Evaluation of Elongation Criteria and Friction Loss in Ground Anchors
Final Report
Prepared by: John P. Turner and Benjamin J. Turner Dan Brown and Associates, PC
Submitted to: Deep Foundations Institute Committee on Tiebacks and Soil Nailing
October 16, 2014
EXECUTIVE SUMMARY
This report describes a research project for evaluating the applicability of the widely accepted 80 percent criterion for elongation of ground anchors to anchors with unbonded lengths exceeding 100 feet. This issue is driven by several recent projects involving ground anchors for landslide stabilization in which a significant percentage of the anchors did not meet the criterion that requires measured elongation during proof load testing of at least 80 percent of the theoretical elastic elongation. The projects involved anchor unbonded lengths in the range of 85 to 220 feet, which is outside the range traditionally used in practice, although anchors of this length are being used more frequently for landslide stabilization. The principal objective of this research is to address whether the widely accepted criterion of 80 percent elongation is applicable for such applications, and whether other factors affect the ability of anchors to meet the criterion.
Analytical methods for predicting transfer of load along the length of steel strand due to friction loss are used routinely in the prestressed concrete industry. These analytical expressions provide a rational framework for quantifying changes in load due to friction along the length of a ground anchor in terms of a ‘wobble coefficient’ (K) as defined in Aalami (2004). Values of the wobble coefficient for ground anchors can only be determined by back‐calculating from load tests, i.e., fit the value of K to the appropriate analytical expression based on the known test load and measured percent elongation. The analytical basis is first developed and shown to provide a tool for evaluating results of anchor load tests to determine the magnitude of expected elongation as a function of unbonded length. Next, a database of anchor load tests is used to back‐calculate values of K for anchors with unbonded lengths in the range typically used in geotechnical applications (< 100 feet). These values of K are then used to calculate expected friction loss for anchors with high unbonded lengths (100 to 250 feet) to evaluate whether the 80 percent criterion is reasonable.
The primary findings of this research are:
Field data data show a general trend of increasing rate of friction loss with increasing unbonded length, i.e., longer anchors are more likely to fail the 80‐percent minimum elongation criterion. Shallow anchor inclination appears to be a strong contributor to higher friction loss because it makes placement of the anchor into the hole difficult, requiring the anchor to be forced in, which may induce additional curvature and twisting; Factors that contribute to alignment deviations of the anchor drill hole, such as obstructions, discontinuities, or alternating hard and soft layers, also contribute to curvature and increase friction loss; Factors that result in forcing the anchor into the hole, which for the cases considered involved a combination of long anchors, shallow inclination, and alignment deviations, increases the probability of anchor damage. For example, failure of the seal between the bond and unbonded segments of the anchor may allow grout to penetrate the sheathing, preventing elastic deformation of the strands.
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Measures that can be taken to mitigate the effects of anchor friction loss include:
Higher inclination angles; if the project conditions allow, use of steeper inclination angles reduces curvature by allowing gravity to assist in stretching the anchor and making installation easier. Two‐stage grouting in which the bond zone is grouted and an alignment load is applied to straighten the unbonded length before it is grouted. This procedure is more time‐consuming and difficult to perform, and hence not utilized routinely in North American practice, but warrants consideration where high unbonded lengths (> 100 ft) and shallow inclination angles are required. Use of instrumentation for: (a) monitoring and correcting for hole alignment, and (b) direct measurement of load transfer to the bond zone, such as strain gages or direct‐force measuring devices that can be mounted to the anchor strands. Item (b) allows direct verification of the change in load over the unbonded length (friction loss) as well as the load transferred to the bond zone which provides the stabilizing force.
Regardless of whether anchors pass or fail the 80‐percent criterion, slope stability analyses that include the resisting force of the anchor should only consider the magnitude of load that is expected and specified to reach the bond zone. If the designer requires more resisting force to reach a target factor of safety, larger anchors or a higher minimum elongation criteria must be specified. Likewise, anchors that fail the 80‐percent criterion do not necessarily have to be rejected outright if additional slope stability analysis considering the actual magnitude of load reaching the bond zone can be shown to satisfy the target factor of safety when supplemental anchors are added. This recommendation is consistent with the PTI specifications (2004) although it is not typically included in project specifications.
Considering that many anchors from the database with unbonded lengths in the range of 100 to 200 feet satisfied the 80‐percent criterion, a modified minimum elongation acceptance criterion for long anchors is not recommended at this time. Additional data will potentially allow us to draw quantitative conclusions about the influence of specific parameters such as anchor hole inclination and the manufacturing processes used by various anchor manufacturers, and could lead to more definitive recommendations in the future. This study should be considered preliminary and the issue of friction loss in ground anchors should be the subject of additional research.
