A Method for Predicting Pile Bearing Capacity From Dynamic Penetration Tests

. This paper presents a new method for predicting the axial capacity of piles from dynamic penetration tests which is based on the concepts of soil dynamics and principles of energy conservation. The energy delivered to the hammer-rod-sampler system and transferred to the soil is computed from the numbers of blow counts N spt and is analytically con-verted in a penetration dynamic force. The dynamic force allows the unit resistance mobilized in the SPT sampler (model) to be determined, which is then used to predict the unit resistance mobilized in a prototype pile. The strong direct relationship between the ultimate resistance of driven steel piles and the SPT dynamic force, without any bias of soil type, validates the method. Extension of the method to other pile types requires empirical parameters to account for installation effects. Predictions of 89 instrumented static pile load test database demonstrate that the proposed methodology can be efficiently used in the assessment of axial pile capacity, providing a practical way of increasing reliability in pile design by accounting for effects controlling dynamic penetration.


Introduction
The prediction of pile bearing capacity can be achieved using different methods of analysis such as interpretation of data from full-scale pile load tests, dynamic analysis and testing based on wave equations, static analysis based on soil properties and static analysis using the results of in situ tests. Given to the fact that penetration tests are used worldwide as the primary index test for site characterization, traditional methods of pile analysis and design often rely on empirical approaches based on SPT and CPT data (e.g. Bustamante & Giasenelli, 1982;Ruiter & Beringen, 1979;Aoki Velloso, 1975 ). These methods may produce inaccurate responses and unreliable predictions, because pile design depends on soil stratigraphy, pile characteristics, driving and installation methods, drainage and loading conditions. Applicability is therefore restricted to the database upon which the method has been developed and tested, and local experience and engineering judgment still plays an important role in pile analysis and design.
Among existing approaches, those established on the bases of SPT results receive severe criticism for their empirical nature, simplified assumptions, scattered predictions and discrepancies between predicted and measured loads. Although considerable literature is available on this matter, there is no single method of pile design based on dynamic penetration that has some theoretical background other than statistical.
Previous efforts have been made to estimate an average static resistance mobilized during sampler penetration (Schmertmann;1979;Aoki et al., 2004). An alternative method for the interpretation of dynamic penetration tests was proposed by Odebrecht et al. (2005) and Schnaid et al. (2008) from which the energy delivered to the rod string is used to calculate a dynamic force that represents the soil reaction to the penetration of the SPT sampler (F d ). Lobo (2007) used this dynamic force to develop an approach for predicting the axial bearing capacity of piles and Lobo et al. (2009) demonstrated the applicability of the approach by comparing measured and predicted ultimate loads from a database of 272 full scale load tests. Langone (2012) presented an independent assessment based on the interpretation of results from fully instrumented pile load tests. These results are presented in this paper and are used to validate a method for estimating the axial capacity of vertically loaded isolated piles.

Theoretical Developments
The proposed approach is based on the concepts of soil dynamics and principles of energy conservation. By computing the total energy delivered to the soil, Odebrecht et al. (2005) demonstrated that the potential energy (PE h+r ) has to be expressed as a function of the nominal potential energy (E*), permanent sampler penetration (Dr) and weight of both hammer and rods, as well as three efficiency coefficients designed to account for energy losses during the energy transference process: where M h is the hammer weight; M r the rod weight; g the gravity acceleration; and h 1 , h 2 and h 3 the efficiency coefficients. The nominal potential energy E* represents a part of the hammer potential energy to be transmitted to the soil. An additional hammer potential energy is given by M h g Dr and the other part is transmitted by the rod potential energy M r g Dr which cannot be disregarded for tests carried out at great depths in soft soils, i.e. conditions in which Dr and M r are significant. Equation 1 requires a previous calibration of efficiency coefficients, which as a preliminary estimate for Brazilian SPT configurations can be assumed as h 1 = 0.76; h 2 = 1 e h 3 = (1-0.0042l), where l is the total rod length, (Odebrecht et al., 2005). Note that h 3 is adimensional, so the number before l has a m -1 dimension. Since Eq. 1 gives the energy effectively delivered to the soil, with all losses accounted for by means of the efficiency coefficients, it is in principle possible to use this potential energy to calculate the mean dynamic reaction force (F d ) applied to the soil during sampler penetration Schnaid et al., 2004;Schnaid, 2005): The sampler-soil interaction model is therefore represented by a dynamic mean reaction force that is calculated from the work produced by the non-conservative forces derived from the potential energy produced by the hammer-rod-sampler system.
The dynamic force F d can now be used as an input value to compute the pile axial load by combining bearing capacity theory to the principles of cavity expansion. The ultimate axial load capacity of the pile (Qu) is the sum of two components: the end-bearing capacity (Q P ) and the shaft friction capacity (Q L ), which can be expressed as: where q p is the unit end bearing resistance, f l local shaft friction, U the perimeter of the pile, A p the area of the pile base and DL a pile length segment. Unlikely the cone, where the tip resistance q c shows strong correlation with q p and f l , the dynamic force F d has to be interpreted in order to estimate these two variables. Interpretation does not include specific considerations regarding the drainage paths around the penetrating sampler.

