An experimental investigation of soil arching within basal reinforced and unreinforced piled embankments

Geotextiles and Geomembranes (00) 7 www.elsevier.com/locate/geotexmem An experimental investigation of soil arching within basal reinforced and unreinforced piled embankments Chen Yun-min, Cao Wei-ping, Chen Ren-peng Department of Civil Engineering, Institute of Geotechnical Engineering, Zhejiang University, ] Zheda Road, Hangzhou 007, PR China Received September 00; received in revised form May 007; accepted 7 May 007 Available online 9 July 007 Abstract Geotechnical engineers face several challenges when constructing embankments over soft soils. These include potential bearing failure, intolerable settlement, and global or local instability. Piled embankments provide an economic and effective method to construct roads on soft soils. Soil arching developed within such embankments has significant influence on its behavior. A total of model tests were conducted to evaluate the effects of pile subsoil relative displacement, embankment height, cap beam width and clear spacing, and geosynthetics with different tensile strengths on stress concentration ratios and settlements in the embankments. The test results indicate that stress concentration ratio varies with pile subsoil relative displacement and has upper and lower bounds. A higher ratio of embankment height to cap beam clear spacing, as well as a higher ratio of cap beam width to clear spacing, would result in a higher stress concentration ratio. The inclusion of a geosynthetic membrane can increase the stress concentration ratio. When the embankment height to the cap beam clear spacing ratio, h/s, is less than., apparent differential settlements may occur on the surface of embankment. When h/s is greater than., however, no apparent differential settlements will occur on the embankment surface. In addition, experimental results were also compared to several current design methods. r 007 Elsevier Ltd. All rights reserved. Keywords: Piled embankments; Model test; Soil arching; Stress concentration ratio; Settlements. Introduction Piled embankments are increasingly used to construct highways on soft soils due to their rapid construction, low costs, and small total and differential settlements compared to the traditional soft soils improvement methods such as preloading, vertical drains or grouting injection (Magnan, 99; Shen et al., 00). The interactions among embankment fill, geosynthetic reinforcement, pile (cap) and foundation soil are complex and can be schematically described as shown in Fig.. Since compression stiffness of the pile is greater than that of the foundation soil, the embankment fill mass directly above the foundation soil has a tendency to move downward. This movement is partially restrained by shear stress, t, from the embankment fill mass directly above the pile cap. The shear stress Corresponding author. Tel.: + 7 797; fax: + 7 799. E-mail address: caowp@zju.edu.cn (C. Wei-ping). increases the pressure acting on the pile cap but reduces the pressure on the foundation soil. This load transfer mechanism was termed the soil arching effect by Terzaghi (9). The inclusion of geosynthetic reinforcements complicates the load transfer mechanism. The soil arching has a significant influence on the behavior of piled embankments. Stress concentration ratio, n, is an important parameter to assess the degree of soil arching and is defined by Han and Gabr (00) as follows: n ¼ s p, () s s where s p is the applied pressure on the pile cap and s s is the average pressure applied on the foundation soil. n ¼ represents no soil arching. The greater the value of n, the higher the degree of soil arching. If the degree of soil arching is not sufficient, too much embankment load will be born by the foundation soil and the pile subsoil relative displacement, Ds (Fig. ) will be reflected to the top of the embankment and an unacceptable differential settlement 0-/$ - see front matter r 007 Elsevier Ltd. All rights reserved. doi:0.0/j.geotexmem.007.0.00

C. Yun-min et al. / Geotextiles and Geomembranes (00) 7 Nomenclature a c arching coefficient b cap beam width c cohesive strength of embankment fill C c coefficient of curvature G specific gravity h embankment height h c embankment critical height h e equal settlement plane height K empirical constant in Terzaghi s trench model K p ¼ðþsin fþ=ð sin fþ n stress concentration ratio geosynthetic reinforcement tensile strength T g s cap beam clear spacing a coefficient of distribution uniformity of soil pressure on the foundation soil s p vertical soil pressure applied on pile cap s s vertical soil pressure applied on soft soils s r radial stress in sand arch s y tangential stress in sand arch g unit weight of embankment fill t shear stress d ¼ b=ðs þ bþ f internal friction angle of embankment fill f max peak secant angle of shearing resistance Ds pile subsoil relative displacement Ds c critical pile subsoil relative displacement may occur, which would harm normal function and durability of the embankment. However, too large value of the stress concentration ratio, n, implies that nearly all the embankment load will be born by the piles and high costs. Consequently, a thorough understanding of soil arching mechanism within piled embankments is essential for engineering design. A number of research studies associated with this subject have been performed in the past two decades. Hewlett and Randolph (9) conducted D model tests and presented a semi-spherical model to describe soil arching, but the effects of geosynthetic reinforcement and pile subsoil relative displacement on soil arching were not considered. Low et al. (99) undertook D model tests to evaluate soil arching. However, the settlements in the embankment and the influence of geosynthetic reinforcements with different tensile strengths on soil arching were not considered. In addition, pile subsoil relative displacement was not taken into account. Chen et al. (00) improved the semispherical model initiated by Hewlett and Randolph (9), but the effect of geosynthetic reinforcement was not evaluated. Marston s formula is applied to estimate the load on the pile cap in the British Standard BS00 (99), but the soil resistance below the reinforcement is ignored. Moreover, the embankment fill material properties are not considered. Han and Gabr (00) and Pham et al. (00) conducted numerical analyses on the embankments. Fig.. Soil arching in piled embankments. Nevertheless, the conclusions on the effect of geosynthetic reinforcement drawn from these numerical analyses are inconsistent. Existing methods for determining the magnitude of arching in piled embankments yield very different results (Russell and Pierpoint, 997; Naughton and Kempton, 00; Stewart and Filz, 00). Moreover, no design methods are available to estimate the total and the differential settlements of the embankments, and a wellaccepted design method is absent. Gabr and Han (00) argued that the effects of soil arching developed in the embankment remained poorly understood, current design methods for such system have not been well verified and that further studies must be performed. In this study, a total of model tests were conducted to evaluate the effects of pile subsoil relative displacement, embankment height, cap beam width and clear spacing, and geosynthetic reinforcements with different tensile strengths on stress concentration ratio and settlements in such embankments. In addition, experimental results have been compared to the predictions of several design methods.. Model tests.. Model test set-up Model test system consisted of a bricked base, two rubber water bags and a tank. Toughened glass was used for the four walls of the tank to allow observation. The system was 00 mm long, 000 mm wide and 0 mm high as shown in Fig.. The base was 0 mm high. The two side walls and the middle wall of the base were used to represent the cap beams. The two water bags, measuring 000 mm long, 00 mm wide and 0 mm high, were placed inside the base and filled with water. On top of that, an embankment of sand was added and water in the two water bags was permitted to flow out gradually under control causing the upper surface of water bags to descend and model the consolidation of foundation soil.

ARTICLE IN PRESS C. Yun-min et al. / Geotextiles and Geomembranes (00) 7 strengths on stress concentration ratio, the settlement of the embankments with a relatively low height and that of the one with relatively high height. Tests, and formed a series to investigate the effects of the cap beam width on stress concentration ratio and settlement of embankment with a relatively low height and without reinforcement... Material properties The sand used in the model tests came from Qiantang River Beach, China. The specific gravity G ¼., the coefficient of uniformity C u ¼. and the coefficient of curvature C c ¼ 0.9. Other characteristics were D 0 ¼ 0. mm, D 0 ¼ 0. mm, D max ¼ mm, e max ¼ 0.9 and e min ¼ 0.. Sand grains were subangular and predominantly quartz. The unit weight of the fill in the tank was.. kn/m and corresponded to a relative density of 77%. At a relative density of %, the peak secant angle of shearing resistance, f max, was found from triaxial tests to be at a confining pressure equal to 0 kpa, and at a confining pressure of 0 kpa. Following the recommendations of Bolton (9), a value of f max ¼ was used in the analyses of results. Three types of geosynthetic reinforcements were used in the model tests with biaxial tensile strengths 0.,.0 and. kn/m at % axial strain... Model test procedure Fig.. Layout of test set-up (unit: mm): (a) top view and (b) side view. The test set-up had two major advantages: () During the embankment sand filling, no water in the two water bags was released and no consolidation occurred in the foundation soil at this stage. () As soon as the water in the two water bags was discharged, consolidation begins but the consolidating process is much quicker than that of real soils and the test can be completed within a short time... Program of experiments The experimental program is detailed in Table. A preliminary investigation into the influence of the embankment height on stress concentration ratio, n, and settlement of the embankment without geosynthetic reinforcement was based on Tests 7. Tests 0 and Tests were performed to examine, respectively, the effect of geosynthetic reinforcement with different tensile After installation of the test set-up and filling water into the two bags so that the top surface of the water bag was in level with the top of the cap beams, seven soil stress transducers (SSTs) were placed on the top of water bags and the middle cap beam as shown in Fig. (a). According to Eq. (), the stress concentration ratio, n, is the ratio of pressure of SST to the average pressure of the others. In the case of Tests 0 and Tests, after installation of SSTs, geosynthetic reinforcement was laid across the two water bags and the middle cap beam and fixed on the top of the two side cap beams. In Tests and, prior to placing the SSTs, toughened glass plates, 990 mm long and mm thick, with width of 0 mm (for Test ) or 0 mm (for Test ), 90 mm (for Test ) or mm (for Test ) were fixed on the top of the middle cap beam and the two side cap beams, respectively. A layer of sand mm thick was then poured on the top of the water bags and leveled with the top of the toughened glass plates. SSTs were placed as shown in Fig. (a). Dry sand was poured evenly on the cap beams and the two water bags in the tank by using a funnel modified from a metal pail. The funnel had an outlet fitted with a plastic hose with a net diameter of 00 mm. The funnel was inverted by a crane so that the outlet of the hose was pointing downwards and the distance between the point where the sand was discharged and the sand surface was 00 mm throughout the tests. For each 00 mm increment

C. Yun-min et al. / Geotextiles and Geomembranes (00) 7 7 Table Experiment details Test no. Embankment height h (mm) Width of middle cap beam a b (mm) Cap beam clear spacing s (mm) Geosynthetic tensile strength T g (kn/m) Notes 0 0 00 h/s ¼ 0.7 0 0 00 h/s ¼ 0.9 70 0 00 h/s ¼. 0 0 00 h/s ¼. 90 0 00 h/s ¼. 00 0 00 h/s ¼. 7 00 0 00 h/s ¼.0 0 0 00 0. h/s ¼ 0.7 9 0 0 00. h/s ¼ 0.7 0 0 0 00. h/s ¼ 0.7 00 0 00 0. h/s ¼. 00 0 00. h/s ¼. 00 0 00. h/s ¼. 0 0 70 b/s ¼ /. 0 0 00 b/s ¼ / a The width of the side cap beam is half the middle cap beam width. in layer thickness, the sand surface was leveled and the height of sand and SSTs readings were recorded. The unit weight of the sand fill was.. kn/m in the tests. Along the observation wall, a strip of paper 00 mm long and 00 mm wide was laid on the top of each layer of sand, the paper had almost no tensile strength to avoid influencing sand behavoir. Marks were made on the outer side of the observation wall at the height of each layer of paper to observe the settlements of the fill. After completion of the embankment filling, an equal amount of water in the two water bags was discharged simultaneously and at the same rate. The settlements and SSTs readings were recorded h after each time the water was discharged. For each of the tests, the same process was repeated times. The test set-up had a D symmetry and the experiments in the study were designed to simulate plane soil arching in the embankments. Along the length direction of the water bags, four rigid iron strips measuring 90 mm in length, 0 mm in width, and. mm in thickness were affixed on the top of each water bag and spaced at 00 mm centers to ensure that deformation of the top surface of the water bag was similar to that of a single-direction slab rather than that of a two-direction slab under transverse loading. After each water discharge, the settlement of the top surface of the water bags in the mid-span over their width was equivalent to the pile subsoil relative displacement, Ds. Wall friction could influence the test results. Low et al. (99) used Perspex for the two long walls of the tank in their experiments, and a wall friction of 0. kpa was calculated. Compared to toughened glass, Perspex is soft and flexible and has a greater wall friction compared with that of toughened glass used in the study, which was determined to be 0.0 kpa. In view of the low value of wall friction, this effect was ignored in this series of tests. As the principles of similarity between the physical model and prototype were not strictly maintained, the results obtained from the model tests are more qualitative than quantitative and cannot be directly extrapolated to real embankments, but they are useful to gain a better understanding of the mechanism of soil arching in embankments and can be used to verify the validity of current design methods (James, 97).. Test results.. Soil pressures on the soft soils and cap beam The variation of soil pressure showed nearly identical characteristics in all tests, and only the results of Test 7 are presented herein (Fig. ). As shown in Fig. (a), the increase in soil pressure is almost linear during embankment filling. When the embankment height was less than 00 mm, all soil pressure readings were nearly the same. Beyond 00 mm high, soil pressure on the cap beam was greater than that on soft soils. Soil pressure on the cap beam reached 0. kpa at height 00 mm, while the maximum soil pressure on soft soils was 7. kpa. This implies that soil arching occurred during embankment filling. Fig. (a) also shows that soil pressures on soft soils were not uniformly distributed. Fig. (b) shows the variation of soil pressures during the process of water discharge from water bags. With an increase in the pile subsoil relative displacement, Ds, the soil pressure increased on the cap beam and decreased on soft soils. When the pile subsoil relative displacement, Ds, was about mm, pressure on the cap beam and soft soils reach a maximum value of.97 kpa and a minimum average value of. kpa, respectively. Then, with a continuous increase in pile subsoil relative displacement, Ds, soil pressure on the cap beam decreases gradually and