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1. INTRODUCTION AND PROBLEM STATEMENT
Steel strand used in concrete pre‐stressing applications or in ground anchors for geotechnical applications exhibit variations in load along the length of the strand during stressing. For strand encased in grease‐ filled plastic sheathing, which is intended to allow the strand to elongate freely, some load can still be transferred by friction between the strand and the grease and between the grease and sheathing. The sheathing then transfers load to the surrounding grout and, in the case of ground anchors, to the surrounding soil or rock. A widely used criterion for ground anchor acceptance based on load testing is that the measured anchor elongation be required to achieve a minimum value of 80 percent of the theoretical elastic elongation, based on the well‐known relationship Δ = PL/AE where P = load applied at the anchor head, L = anchor unbonded length, A = cross‐sectional area of steel strand, and E = modulus of elasticity of the steel strand. This criterion allows the actual elongation to be 20 percent less than the theoretical elastic value, presumably because the load over the unbonded length is decreasing with distance from the anchor head. This decrease in load is referred to as friction loss.
The 80 percent criterion has served the ground anchor industry well. It provides a rational and practical means to evaluate the ability of an anchor to transfer most of its load (80 percent or more) between the anchor head and the bond zone. In most applications, a properly manufactured and properly installed ground anchor will meet the 80 percent elongation criterion easily. However, several cases in recent years in which anchors being used for landslide stabilization and having unbonded lengths in the range of 85 to 220 feet resulted in unusually high failing rates with respect to the criterion. This raises the question of whether the 80 percent criterion is applicable to all ground anchors or if it should be limited to anchors within a certain range of unbonded length. In particular, the question is whether friction loss increases with unbonded length to a point at which the anchor elongation can be expected to fall below 80 percent of theoretical elongation. If that is the case, acceptance criteria for anchors with long unbonded lengths, such as are now being used in landslide stabilization applications, may require modification from the 80 percent criterion.
Section 2 of this report presents the analytical approach for evaluating the change in load along the length of a pre‐stressing strand, in terms of friction loss. This analysis provides a framework for quantifying friction loss in ground anchors when load testing is conducted with measurements of elongation. Section 3 introduces the factors having the potential for increasing friction loss in ground anchors. Section 4 presents case histories of anchors not meeting the 80 percent criterion, while Section 5 presents data from case histories in which anchors met the criterion. These cases are compared in an attempt to identify the factors that result in less than 80 percent elongation. Anchor unbonded length appears to be a major factor; however other variables come into play, including anchor inclination (from horizontal), installation methods, deviation of the drill hole alignment, and subsurface conditions that contribute to drill hole deviation. Section 6 describes a landslide stabilization project in which long anchors successfully met the elongation criteria, and identifies the factors that enabled the criterion to be met. Section 7 provides recommendations on incorporating anchor forces into limit equilibrium slope stability analyses. Finally, Section 8 summarizes the study and presents recommendations for minimizing friction loss in ground anchors and suggestions for further research.
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2. ANALYSIS OF FRICTION LOSS IN STRAND ANCHORS
The following relationship is often cited (e.g., see AASHTO LRFD Bridge Design Specifications Section 5.9.5.2.2, ACI‐318 Section 18.6.2, or the PTI Post Tensioning Manual) as an approximation of load (P) as a function of distance (x) from the anchor head:
‐[αμ +Kx] P(x) = Po e (1) where: P(x) = load in anchor at distance x from anchor head Po = load at anchor head (at x = 0) α = change in angle of the strands (radians) from the stressing point to distance x = coefficient of angular friction K = wobble coefficient of friction (radians per unit of length) x = distance from the stressing point
The first term in the exponent, αμ, represents the effect of cumulative change in angle up to a distance x and is useful for calculating friction losses in pre‐stressing applications where the strand is supported at known locations in the structure (e.g., the strand is draped over supports in the concrete form). For prestressed concrete applications, α can be evaluated incrementally over each support interval. For ground anchors the strand is not supported at constant intervals and the αμ term is not applicable. All effects of friction loss are lumped into the single parameter, K. Equation 1 reduces to:
‐Kx P(x) = Po e (2)
The parameter K is referred to as the wobble coefficient and is the product of angle change per unit of length (radians/ft) and the coefficient of angular friction μ for the sheathed strand with grease (Aalami (2004).
Thus, the normalized load at a distance x from the anchor head is given by: