Lateral Pile Analysis Frozen Soil Strength Criteria

Prudhoe Bay, Alaska, is an oil field unit at latitude 70°30′ N and longitude 148°30′ W. Onshore structures are supported by pile foundations embedded in a layered frozen soil profile. These piles receive lateral structural loads from wind gusts, storms, and seasonal temperature change of building material. LPile is a commercially available computer program that analyzes the effects of lateral loads on piles embedded in a layered soil profile; it was developed by Ensoft. The public domain predecessor program COM624 can be used in lieu of LPile. LPile constructs $p\text{-}y$ curves using shear strength and strain criteria. Based on the curves and the lateral pile load, it calculates a soil modulus that is used in computing deflections, moments, and flexural stresses along a pile’s shaft. Required computer inputs are pile structural properties and dimensions, and soil profile and strength criteria. The pile designer needs to provide the structural properties and dimensions. The soil profile must be determined by subsurface exploration. Frozen soil strength criteria needed to construct $p\text{-}y$ curves are presented in this paper.

Frozen soil strength can be categorized into fine-grained and coarse-grained criteria. Fine-grained frozen soil at Prudhoe Bay and throughout most cold regions is nonplastic silt with more than 90% passing the number 200 sieve size. It has a water content greater than a 30%. Hanover silt, which has been used as a research frozen soil by the Cold Regions Research Engineering Laboratory (CRREL), meets those criteria (Sayles and Haines 1974). Coarse-grained frozen soil at Prudhoe Bay and throughout most cold regions is sand and gravel with less than 10% passing the number 200 sieve size. It has a water content less than a 30%. Manchester fine sand and Ottawa sand, which have both been used as a research soil by the CRREL, meet those criteria (Sayles 1968). Frozen soil that has a water content less than 50% is considered ice-poor, and greater than 50% is considered ice-rich (Weaver and Morgenstern 1981).

Frozen soil has more strength as its temperature decreases, as illustrated in Fig. 1. Greater (conservative) lateral pile deflections and flexural stresses will be calculated when a lower strength is used in this analysis. The soil’s warmest temperature, therefore, should be used in selecting its design strength.

When frozen soil is subject to a sustained load it will strain over the duration, or creep. Frozen soil strain can be modeled with three successive stages of creep: attenuating or primary, sometimes steady or secondary, then accelerating or tertiary if its yield strength is exceeded. As illustrated in Fig. 2, fine-grained frozen soil strain can be modeled as having primary then secondary creep until its yield strength is exceeded (Weaver and Morgenstern 1981). As also illustrated in Fig. 2, coarse-grained frozen soil can be modeled as having primary creep until its yield strength is exceeded (Weaver and Morgenstern 1981).

Because frozen soil has less strength as its load duration advances, the longest likely load duration for each design condition should be used in selecting its strength. Four common cold regions lateral design conditions with different load durations are described in Table 1.

The average annual ambient temperature at Prudhoe Bay is $-12°\mathrm{C}$. During the summer season months of June, July, and August, the average ambient temperature is 5°C. During the winter season months of January, February, and March, the average ambient temperature is $-30°\mathrm{C}$. Storms lasting 1–10 days may occur at any time with wind speeds between 30 and $50\mathrm{km}/\mathrm{h}$ and gusts up to $80\mathrm{km}/\mathrm{h}$.

Permanently frozen soil (permafrost) typically exists at depths between 0.6 and 360 m at Prudhoe Bay. Above 0.6 m is the thermal active layer, which thaws during the summer then refreezes during the subsequent winter. Strata below 360 m are warmed by terrestrial energy to be above 0°C so they aren’t frozen. Piles at Prudhoe Bay are embedded in about 8 m of soil. Soil temperature fluctuates annually within that depth because of the seasonal ambient changes. The typical coldest and warmest annual permafrost soil temperature profiles, which are, respectively, during spring and autumn, are illustrated in Fig. 3.

