit weights for the case of a water table below the ground surface, and in such a case the reference elevation for determining excess head would instead be the top of the water table. The USACE (1992) relief well design guidance requires, and the design program (Figure 4) was written such, that excess head used to calculate uplift is determined based on the greater of the computed average net head in the plane of wells (Hav) and the net head midway between wells (Hm). The stated design guidance logic is that although the maximum landside head will always occur midway between wells for a fully-penetrating system, the average head may exceed the head midway between wells for a partially-penetrating system. As discussed below, fully-penetrating system designs were validated against plan finite element modeling during this design work. It is recommended for future research, that the requirement of designing partially-penetrating systems based on average head values be further explored; for instance, it is envisioned that three-dimensional modeling may demonstrate such a design approach could be conservative in certain cases if the head at the landside blanket base is less than average head values. Such proposed research was beyond the scope of this remedial design work but is mentioned for future consideration. Specifically, the uplift factor of safety at the well line resulting from the design well spacing (FSuplift-a) is computed in the Deterministic Design Results section of the design program (Figure 4) as:

waexcess

blbblauplift h

ZFS

where Zbl is thickness of landside blanket strata, b-bl is effective buoyant weight of landside blanket strata, and hexcess-a is excess head above the top of ground or tail water if it is above top of ground. The value of hexcess-a is computed as the tail water elevation plus the greater of Hav and Hm minus the greater of the tail water and top of ground elevations. As mentioned above, the design program also projects head values at the downstream embankment toe and at a user-specified distance landward of the well line. These projections provide a basis for additional recommended hand calculations to ensure adequate FS values away from the well line (e.g. where uplift resistance may differ due to blanket or topography variation). Barrier Affects and Effective Seepage Entrance Estimation

As discussed above, effective seepage entrance and exit conditions are user-specified in the Load and Underseepage Geometric Parameters section of Figure 4, or the program alternatively calculates them based on other input parameters. In some cases piezometric data do not provide a basis for estimating these conditions, and they are not directly determinable from established (open entrance/exit, blocked entrance/exit, or infinite blanket) equations. For the profile 1AG shown in Figure 3, historic piezometric data did not exist, but the landward blanket conditions allowed the effective seepage exit distance (x3) to be approximated by infinite blanket equations. The upstream blanket conditions however, do not conform to established approaches, as borrow pits through the blanket are now filled with materials having different composition. Further, the partially-penetrating seepage/piping barrier installed through the embankment centerline into the aquifer foundation affects flow. To account for barrier affects and estimate the effective seepage entrance distance (x1) for use in the relief well design program, an analytical approach was developed which utilized section finite element seepage modeling in conjunction with the design program; similar equations are presented below which are applicable for plan finite element modeling. The x1 distance was calculated using the below approach and its value was then input to the design program.

The net seepage gradient (∆M) towards an infinite well line, parallel to an infinite line source, is computed as:

w

av

w

av

xx

H

xLx

HHM

321

The single well discharge (Qw) is derived from Darcy’s law and can be expressed in different forms as:

w

av

w

av

w

av

w

avw xx

HaD

xLx

HHaDQQ

xx

H

xLx

HHaDMaDQ

3

e

21

e21321

ee KKKK

where Ke is the transformed foundation effective hydraulic conductivity, D is the transformed foundation thickness, and Q1 and Q2 are foundation flows towards and bypassing the well respectively. By formulating foundation flow and net seepage gradient in separate (upstream and downstream of the well) components (shown in far right equation of the above Qw

expression), Hav, x1, x3, and Qw can then be expressed as follows for the case of a section finite element model:

aD

xxaq

aD

xLxaqHH ww

ave

32

e

211

KK

2

1

e

1

KLx

aq

HHaDx w

av

wav x

aq

aHDx

2

e

3

K

aqaqQQQw 2121

where q1 and q2 are foundation flows (per 1 foot wide section model) towards and bypassing the well respectively. These quantities were directly measured by vertical flux sections in the profile 1AG model (Figure 3); the flux sections extended from just above the foundation top to below the foundation bottom, and were located close to the well on the pool and land