End-bearing
Estimating end bearing requires specific considerations regarding the mode of penetration of the sampler. Ideally a simple inspection of the soil plug inside the sampler is sufficient to identify whereas plugged or unplugged penetration has taken place at the depth of the pile tip. However this is not done in current investigation practice and, for the sake of simplicity, the proposed method was developed for piles embedded in stiff soils where sampler penetration is generally plugged (implying that floating piles would require different treatment). Plugged penetration is an assumption of the proposed methodology; other assumptions can be made within the same framework of energy propagation and energy conservation principles leading to slightly different results.
In a plugged penetration mode, the dynamic force is the sum of two terms: shaft friction and end-bearing resistance. By combing bearing capacity to cavity expansion (Vésic, 1972) it is possible to calculate the relative contribution of these two terms for a set of typical parameters. Use of Vésic's formulation follows recommendations from Eurocode 7 (1997) and API RP2A (2000). A parametric analysis demonstrates that end-bearing corresponds to 60% to 80% of the measured penetration force ) which justifies considering the SPT bearing resistance q p,spt as 70% of the total measured penetration force: being a p the area of the sampler base (p5.1 2 /4 = 20.4 cm 2 ). Extrapolating measurements from penetration tests to real scale pile load test data is therefore a direct process that is not biased by soil conditions, pile length (L), pile diameter (D) and pile aspect ratio (L/D). In doing so, a recommendation is made to calculated F d from the average N value taken in the zone of 2.0 pile diameters (D) above and below the pile tip, which is consistent to previously reported studies in both SPT and CPT interpretation data (e.g. Bazaraa & Kurkur, 1986;Briaud & Tucker, 1988;.

Shaft friction
The shaft friction calculated by the SPT (f l,spt ) is simply the dynamic force divided by the inner and outer areas of the sampler, expressed as: being a l the area of the sampler shaft. In this case, friction components mobilized inside and outside the sampler are considered to be the same. This assumption has been numerically evaluated by Lobo (2010) and it is believed to reproduce the basic mechanism that takes place during penetration in soft and loose materials.
The measured values of f l,spt can then be integrated along depth to estimate the actual pile shaft, and by doing so a number of simplified considerations are necessary: i the sampler shaft friction has been shown to be much greater than the actual pile shaft friction due to what has been generally recognized as scale effects. These effects need to be considered when extrapolating measurements from penetration tests to real scale pile load test data, as already established by previous interpretation methods using SPT and CPT results (e.g. De Ruiter & Beringem, 1979; Bustamante & Gianeselli, 1982). Lobo et al. (2009) proposed reducing f l,spt by a factor of 0.2 based on a comprehensive analysis comprising 271 real scale pile load tests. Della Rosa (2009) observed scale effects of the same other of magnitude when performing tests using SPT with diameters ranging from 3.6 to 7.2 cm. Langone (2012) confirmed these observations when interpreting instrumented pile load tests; ii the shaft friction developed on a pile in tension is smaller than that mobilized by a pile loaded in compression (e.g. Lehane et al.,1993;de Nicola & Randolph (1993); Jardine et al., 2005;Lehane et al., 2007). This effect is not considered in the current analysis which implies that the predicted friction resistance corresponds to a pile loaded in compressions and should be reduced for a pile under tension; iii in driven piles, the shaft capacity is known to habitually increase with time (e.g. Axelsson, 1998;Jardine et al., 2005a;Lehane et al., 2005a. Data considered in the present analysis generally represents long term conditions where installation effects have been partially settled; iv strains in the pile that have been mobilized before the start of the test due to residual load must be considered, and in cases where these values are reported the residual loads were adjusted before establishing the true load distribution (i.e. the true load is, mainly, the sum of the installation load distribution -locked in stresses -with the load measured during the load test); The reasoning for these simplifying assumptions is to keep the method simple and straightforward for application in design, but it does not restrain future modifications within the same framework (that could be easily implemented).
In summary, the contributions of both end-bearing and shaft friction can be computed directly from the penetration force and the general formula for calculating the ultimate axial load capacity of the pile (Eq. 3) becomes: The 0.2 value in Eq. 6 accounts for scale effects. In this general formula, a dynamic force is used to compute the static long term capacity of a pile which implies on disregarding visco-effects and pore-water pressures generated during the dynamic penetration of the sampler. As in all SPT-based methods ignoring these effects may induce errors in low permeable soils such as clays and silts. Since design procedures mainly involve considering the long term pile capacity, SPT data can be generally applied to sands, non-cohesive granular soils and most residual soil formations.