Vegetation covering the ground surface at Prudhoe Bay is known as tundra. A 1.5-m gravel pad is commonly constructed over the tundra at building facilities. These gravel or building pads provide stable areas that vehicles can operate on. The 1.5 m of gravel also thermally isolates the underlying permafrost from additional solar radiation, of which gravel absorbs more than does the tundra. As illustrated in Fig. 3, the design soil profile at Prudhoe Bay can be divided into three layers below tundra areas and four layers below building pad areas. At tundra areas, the thermal active layer consists of silt with decaying organics. Where 1.5 m of gravel is placed over the tundra, its weight compresses the silt with organics to be about 0.3 m thick. The thermal active layer at building pads consists of the gravel and underlying 0.3 m of silt with organics. Fine-grained soil 1.5 m deep is below the thermal active layer. Coarse-grained soil is below the fine-grained.

Reese (1975) developed LPile and its predecessor programs to model and analyze the effects of lateral loads on piles embedded in a layered soil profile. It uses a fourth-order differential equation, which was developed by Hetenyi (1946) that incorporates a nonlinear soil response. The differential equation assumes that a pile is a linearly elastic beam, and a soil’s response to its lateral deflection can be represented as a line load. The differential equation isin which $EI$ = pile flexural rigidity; $x$ = depth along the pile shaft; $y$ = lateral pile deflection at depth $x$; $Q$ = axial pile load; and $E_{sx}$ = secant modulus of the soil’s response to a lateral load at depth $x$.

The secant modulus of a soil’s response to a lateral pile load can be described in terms of a $p\text{-}y$ curve, which equates soil response ($p$) to a lateral deflection ($y$) at incremental depths below the surface. The procedure to construct $p\text{-}y$ curves for different soil types and loading conditions was developed by Matlock (1970) and is described by Reese (1975, 1977). It assumes that the stress-strain curve for soil in a laboratory triaxial test and the $p\text{-}y$ curve of soil response have similar shapes. The $p\text{-}y$ curves are usually nonlinear and depend upon several parameters, including pile diameter, depth, soil shear strength, and stress-strain characteristics. This procedure assumes the soil response at a particular depth is independent of that at another depth. That assumption is valid for lateral pile load deflections (Reese 1977), so each layer of soil, which has unique strength characteristics, can be modeled separately using the procedure.

The procedure to construct $p\text{-}y$ curves for piles embedded in a layered soil profile is described as follows:

Measured fine-grained frozen soil short-term shear strengths are presented in Fig. 4 for temperatures between 0 and $-10°\mathrm{C}$. These short-term shear strengths were measured by triaxial quick tests with durations between 21 and 141 s. The quick tests were performed by the CRREL on Hanover silt (Sayles and Haines 1974) and on ice-rich soil samples obtained at Prudhoe Bay by Harding Lawson Associates (HLA) (“Alaska Gas Conditioning Facilities,” unpublished report, 1981). A linear regression analyses has been performed to calculate the variation of measured shear strengths from their average. The best-fit data line, which is based on the average shear strength increasing with a decrease of temperature, is presented in Fig. 4. The calculated coefficient of variation (cov) for measured shear strengths from their average is 0.18. Measured fine-grained frozen soil shear strengths therefore have a 68% probability of varying within 18% from their average. They also have a 95% probability of varying within 36% from their average.

Criteria to be used in calculating fine-grained frozen soil strength for load durations of 1, 2, 3, 4, 10, 30, 90, and 120 days, and 20 years, are presented in Table 2. To calculate a shear strength for a certain temperature and load duration, obtain the fine-grained frozen soil short-term shear strength from the average presented in Fig. 4, then multiply that by its reduction factor from Table 2. The 0.35 reduction factor for a 1-day load duration is based on results of many shear strength tests, with durations ranging between 21 s and 182 days, performed on Hanover silt and other soil. Other reduction factors have been generated by calculating relative ratios to the 1-day strength using the ice and ice-rich soil flow law published by Weaver and Morgenstern (1981).

Weaver and Morgenstern (1981) concluded that a parabola with an exponent of 3 ($n$-value) should be used to model the stress-strain behavior of fine-grained frozen soil. The failure strain for each reduction factor has been selected from the results of many triaxial tests performed on fine-grained frozen soil (Sayles and Haines 1974; HLA, “Alaska Gas Conditioning Facilities,” unpublished report, 1981; Duane Miller & Associates, “Over the Horizon—Gulkana,” unpublished report, 1989; Yuanlin and Carbee 1987). Strains at one-half the ultimate shear strength (${\epsilon }_{50}$), which are presented in Table 2, have been calculated by dividing the selected failure strains by eight.

If lateral pile loading exceeds these strength criteria then tertiary creep (yield) might occur. When the average shear strength is used in an analysis (safety factor equal to 1.00), it will have a 50% probability of being exceeded during loading. If an 84% confidence of not being exceeded during loading is desired, then the average shear strength of fine-grained frozen soil should be reduced by a safety factor of 1.22. If a 97.5% confidence of not being exceeded during loading is desired, then the average shear strength of fine-grained frozen soil should be reduced by a safety factor of 1.56. Coefficients of variation for these safety factors, which are presented in Table 3, have been calculated using results of the linear regression analysis performed on measured fine-grained frozen soil shear strengths.

Measured coarse-grained frozen soil short-term shear strengths are presented in Fig. 5 for temperatures between 0 and $–10°\mathrm{C}$. These short-term shear strengths were measured by triaxial quick tests with 7 to 76 s durations. They were performed by the CRREL on Manchester fine sand and Ottawa sand (Sayles 1968). A linear regression analysis has been performed to calculate the variation of measured shear strengths from their average. The best-fit data line, which is based on the average shear strength increasing with a decrease of temperature, is presented in Fig. 5. The calculated coefficient of variation for measured shear strengths from their average is 0.10. Measured coarse-grained frozen soil shear strengths, therefore, have a 68% probability of varying within 10% from their average. They also have a 95% probability of varying within 20% from their average.

Criteria to be used in calculating coarse-grained frozen soil strength for load durations of 1, 2, 3, 4, 10, 30, 90, and 120 days, and 20 years, are presented in Table 2. The 0.40 reduction factor for a 1-day load duration is based on results of many shear strength tests, with durations between 7 s and 146 days, performed on Manchester fine sand and Ottawa sand. Other reduction factors have been generated by calculating relative ratios to the 1-day strength using the ice-poor soil flow law published by Weaver and Morgenstern (1981). That flow law was generated based on the results of shear strength tests performed on Ottawa sand.

Gregory et al. (2003) concluded that a parabola with an exponent of 4 ($n$-value) should be used to model the stress-strain behavior of coarse-grained frozen soil. The failure strain for each reduction factor has been selected from results of many triaxial tests performed on coarse-grained frozen soil (Sayles 1968; Gregory et al. 2003). Strains at one-half of the ultimate shear strength (${\epsilon }_{50}$), which are presented in Table 2, have been calculated by dividing the selected failure strains by sixteen.

When the average shear strength is used in an analysis (safety factor equal to 1.00), it will have a 50% probability of being exceeded during loading. If an 84% confidence of not being exceeded during loading is desired, then the average shear strength of coarse-grained frozen soil should be reduced by a safety factor of 1.11. If a 97.5% confidence of not being exceeded during loading is desired, then the average shear strength of coarse-grained frozen soil should be reduced by a safety factor of 1.25. Coefficients of variation for these safety factors, which are presented in Table 4, have been calculated using results of the linear regression analysis performed on measured coarse-grained frozen soil shear strengths.

During November 1971, lateral pile load tests were performed at Inuvik, Northwest Territory, Canada. The soil profile, load test procedures, and results were reported by Rowley et al. (1973, 1975). The soil profile at Inuvik used in analysis for this paper is illustrated on Fig. 6. Lateral loads were applied to several piles including a 0.3-m timber pile (T-2-L) and a 0.27-m steel pipe pile (S-5-L). Each pile was step-loaded four times for durations between 10 and 30 h. Total load test durations ranged from 68 to 82 h. Pile deflections, which were measured 0.55 m and 0.36 m above the surface, are presented in Figs. 7 and 8, respectively, for piles T-2-L and S-5-L.

