Strength assessment during shallow penetration of a sphere in clay

Transcription

1 Morton, J. P. et al. (24) Géotechnique Letters 4, , Strength assessment during shallo penetration of a sphere in clay J. P. MORTON*, C. D. O LOUGHLIN* and D. J. WHITE* Strength interpretation from the measured penetration resistance of full-flo penetrometers, such as the T-bar and ball, is generally based on a constant bearing capacity factor associated ith a deep flo-round mechanism. This approach may underestimate the strength of near-surface sediments, hich is becoming increasingly important for the design of offshore infrastructure such as pipelines, steel catenary risers and mudmats. This paper describes a series of centrifuge experiments designed to capture the change in the capacity factor of a ball penetrometer during shallo penetration. A rigorous consideration of soil buoyancy is provided. This is an important consideration in soils ith a higher strength to self-eight ratio because a cavity is formed by the passage of the ball and remains open to greater depths. The depth at hich a full-flo mechanism develops is related to the dimensionless strength ratio, expressed as the ratio of the undrained shear strength to the effective unit eight and penetrometer diameter. This observation forms the basis for proposed formulations that describe the evolution of the bearing capacity factor ith depth for different dimensionless strength ratios. These formulations can be used to determine more accurately the undrained shear strength of near-surface soil over the range of dimensionless strength ratios that is of interest to offshore applications. KEYWORDS: bearing capacity; centrifuge modelling; penetrometers; shear strength; site investigation ICE Publishing: all rights reserved NOTATION A s c v D F buoy F s H c k m N b N b-deep N b-shallo q b q m q net Q s s u u v op a c9 s v s9 v projected area of the sphere shaft area coefficient of vertical consolidation diameter of penetrometer soil buoyancy evolving soil resistance cavity depth undrained shear strength gradient plastic volumetric strain ratio bearing capacity factor deep bearing capacity factor shallo bearing capacity factor buoyancy resistance measured bearing pressure net penetration resistance soil resistance undrained shear strength hydrostatic pore pressure penetration rate ball invert depth normalised operative depth net area ratio of the load cell core to the shaft area effective unit eight of the soil overburden pressure vertical effective stress INTRODUCTION For a deeply embedded ball penetrometer, a full-flo mechanism that is symmetrical above and belo the ball is operative and the undrained shear strength, s u, can be interpreted from the measured bearing pressure, q m, Manuscript received 4 July 24; first decision 6 August 24; accepted 5 September 24. Published online at.geotechniqueletters.com on October 24. *Centre for Offshore Foundation Systems, University of Western Australia, Perth, WA, Australia according to s u 5q m /N b-deep. Hoever, at shallo penetration depths, a full-flo mechanism does not develop and s u should be interpreted from the measured penetration resistance using a bearing capacity factor N b-shallo,n b-deep. Adopting an appropriate N b-shallo, and accounting for its evolution to N b-deep ith depth, is an important aspect of quantifying s u over the upper 2 m of the seabed. This is critical for the design of almost all shalloly embedded offshore infrastructure (Puech et al., 2) including subsea pipelines, steel catenary risers and mudmats. Large-deformation finite-element (LDFE) analyses on a T-bar (White et al., 2; Tho et al., 22), spudcan (Hossain et al., 25) and ball penetrometer (Zhou et al., 23) have shon that the transition depth from N b-shallo to N b-deep is dependent on the dimensionless strength ratio s u /c9d, here c9 is the effective unit eight of the soil and D is the diameter of the penetrometer. Higher strength ratios are associated ith a delay in the transition to a steady N b-deep. Correlations for the transition depth and N b-shallo have been derived and, in the case of the T-bar and ball, a basis for correcting penetration data ithin the shallo zone has been proposed (White et al., 2; Zhou et al., 23). Hoever, from the perspective of a spherical penetrometer, hich is the focus of this paper, the range of strength ratios previously examined (s u /c9d52?95 44?25 (Zhou et al., 23)) is narroer than the range that is of practical interest for offshore problems. For example, a 25 mm diameter freefall spherical penetrometer (for measuring the strength of the seabed (Morton & O Loughlin, 22)) penetrating very soft soil is associated ith lo values of s u /c9d approaching? at one diameter embedment, hereas an 8 mm piezoball penetrating the seabed ith a crust strength of <2 kpa is associated ith high values of s u /c9d, approaching 4. The motivation for this study as to experimentally capture the variation in N b-shallo ith depth for a ball penetrometer embedding into clay over a ide range of s u /c9d. The experimental data are combined ith reinterpreted 262 Donloaded by [ University Of Western Australia] on [23//5]. Copyright ICE Publishing, all rights reserved.