Database
An extensive search in the literature was conducted by Langone (2012) to identify instrumented pile load test publications with SPT penetration soundings adjacent to tested piles. A database of 89 instrumented incremental static load tests in different soil formations has been carefully reviewed in order to evaluate their suitability for the current research, considering availability of proper documentation on the pile data (installation and testing), subsurface exploration and general geotechnical laboratory and in situ testing data. Although all piles were subjected to static load tests, the loading procedure changed considerably reflecting local practice and standards, introducing errors and uncertainties to the overall analysis.
The ultimate axial load capacity for each pile was determined using the criterion recommended by the Brazilian Standard NBR 6122:2010, as illustrated in Fig. 1. Tests were chosen for their high degree of mobilization of pile capacity and the availability of reliable load-settlement relationships. However in several cases the Vander der Veen method (1953) had to be used to extrapolate the measured load-settlement curve of pile load tests that have not reached the required displacement of D/30 plus the elastic deformation of the pile.
Besides the proposed method, other semi-empirical and theoretical methodologies were employed for comparison purposes. The semi-empirical methods reflect the Brazilian engineering practice of foundation design: Aoki & Velloso (1975) and Décourt & Quaresma (1978). Since these methods were developed in Brazil, the energy efficiency is assumed to be of the order of 75%.
The theoretical approach uses bearing capacity theory associated with cavity expansion (Vésic, 1972). Vesic's approach to cavity expansion applied to cohesive-friction soils introduces some minor errors to the analysis because it does not consider the effect of cohesion in inhibiting dilation, as demonstrated by Mantaras & Schnaid (2002) and Schnaid & Mantaras (2003). When laboratory tests or soil parameters were not reported, SPT correlations were employed to estimate the friction angle (f) and the Clam-Clay model (S u = 0.25 s ' v ) used to estimate the undrained shear strength.

Prediction and Performance
The ultimate axial load capacity of the pile predicted by dynamic penetration methods (Q U ) is compared to the measured pile capacity as obtained from the instrumented pile load tests using the Brazilian NBR 6122 failure criterion. By doing so, the predictive performance is presented and discussed. A summary of essential information related to the pile tests is shown in Table 1, including the pile size, type, length, location of the load test, the measured and predicted ultimate axial load capacity.
Initially the analysis concentrates on driven piles. End-bearing capacity (Q P ) and shaft friction capacity (Q L ) are computed from the measured data, as illustrated in Fig. 2 for a load test carried out in Brazil and reported by Falconi & Perez, (2008). This figure presents the loadsettlement curve measured at the pile head and the actual load distribution along the pile at the final loading stage, as well as the SPT profile representative of ground conditions. The subsoil consists of a superficial 10 m thick fine silty sand layer, medium to dense, overlain a thick soft to very soft marine silty clay. Residual soil is encountered below 51 m depth. The tested H-pile was instrumented by strain gages placed at selected levels to determine the load distribution for each load applied to the pile head. Comparisons of measured and predicted loads cover the 4 methods used as reference in the present study. In this par-ticular case, the the proposed method and the theoretical approach slightly underestimate the skin friction distribution whereas the semi-empirical methods overestimate the measured data.
Once the interpretation of each load test was completed, the measured and predicted values of Q P , Q L and Q U were directly compared, as shown in Figs. 3, 4 and 5, respectively. In steel driven pile predictions, a limiting value of N 60 £ 100 was arbitrarily adopted.
Important observations derived from analysis can be summarized as follows: • The proposed method predicts measured capacity values that are in general agreement with Brazilian practice; • As previously stated, the method relies entirely on wave propagation and energy conservation, requiring a single empirical factor to account for scale effects; • The predictions of shaft resistance are much less scattered than predictions of end-bearing resistance. Errors in interpreting the measured values of end-bearing may be attributed to misleading evaluation of closed and open-ended piles, as well as the insufficient displace-ments at the pile tip during load tests to mobilize full end-bearing resistance; • The proposed method shows no apparent bias of measured and predicted data with pile length (L), pile diameter (D), pile aspect ratio (L/D) and (more importantly) soil type. The principle of energy conservation combined to wave propagation analysis captures the influence of soil type.