sides. As stated above x3 was calculated (as 726 feet) by the design program (Figure 4), and a constant (tail water elevation of 13 feet) head boundary condition was applied at this distance along the downstream section model vertical face. The pool elevation was set as 30 feet (constant head boundary condition applied along the upstream ground surface), and the upstream model vertical face consisted of infinite elements. A constant head boundary condition of 13.54 feet was applied to the relief well riser top nodes; it was equivalent to the total well losses calculated by the design program (Figure 4) plus the tail water elevation. Well losses affect the x1 value which is calculated and vice versa, and therefore an iterative approach of running the section model and the design program was taken to determine best estimates for both. With x3 and other parameter values equivalent in the section model and design program (xw = 78 feet, Ke = 16.77 feet/day, D = 520 feet), and with q2 measured from the section model (8.63 feet3/day), Hav was calculated (using the right equation in the above Hav expression) as 0.641 feet. Using this value with q1 measured from the section model (203.27 feet3/day), and L2 = 260 feet, x1 was then calculated (using the above x1 equation) as 364 feet; this value was input to the Load and Underseepage Parameters section of Figure 4 and used for well system design. Had x1 been initially known rather than x3 in this example, a similar approach as was taken to solve for x1 could have been taken to solve for x3 (using the left equation in the above Hav expression and the above x3 equation). When applying the above approach to a section model without the partially-penetrating seepage/piping barrier installed, the calculated x1 value was 311 feet, or 53 feet less than it is with the barrier. As discussed above, the design spacing for the preferred remedial alternative (with barrier and x1 = 364 feet) is 100 feet in profile 1AG, whereas separate analysis indicates 95 foot spacing would be required without the barrier to achieve the same FS and reliability (as discussed below); note the barrier provides additional benefits not reflected in an analysis pertaining only to affects on well spacing. Equations similar to those presented above for a section model, which can be used if desired for a plan model are:

aD

xxDq

aD

xLxDqHH ww

ave

32

e

211

KK

2

1

e

1

KLx

Dq

HHaDx w

av

wav x

Dq

aHDx

2

e

3

K

DqDqQQQw 2121

where q1 and q2 are foundation flows (per 1 foot thick plan model) towards and bypassing the well respectively. They can be measured by horizontal flux sections extending across a plan model and located close to the well on the pool and land sides. Reliability Analysis

As discussed above, designed relief well system geometry was required to satisfy project-specific FS criteria and be demonstrated as reliable to be considered appropriate. The input property values shown in Figure 4 are expected values and not conservative design values (e.g. 33-percentile saturated densities for blanket soils) often used during deterministic design work. To consider uncertainty related to input parameters and demonstrate design reliability, an additional Excel program (Figure 5), generally referred to as the reliability module was developed and linked to the design program (Figure 4). After the user specifies input parameters in the design program and statistics for random variables in the reliability module, the likelihood of the FS against uplift (heave) being less than unity for the relief well design is automatically estimated. The reliability module employs the Taylor’s Series expansion (Baecher and Christian, 2003; USACE, 2006) which involves calculating FS using expected input values, and then varying key random variables (input parameters having significant uncertainty and determined analysis significance across their conceivable values range) one at a time and calculating FS values. For the reliability module, the variables which typically govern the outcome of a relief well system design were built into the program as the random variables and the user is required only to input their statistics. Each random variable is used at plus one and minus one standard deviation (σ), a variance for each random variable is calculated using the difference in the resulting FS values, and the variance for all random variables is summed and used to determine the reliability index (β) and Pr(H). Pr(H) represents the probability that the FS against heave is less than unity given the analysis pool, while β is a relative measure of condition and provides a qualitative estimate of expected performance. Reliability (R) represents the probability that the FS will not be less than unity given the analysis pool. The user also inputs Pr(Pool), the analysis pool annual loading probability, and the program calculates Pr(H & Pool), the annual heave probability considering the pool.

In Figure 5 the reliability analysis results for the profile 1AG (Figure 3) well system design (Figure 4) are shown for the Maximum Pool (static elevation of 30 feet); the event return period is ~10,000 years. Detailed description of how σ values were determined for all random variables is beyond the scope of this paper, but their origin is briefly discussed.

Figure 5. Reliability analysis module of the deterministic relief well system design program (Figure 4) showing user inputs (red text) and results for profile 1AG (Figures 3). Deterministic analysis and uncertainty consideration result in design geometry for this profile of fully-penetrating wells on 100 foot centers.

Sensitivity analyses determined the critical tail water elevation with regard to producing the minimum FS occurred for profile 1AG at the expected value. Since the FS improved at both plus and minus one σ (possible since FS is a function of net head on the system, uplift resistance which is affected by tail water, and other factors), the tail water σ was specified as zero so inaccurate variance would not be incorporated into the analysis. The landside top of ground elevation σ was determined by considering the range of profile surface elevations (as they would exist after remedial construction) using recently acquired lidar data. The σ values for effective seepage entrance and exit distances were determined by varying site material properties which govern the calculated values of these parameters across their likely ranges. The landward blanket thickness and effective saturated weight σ values were determined by considering the range of blanket thicknesses encountered in profile 1AG borings assuming (based on available data, but intentionally conservative as well given sparse data in some locations) that the blanket could potentially be composed entirely of organic or inorganic materials. The σ values for foundation thickness, effective horizontal hydraulic conductivity, and ratio of effective horizontal and vertical hydraulic conductivities were determined based on regional information, all data acquired during a R1A constant rate pumping test, and surficial aquifer conductivity ranges in a prior USGS (1977) study. The well efficiency σ value was based on judgement, prior pump-testing and relief wells experience, and estimated future maximum practical and lowest tolerable well efficiency values.

The relative contribution of individual variable uncertainties to the estimated reliability is apparent from the results in Figure 5, which indicate that uncertainty and variation of landside blanket thickness and effective weight, and landside top of ground elevation in profile 1AG have the most significant affect. Designing a relief well system geometry (with a spacing of 163 feet for fully-penetrating wells) which only satisfied the FS design criteria (FS of 1.5) did not pass engineering judgement based knowledge of the site, nor did the resulting reliability (e.g. probability of heave given the analysis pool of 5 percent and β of 1.6) provide a strong basis for arguing the design was demonstrated as reliable. Considering in iterative fashion the results of deterministic and reliability analyses, and employing engineering judgment as to what well system geometry provided an appropriate degree of reliability in addition to meeting design requirements, the well system design for profile 1AG was specified as fully-penetrating wells on 100 foot centers. As shown in Figure 5, the resulting reliability for this design well geometry (e.g. reliability given the analysis pool of 99.9 percent and β of 3.1) provides a much stronger basis for arguing that the design is demonstrated as reliable in addition to meeting design requirements and passing judgement. A similar approach (involving consideration of deterministic and reliability analyses results) was taken towards designing well system geometry for the other sub-reaches of R1A, with the resulting designs varying based on the conditions of sub-reaches. Design Program and Plan Finite Element Model Comparison

Following relief well system design for profile 1AG as discussed above, plan finite element modeling was performed for verification of results. Such a comparison was directly possible since the well system design involves fully-penetrating wells. The plan model was constructed with parameters specified equivalent to those in the design program (Figure 4). Most parameters are annotated in Figure 6, and custom Excel plots generated using the plan model output are presented to illustrate the different resultant head values. Constant head boundary conditions of 30 and 13 feet were specified along the east and west plan model faces (in the x-direction) to represent the pool and tail water respectively. The north and south plan model faces (in the y-direction) were impervious boundaries located 100 feet apart (representing the design well spacing), and nodes representing a relief well were centrally located between the top and bottom faces. This agreed with the design program assumption that there is no flow across planes centered between wells and normal to the well line (i.e. no overall system longitudinal component of flow). The lower and upper plan model faces (in the z-direction) were also impervious boundaries, and this agreed with the impervious confining unit beneath the site foundation, and the equivalent lengths of impervious upstream and downstream top strata that the design program approaches utilized to represent the site surficial blanket conditions. A constant head boundary condition of 13.54 feet was applied to the relief well nodes; this was equivalent to the total well losses calculated by the design program (Figure 4) plus the tail water elevation. The plan model foundation (1 foot thick, homogenous and isotropic) was specified with an effective hydraulic conductivity of 16.8 feet/day. The resultant plan model head distribution (Figure 6) was the same as it would have been had the plan model thickness been equivalent to the transformed foundation thickness (D) in Figure 4, however, the resultant difference in foundation flows towards and bypassing the plan model well (q1 minus q2) was multiplied by D to obtain a single well discharge (Qw) for comparison with the design program single well discharge. For reference, the values of q1 and q2 measured from the plan model flux sections were 37.38 feet3/day and 3.58 feet3/day respectively. As seen in Figure 6, plan model results are similar to those from the relief well system design program (Figure 4). For example, the design program yielded: Qw of 90.5 gpm, Hav of 1.42 feet, and Hm of 1.64 feet, while the plan model yielded: Qw of 91.3 gpm, Hav of 1.38 feet, and Hm of 1.60 feet.

Conclusions

To reduce risk associated with seepage instability, the preferred remedial alternative for R1A of HHD involves the

construction of a partially-penetrating seepage/piping barrier through the embankment and near-surface consolidated strata,

Xw = 78'Dike CLWell Line D/S Dike Toe

X3 = 726'

U/S Dike ToeHead = 13' Head = 30'

S = 624'q2 q1

X1 = 364'

a = 100'

L2 = 260'

HHD - R1ASTATION 1568+00

14

15

20

25

Offset from Dike CL (ft)

-850 -800 -750 -700 -650 -600 -550 -500 -450 -400 -350 -300 -250 -200 -150 -100 -50 0 50 100 150 200 250 300 350 400 450 500 550

Dis

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ong

Dik

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Figure 6. Finite element (plan) seepage model (top) for profile 1AG (Figure 3) developed using similar input parameter values as those entered in and calculated by the relief well design and analysis program (Figure 4). Plots generated from the plan model output are shown to illustrate resultant head values (bottom). The results in Figure 4 (for fully-penetrating wells on 100 foot centers) indicate a well discharge (Qw) of 90.5 gallons per minute (gpm), an average net head in the plane of wells (Hav) of 1.42 feet, and a net head midway between the wells (Hm) of 1.64 feet, while the above plan model results indicate a Qw of 91.3 gpm, a Hav of 1.38 feet, and a Hm of 1.60 feet. The plan model well head was specified as 13.54 feet to simulate the total (elevation and efficiency) well losses in Figure 4.

and a landward seepage berm, which is coupled with a relief well system for blanket aquifer foundation condition regions. The barrier will address embankment through seepage concerns and assist towards addressing under seepage concerns; its depth (from the embankment crest) will range from 55 to 65 feet. The seepage berm will have a width of 4 times the dike height (e.g. 100 feet where the dike is 25 feet tall), and will have thicknesses of 5 feet and 2 feet at the dike and berm toes, respectively. Where present (everywhere except northern-most R1A), the thickness and relatively impervious nature of the continuous blanket does not allow enough dissipation of foundation head with increasing distance downstream such that the relatively light weight of the blanket can provide adequate resistance to remaining uplift pressure beyond the berm toe. Required pressure relief will be achieved by fully-penetrating (determined to be optimal approach) relief wells, with the required well spacing varying across R1A depending on the conditions in different sub-reaches. To determine appropriate geometry across different sub-reaches, three-dimensional aspects relevant to (the laterally non-continuous) wells were considered utilizing a developed design program in conjunction with supporting two-dimensional finite element modeling. For profile 1AG (located in the southern portion of R1A and used to illustrate the design process), appropriate geometry was determined to consist of fully-penetrating relief wells located at the seepage berm toe on 100 foot centers. By locating the well line landward of the embankment toe at the seepage berm toe, discharge will drain immediately into a swale (which will be constructed to provide a filtered exit and adequate uplift resistance) rather than having to be conveyed through a collector system installed through the berm. The designed well system geometry satisfies design criteria and engineering judgement, is demonstrated as reliable, and is optimized for cost.