Deflections calculated using LPile with the strength criteria and a safety factor of 1.00, for 1-day, 2-day, and 3-day load durations are compared in Figs. 7 and 8 to those measured at piles T-2-L and S-5-L. Calculated deflections for pile T-2-L are similar to those measured. Calculated deflections are less than those measured for the 89-kN, 178-kN, and 267-kN lateral loads on pile S-5-L. Calculated deflections for the 356-kN lateral load on pile S-5-L are slightly greater than measured deflections. When the shear strengths are reduced by a safety factor of 1.22 the calculated deflections for the 178- and 267-kN loads on pile S-5-L are closer to those measured. Differences between calculated and measured deflections should be expected when comparing results of a design approach using a model to load tests because of unaccounted-for variations in frozen soil type, strength, and profile. The comparison of calculated deflections to Inuvik pile load test measurements indicates that reducing shear strengths by a safety factor of 1.22 will ameliorate most of those unaccounted-for variations.

Nixon (1984) developed a procedure to analyze the effects of lateral loads on piles embedded in frozen soil. The procedure uses a finite-difference computer program that analyzes flexible piles embedded in a viscous medium. It uses secondary creep criteria for ice-rich soil presented by Weaver and Morgenstern (1981) as the viscous medium’s properties. Neukirchner and Nixon (1987) used that computer program to analyze a laterally loaded pile embedded in ice-rich permafrost. Their assessed pile was a 457 mm diameter, 13 mm thick steel pipe, embedded 3.048 m into ice-rich soil at $–5°\mathrm{C}$. They analyzed a 89-kN lateral load applied 1.829 m above the surface to that pile for 120 days. Deflections calculated using LPile, a safety factor of 1.00, and the 120-day fine-grained strength criteria, which has a 0.10 reduction factor, are 20% less than what they predict. Deflections calculated using a 0.09 reduction factor are close to what they predict. So deflections calculated using the strength criteria are within 20% of those predicted by Neukirchner and Nixon (1987) and sensitive to incremental differences in reduction factors.

Pipelines aligned across the tundra at Prudhoe Bay are typically supported by 325 mm diameter, 10 mm thick steel pipe piles embedded through the natural layers of silt with organics and fine-grained and coarse-grained frozen soil. Deflections and moments for those piles under short-term, 1-day, 90-day, and 20-year load durations were calculated using the strength criteria, autumn temperature profile, a safety factor of 1.22, and LPile. Results of the analysis for a 40-kN lateral load are presented in Fig. 9. They indicate that piles embedded through the tundra soil profile will have an increase of moment as the load duration advances to 20 years. The depth of fixity, for maximum moment calculations, increases from a 0.6-m to a 1.2-m depth as the load duration advances. This increase in the depth of fixity is due to the strength decrease that fine-grained and coarse-grained frozen soils have because of their creep strength loss as the load duration advances.

Structures for oil-production facilities on building pads at Prudhoe Bay are typically supported by 457 mm diameter, 13 mm thick steel pipe piles embedded through gravel placed over the silt with organics and fine-grained and coarse-grained frozen soil. Deflections and moments for that pile were calculated using short-term and 20-year strength criteria, the autumn temperature profile, a safety factor of 1.22, and LPile. Results of the analysis, for an 80-kN lateral load, are presented in Fig. 10. They indicate that piles embedded through 1.5 m of gravel will have nearly the same moment as the load duration advances to a 20-year duration. The depth of fixity almost stays steady at a 0.6-m depth below the pad surface as the load duration advances because most of the lateral load for this pile is absorbed by the thawed surface layer of gravel, which does not have a strength loss because of creep as the load duration advances.

A design approach has been presented to analyze the effects of lateral loads on piles embedded in a layered frozen soil profile using the computer program LPile. Fine-grained and coarse-grained frozen soil shear strength and strain criteria have been presented to be used in the construction of $p\text{-}y$ curves for an analysis with LPile. These strength criteria account for frozen soil particle size, temperature, and load duration. They are based on an amalgamation of published and unpublished laboratory strength test results. Comparison between deflections calculated using the strength criteria and LPile to those measured by lateral pile load tests performed at Inuvik indicates that reducing shear strengths by a safety factor of 1.22 will ameliorate most unaccounted-for variations in soil profile. Future laboratory strength and lateral pile load tests should be performed to increase the understanding and knowledge of frozen soil strength and refine the criteria as appropriate.