2 Strength assessment during shallo penetration of a sphere in clay 263 LDFE results (Zhou et al., 23) and form the basis of a ne correlation that describes the evolution of N b ith depth. EXPERIMENTAL DETAILS The problem is addressed through centrifuge tests carried out at g in the University of Western Australia (UWA) beam centrifuge. The penetration resistance response and the degree of hole-closure ere analysed for nine penetrometer tests using a?3 mm diameter ball ith a 4?8 mm diameter shaft, penetrating a kaolin clay sample ith a progressively higher overconsolidation ratio (OCR). A constant penetration rate of mm/s as adopted such that the non-dimensional velocity vd/c v <3 (v is the penetration rate, D is the sphere diameter and c v is the coefficient of vertical consolidation <2?8 m 2 /year (Cocjin et al., 24)) and the response is primarily undrained (House et al., 2). A video recording observed the progressive hole-closure during each test and provided a means of determining the depth at hich the cavity, formed by the passage of the ball, closed over. The experimental arrangement is shon in Fig.. EXPERIMENTAL PROCEDURE Preparation of clay specimen The sample as prepared by mixing kaolin poder ith ater in a vacuum mixer at a moisture content equal to tice the liquid limit (2%). A drainage sand layer at the base of the sample alloed to-ay drainage during self-eight consolidation in the centrifuge at g, and vertical drains in the corners of the sample ensured there as no hydraulic gradient over the height of the sample. A nominal mm layer of free ater as maintained throughout testing. In order to investigate the range of s u /c9d of interest (spanning to orders of magnitude), the local s u as progressively increased by scraping a 2 mm layer of clay from the surface of the sample beteen each consecutive penetration test (see Fig. 2). This had the effect of increasing the OCR of the clay and increasing s u relative to the (ne) sample surface. Theoretical basis for interpretation of measured ball penetration resistance As the ball penetrates the soil, the measured bearing pressure q m includes the evolving soil resistance q s, expressed in terms of N b, and the resistance due to soil buoyancy, q b Fig. 2. A scraped soil sample before a test q m ~q s zq b ~N b s u z F buoy () here F buoy is the soil buoyancy force and is the projected area of the sphere. If the ball is deeply embedded such that the soil flos around the ball during penetration, the buoyancy force can be calculated from Archimedes principle; that is, the buoyancy force is the volume of the displaced soil multiplied by the effective unit eight of the soil, F buoy 5 (pd 3 /6)c9. Hoever, during initial penetration, the soil does not flo around the ball. Instead, a cavity is created above the ball and the soil that ould have filled this void is instead accommodated by heave at the soil surface. To capture this heave effect, a simple multiplier can be applied on F buoy, as proposed previously for the penetration of cylindrical and spherical geometries (e.g. Merifield et al., 29; White et al., 2; Chatterjee et al., 22; Zhou et al., 23). An alternative approach to derive this multiplier directly, is to consider the ork required to lift the soil that is displaced by the incrementally advancing ball. This can be done by assuming a cavity geometry formed by the advancing ball, hich is approximated here as an inverted cone for all considered values of s u /c9d, prompted by camera observations (e.g. see Fig. 3) and supported by LDFE simulations (Zhou et al., 23). At a ball invert depth of #?5D (Fig. 4(a)), all of the soil displaced by the advancing ball is lifted to the soil surface. The ork done then becomes the eight of the Actuator Ball penetrometer Camera Water Kaolin clay Sand Fig.. Experimental arrangement in the beam centrifuge Donloaded by [ University Of Western Australia] on [23//5]. Copyright ICE Publishing, all rights reserved.