Other Pile Types
The shaft friction and end-bearing resistance that can be developed on a pile are essentially related to the method of installation that dictates the magnitude of soil displacements and mobilized effective radial stresses. Embed on predicting the response of driven steel piles there is the assumption that q p and f l strongly correlates with F d (or N spt ) since the mechanism of penetration, the large mobilized displacements imparted during installation and the interface friction angle shown some degree of similarity. Therefore variations in pile capacity developed by concrete driven piles, bored piles and continuous flight auger piles cannot be assessed from the same penetration measurement (being a SPT, LPT or CPT).
Extension of the approach to pile types other than driven steel piles requires two empirical factors, one for a proper evaluation of mobilized shaft friction and another for mobilized end bearing resistance: where a and b are the pile type coefficients listed in Table 2 established from linear regression analysis (Lobo, 2005;Langone, 2012). Driven steel piles adopted as reference due to their similarity to SPT sampler penetration are represented by unitary values of a and b. Considering penetration restrain in hard layers and SPT reliability in case of discrete anomalies (localized high penetration values), the N spt was arbitrarily limited according to values listed in Ta       back-analysis of non-instrumented load tests (Lobo, 2007) and by the fact that the measured value may not truly represent the ultimate resistance given the large displacements required for full mobilization; • Bored piles mobilize the lowest a and b coefficients when compared to other pile types, due to stress relieving       induced by the excavation process. In average predicted skin friction underestimates measured values and tip resistance is scattered. Measured and predicted ultimate loads show good agreement; • Continuous flight auger piles, CFAP, produce an intermediate condition between driven and bored piles. Although the a value of steel and CFA piles is the same, it does not necessarily represent similar pile-soil friction, because the oversupply of concrete or grout, and the consequent increase in diameter of CFAP, is disregarded in the analysis. In general predicted skin friction underestimates measured values and tip resistance is scattered. The proposed method is slightly conservative yielding predicted ultimate loads lower than measured. In all predictions, the proposed method yields skin and tip resistance values within the range predicted by empirical methods classically adopted in Brazilian engineering practice. Predicted values generally lay around the best fit line for the predicted/measured pile capacities but, more importantly, for the database of instrumented load tests the method show the highest statistical probability of predicting values within 0.5Qult to 2Qult range. In addi-tion, it is stressed that there is room for reducing scatter of predicted axial bearing capacity in a rational approach by calibrating energy efficiency coefficients to local SPT configurations.

Conclusions
This paper describes a new method developed for predicting the axial bearing capacity of individual piles, showing the strong relationship between the applied energy to SPT penetration test, its dynamic force and the ultimate resistance of steel driven piles. The method relies on energy conservation principles, wave propagation analysis and a number of hypotheses regarding the penetration mechanism. The main conclusions that can be drawn from the current analysis are: • The method provides a valuable means of estimating the response of driven steel piles without having to rely on empirical statistical type of analysis; • The proposed method can be extended to precast concrete driven piles, bored piles and continuous flight au-    ger piles, but empirical coefficients are necessary to account for the method of installation; • Tthere appears to be room for reducing scatter of predicted axial bearing capacity by a proper calibration of energy efficiency coefficients representing the different configurations used in dynamic penetration tests; • The proposed method shows no apparent bias of measured and predicted data with soil type, pile length (L), pile diameter (D), pile aspect ratio (L/D). Clearly the principle of energy conservation combined to wave propagation analysis captures the influence of soil type on the predicted values of axial bearing capacity; These evidences and recommendations are supported by a final, overall picture given in Figs. 15 to 17, in which predicted/measured Q P , Q L and Q U pile capacity values for driven, bored and continuous flight auger piles are simultaneously compared. The comparison to other established methods demonstrate the capability of the proposed SPT method in predicting the bearing capacity of piles: the method has been fully tested and is ready to be used in daily foundation design. Soils