Prior to relief well system installation in R1A of HHD, well screen and filter pack requirements will be determined by completing and analyzing pilot holes. The expected range for filter pack hydraulic conductivity (based on existing foundation data) was evaluated via section finite element modeling, and this indicated head losses due to filter pack alone will not exceed those assumed during system design. To compensate for finite well line affects (design approach assumed an infinite well line), the design well spacing will be decreased towards the end of an R1A sub-reach during installation if it adjoins a sub-reach having a smaller design well spacing or no wells. A relief well system maintenance plan has been developed and will be implemented upon system installation to ensure the efficiency of wells remains adequate (consistent with design assumptions) in the future. With implementation of this preferred risk reduction alternative, a robust instrumentation system will also be installed to allow real-time monitoring of performance conditions and further verification of remedial design assumptions during future high pool events. Design is currently complete for R1A of HHD, comprehensive plans and specifications are being prepared, partially-penetrating seepage/piping barrier construction is underway, and interim risk reduction measures have been implemented. Relief well system design aspects discussed in this paper included a custom computer program which incorporates reliability analysis, an analytical approach which can account for partially-penetrating seepage/piping barrier affects and can allow estimation of effective seepage entrance or exit boundary conditions for cases that do not conform to existing approaches, and the incorporation of variable well line position, well losses, and fluctuating tail water elevation into design solutions. These design approaches should be considered when relevant for future application at other projects.

References Baecher, G. and Christian, J., 2003, Reliability and Statistics in Geotechnical Engineering, John Wiley & Sons, Ltd. Barron, R., 1982, Mathematical Theory of Partially Penetrating Relief Wells, Unpublished report prepared for the U.S. Army

Engineer Waterways Experiment Station. Bennett, P., and Barron, R., 1957, Design Data for Partially Penetrating Relief Wells, International Conference on Soil

Mechanics and Foundation Engineering, v.2. Davis, J., Guy, E., and Nettles, R., 2009a, Herbert Hoover Dike Seepage Remedial Design Concepts, U.S. Society on Dams

Conference Proceedings, 25 p. Davis, J., Guy, E., and Nettles, R., 2009b, Preferred Risk Reduction Alternative for Reach 1A of Herbert Hoover Dike,

Association of State Dam Safety Officials Conference Proceedings, 14 p. Delleur, J., 1999, The Handbook of Groundwater Engineering, CRC Press LLC. GEO-SLOPE International, 2004, Seepage Modeling with SEEP/W, 398 p.

Halpin, E., and Ferguson, K., 2007, USACE Dam Safety: Program Status and Lessons in Transitioning to Risk Informed Approaches, The Journal of Dam Safety, v. 5, pp. 24-36.

Interagency Performance Evaluation Task Force (IPET), 2007, Performance Evaluation of the New Orleans and Southeast

Louisiana Hurricane Protection System, v. 5, app. 8. Mansur, C., and Kaufman, R., 1962, Dewatering, in Foundation Engineering, G.A. Leonards, Editor, McGraw-Hill. Marsland, A., 1961, A Study of a Breach in an Earthen Embankment Caused by Uplift Pressures, International Conference

on Soil Mechanics and Foundation Engineering, v.2. U.S. Army, 1983, Dewatering and Groundwater Control, Technical Manual 5-818-5. U.S. Army Corps of Engineers (USACE), 1956, Investigation of Underseepage and Its Control: Lower Mississippi River

Levees, Technical Memorandum 3-424. USACE, 1992, Design, Construction, and Maintenance of Relief Wells, Engineer Manual 1110-2-1914. USACE, 2006, Reliability Analysis and Risk Assessment for Seepage and Slope Stability Failure Modes for Embankment

Dams, Engineering Technical Letter 1110-2-561. U.S. Geological Survey (USGS), 1977, Hydraulic Conductivity and Water Quality of the Shallow Aquifer, Palm Beach

County, Florida, Water-Resources Investigations 76-119.