3 264 Morton, O Loughlin and White s u, q net /N b-deep : kpa q net 2 N b-deep Normalised depth, ŵ op + DZ scrape s u Transition points Fig. 3. Ball penetrometer and cavity after a penetration test 8 2 Base sand drainage layer displaced soil multiplied by the distance beteen the centroidal height of the embedded ball (a spherical cap) and the soil surface. For?5D. # H c + D, here H c is the cavity depth, only some of the soil displaced by the advancing ball is lifted to the surface. The remainder fills part of the cavity created by the increment of ball penetration, as shon in Fig. 4(b). In this case, the ork done is calculated by adding the gain in potential energy by these to separate elements of soil, resulting in the profile of soil buoyancy ith embedment given in Fig. 4(c). The net penetration resistance q net can be calculated using the measured resistance q m from equation () by correcting for the unequal pore pressure and overburden pressure effects due to the shaft behind the ball (Chung & Randolph, 24) q net ~q m {½s v {u ({a)š A s (2) here s v is the overburden pressure, u is the hydrostatic pore pressure, A s is the shaft area and the parameter a is the net area ratio of the load cell core to the shaft area (a 5?8 for the tests considered here). For a deeply embedded ball, q net and hence the inferred s u corresponds to the mid-height of the ball due to the depth symmetry of the flo-round mechanism. For a shalloly embedded ball, here the full-flo mechanism is not fully developed, the normalised operative depth ^ op is assumed to vary linearly up to the depth here a full floround mechanism occurs, in a similar manner to that Fig. 5. Comparison of strength profiles of Ladd et al. (977) and q net /N b-deep profiles proposed for a shalloly embedded T-bar (White et al., 2) ^ op ~ D {: 5 H c zd D {: 5 (3) Omitted from the above theoretical frameork is any consideration of ho N b evolves during shallo to deep penetration. This has been purposely excluded from the preceding discussion and ill be formulated later in the paper to reflect the experimental results presented in the folloing section. RESULTS AND COMPARISONS In-flight video camera observations The camera as synchronised ith the data acquisition system such that visual observations could be relayed to the measured penetration response. For loer values of s u /c9d, here the open cavity depth as loer and could be captured by the camera, the instances hen soil floed over the ball ere consistent ith the transitional depths inferred from the penetration profiles shon in Fig. 5 (and discussed in the next section). This observation is at variance ith the LDFE results reported by Zhou et al. (23), hich indicate that more penetration is required to establish a deep failure mechanism after full flo of soil over the top of the ball. Change in elevation of soil mass centroid F buoy /c'd Soil flo to surface Displaced soil Partial soil flo D' Soil surface H c Normalised invert depth, /D (a) Displaced soil (b) 3. (c) Fig. 4. Schematic illustration of soil buoyancy due to (a) the sphere and (b) the sphere and conical cavity. (c) Buoyancy function for a typical cavity depth Donloaded by [ University Of Western Australia] on [23//5]. Copyright ICE Publishing, all rights reserved.

4 Strength assessment during shallo penetration of a sphere in clay here s v is the current vertical effective stress, determined from the c9 profile ith depth and the varying acceleration level ithin the centrifuge (93g to 5g over the depth of penetration), and m is the plastic volumetric strain ratio (Schofield & Wroth, 968). The normally consolidated undrained strength ratio (su =s v )nc 5?3, as determined from ball penetrometer tests before scraping the soil surface (i.e. OCR5) using the commonly adopted Nb-deep5?5 (Chung & Randolph, 24). The ratio (su =s v )nc increases to?5 if the measured resistance (hich ignores shaft effects) is considered, similar to (su =s v )nc 5?6 reported by Richardson et al. (29) and Hu et al. (24), and equivalent to an undrained strength gradient ith prototype depth, k5 kpa/m, hich is typical for UWA kaolin. The best agreement beteen equation (4) and the experimental qnet/nb-deep profiles in the overconsolidated samples as obtained using m5 (rather than the commonly reported m5?8), hich reflects the minimal selling time permitted beteen each soil scrape and the subsequent penetration test. Deep mechanism transition depth ^ deep-op are also shon The normalised transition depths in Fig. 5, and ere selected as the depths here the qnet/nb-deep experimental data ere judged to have reached su predicted using equation (4). The final to profiles do not reach the predicted su profile due to the proximity of ^ deep-op are approximated the base drainage sand layer and in these instances on the basis of the Nb variation ith ^ deep-op are also shon in depth, discussed later. Values of Fig. 6 alongside previously reported T-bar (White et al., 2), spudcan (Hossain et al., 25) and ball (Zhou et al., 23) data, but reinterpreted to account for the definition of operative depth adopted here. Further reinterpretation of the ball data of Zhou et al. (23) as made to ascertain ^ deep-op assessed as hen Nb became effectively constant (to ithin,5% of the final value) rather than reaching the limit, hich is difficult to judge and is approached asymptotically. The experimental ball data reported here, together ith the reinterpreted Zhou et al. (23) ball data, no form a unique ^ deep-op and su/c9d for a ball penetrelationship beteen ^ deep-op ), rometer (here su is the undrained strength at hich can be described using c d{a ^ deep-op ~az b su z (5) cd z½(su =c D)=e f Present study Zhou et al. (23), Ball reinterpreted Normalised transition depth, ŵdeep-op Undrained shear strength profiles As discussed earlier, the OCR of the sample as incrementally increased by scraping an additional 2 mm from the sample surface beteen penetration tests. The strength of the sample can then be assumed to vary ith depth according to equation (4), proposed by Ladd et al. (977) su su ~s v OCRm (4) s v nc White et al. (2), T-bar Hossain et al. (25), Spudcan Equation (5)... Normalised strength, su/c'd Fig. 6. Effect of strength ratio su/c9d on transition depth here the fitting constants a56?3, b5?2, c5?3, d5?52, e54?9 and f5?5. Shallo bearing capacity factors Figure 7 shos the experimental variation in Nb ith depth for each penetration test, obtained by dividing qnet by su from equation (4). Each Nb profile follos the same trend, commencing at zero at the soil surface and reaching a steady Nb-deep at the transition depth, hich is entirely dependent on su/c9d. This variation in Nb ith depth can be fitted using equation (6) (also shon on Fig. 7)!p ^ op Nb-shallo ~Nb-deep (6) ^ deep-op and p~:49 su c D {: (7) Nb Normalised operative depth, ŵop During shallo penetration, little or no heave as observed on the soil surface, particularly for tests ith higher values of su/c9d. This is considered to be due to the axisymmetric flo mechanism of the ball, hich reduces the heave compared ith plane strain flo for a cylindrical T-bar or pipeline (Stanier & White, 24). In light of this observation, enhancement of Fbuoy in equation () to account for heave of the soil surface, as considered by Merifield et al. (29), Randolph & White (28) and Stanier & White (24), as not included Equation (6) 3 Nb variation 4 Transition points 5 6 Fig. 7. Measured variation in normalised bearing factor ith normalised embedment depth and equation fit Donloaded by [ University Of Western Australia] on [23//5]. Copyright ICE Publishing, all rights reserved.

5 266 Morton, O Loughlin and White CONCLUSIONS This paper reports on centrifuge tests in hich a ball as penetrated into clay under undrained conditions over s u /c9d5?7 to 2?7 (at the transition depth). The depth at hich an open cavity, formed by the passage of the ball, closed over is considered to indicate the transitional depth ^ deep-op here a full flo-round mechanism develops. A novel analytical solution for the soil buoyancy in the case of an open conical hole has been developed. This rigorous approach is necessary to avoid significant errors in the determination of strength during shallo penetration in soils ith a lo strength to self-eight ratio. For instance, in a clay ith zero mudline strength and an undrained shear strength ratio of s u =s v 5?25, the buoyancy resistance increases to almost 7% of the geotechnical resistance during shallo penetration, and is independent of the penetrometer diameter at all penetration depths. Data from centrifuge experiments, combined ith reinterpreted data from LDFE analyses, sho a unique relationship beteen ^ deep-op and s u /c9d examined over the range s u /c9d<? to 4. Equations that describe the change in ^ deep-op and the capacity factor N b ith s u /c9d are proposed. These equations offer a more rigorous and reliable means of assessing soil strength in the upper fe metres of the seabed. Acknoledgements This ork forms part of the activities of the Centre for Offshore Foundation Systems (COFS), currently supported as a node of the Australian Research Council Centre of Excellence for Geotechnical Science and Engineering and as a Centre of Excellence by the Lloyd s Register Foundation. The Lloyd s Register Foundation invests in science, engineering and technology for public benefit, orldide. REFERENCES Chatterjee, S., Randolph, M. F. & White, D. J. (22). The effects of penetration rate and strain softening on the vertical penetration resistance of seabed pipelines. Géotechnique 62, No. 7, Chung, S. F. & Randolph, M. F. (24). Penetration resistance in soft clay for different shaped penetrometers. Proc. 2nd Int. Conf. on Site Characterisation, Porto 2, No., Cocjin, M. J., Gourvenec, S. M., White, D. J. & Randolph, M. F. (24). Tolerably mobile subsea foundations observations of performance. Géotechnique, in press. Hossain, M. S., Hu, Y., Randolph, M. F. & White, D. J. (25). Limiting cavity depth for spudcan foundations penetrating clay. Géotechnique 55, No. 9, House, A. R., Oliveria, J. R. M. S. & Randolph, M. F. (2). Evaluating the coefficient of consolidation using penetration tests. Int. J. Phys. Model. Geotech., No. 3, Hu, P., Stainer, S. A., Cassidy, M. J. & Wang, D. (24). Predicting peak resistance of spudcan penetrating sand overlying clay. J. Geotech. Geoenviron. Engng ASCE 4, No Ladd, C. C., Foot, R., Ishihara, K., Schlosser, F. & Poulos, H. G. (977). Stress deformation and strength characteristics. Proc. 9th Int. Conf. Soil Mech. Found. Engng, Tokyo 2, Merifield, R., White, D. J. & Randolph, M. F. (29). The effect of surface heave on the response of partially-embedded pipelines on clay. J. Geotech. Geoenviron. Engng ASCE 35, No. 6, Morton, J. P. & O Loughlin, C. D. (22). Dynamic penetration of a sphere in clay. Proc. 7th Int. Conf. on Offshore Site Investigation and Geotechnics, London 7, Puech, A., Orozco-Calderón, M. & Foray, P. (2). Mini T-bar testing at shallo penetration. Proc. Frontiers in Offshore Geotechnics, Perth, Randolph, M. F. & White, D. J. (28). Pipeline embedment in deep ater: processes and quantitative assessment. Proc. Offshore Tech. Conf., Houston, 6. Richardson, M. D., O Loughlin, C. D., Randolph, M. F. & Gaudin, C. (29). Setup folloing installation of dynamic anchors in normally consolidated clay. J. Geotech. Geoenviron. Engng ASCE 35, No. 4, Schofield, A. N. & Wroth, C. P. (968). Critical state soil mechanics. London: McGra-Hill. Stanier, S. A. & White, D. J. (24). Shallo penetrometer penetration resistance. J. Geotech. Geoenviron. Engng ASCE, in press. Tho, K. K., Leung, C. F., Cho, Y. K. & Palmer, A. C. (22). Deep cavity flo mechanism of pipe penetration in clay. Can. Geotech. J. 49, No., White, D. J., Gaudin, C., Boylan, N. & Zhou, H. (2). Interpretation of T-bar penetrometer tests at shallo embedment and in very soft soil. Can. Geotech. J. 47, No. 2, Zhou, H., Hossain, M. S., Hu, Y. & Liu, H. (23). Behaviour of a ball penetrometer in uniform single and double layer clays. Géotechnique 63, No. 8, WHAT DO YOU THINK? To discuss this paper, please up to 5 ords to the editor at journals@ice.org.uk. Your contribution ill be forarded to the author(s) for a reply and, if considered appropriate by the editorial panel, ill be published as a discussion. Donloaded by [ University Of Western Australia] on [23//5]. Copyright ICE Publishing, all rights reserved.