ARTICLE IN PRESS C. Yun-min et al. / Geotextiles and Geomembranes (00) 7 Soil Pressure (kpa) 0 0 0 SST SST SST SST SSTa SSTa SSTa 0 h/s=0.7 h/s=. h/s=. h/s=.0 h/s=0.9 h/s=. h/s=. Soil Pressure (kpa) 0 0 00 00 00 00 000 00 70 0 0 0 0 0 0 Embankment Height (mm) SST SST SST SST SSTa SSTa SSTa 0 Fig.. The variation of soil pressures (Test 7): (a) during embankment filling and (b) during water discharge. reaches a relatively constant value of.0 kpa after DsX mm. Meanwhile the pressures on the soft soils increase and attain a constant average value of 7. kpa... The influence of embankment height on stress concentration ratio and settlements Fig. shows the results of Tests 7. It is observed that, for different magnitudes of embankment height to cap beam clear spacing ratio, h/s, the stress concentration ratio versus pile subsoil relative displacement had the same characteristics. With an increase in pile subsoil relative displacement, Ds, stress concentration ratio increased and reached a maximum value, then decreased gradually and maintained nearly a constant value. The larger the ratio h/s, the higher the stress concentration ratio, and the greater the difference between the maximum value and constant value. Han and Gabr (00) and Murugesan and Rajagopal (00) reported that a higher embankment Fig.. Influence of embankment h/s ratio on stress concentration ratio. height would result in a higher stress concentration ratio. Results from current investigations are in close agreement with their observations. A higher value of stress concentration ratio indicates that a higher percentage of the embankment load is transferred to cap beams. Fig. also shows that soil arching is strongly dependent on pile subsoil relative displacement, and there exists a critical relative displacement, Ds c (Ds c ¼ mm), at which the soil arching developed most effectively and beyond which there may be less effective arching. In other words, the stress concentration ratio has upper and lower bounds. In Tests, when h/sp., it was observed that the surface of the embankments was non-uniform implying differential settlement occurred on the top of the embankments. Fig. (a) shows the settlement of the embankment for Test when pile soil relative displacement Ds ¼ mm. As can be seen, at height 00 mm, the maximum differential settlement was mm, and the maximum differential settlement at the top of the embankment was mm. This is the coupled effects of soil arching and the compression of the embankment fill. When h/sp., the embankment height was relatively low and no completed soil arch was formed and the pile subsoil relative displacement, Ds, was reflected on the surface of the embankment, and differential settlement occurred. In Tests 7, when h/sx., the settlements in the lower part of the embankment were non-uniform, but the embankment surface remained almost horizontal. Fig. (b) shows the settlements of the embankment for Test 7 when the pile subsoil relative displacement Ds ¼ mm. As can be seen, at height 00 mm, the maximum differential settlement was mm, but the differential settlement on the top of the embankment was only mm. This is because, when h/sx., embankment height was relatively high, a completed soil arch was formed and an equal settlement plane existed and pile subsoil relative displacement, Ds, was restrained below the equal settlement

C. Yun-min et al. / Geotextiles and Geomembranes (00) 7 9 Embankment Height (mm) Embankment Height (mm) 00 00 00 00 0 00 000 00 00 00 7mm mm mm mm mm 0mm Water Bag Water Bag Side Cap-beam Middle Cap-beam Side Cap-beam 9mm 9mm 9mm mm 0mm 0mm mm 9mm mm 7mm 00 mm mm 0 Water Bag Water Bag Side Cap-beam Middle Cap-beam Side Cap-beam Fig.. Pictures of deformed embankments (not to scale): (a) Test and (b) Test 7. plane. As a result, no apparent differential settlement occurred on the embankment surface. Deformations in embankments of Tests 7 also suggest that the height of the equal settlement plane, h e, is about.. times the cap beam clear spacing, i.e., h e ¼ (..)s. To ensure that no differential settlement occurs on the embankment surface, a minimum embankment height of.s is necessary... The influence of geosynthetic reinforcements on stress concentration ratio and settlements The influence of geosynthetic reinforcements with different tensile strengths on stress concentration ratio is shown in Fig. (a) for the case of low embankment height. Compared to Test, the inclusion of reinforcement can improve the stress concentration ratio, but when the reinforcement tensile strength was low as in Test, the effect was not significant. When the reinforcement with a high tensile strength was used as in Tests 9 and 0, the effect was significant. Fig. (b) presents the results of Test and Tests, showing the influence of geosynthetic reinforcement on stress concentration ratio in the case of an embankment with a relatively high height (h/s ¼..). Although the relationship of stress concentration ratio versus pile subsoil relative displacement exhibits similar characteristics to that in Tests 0, the difference is apparent. For the same reinforcement, the effect for improving the stress Test TesT Test9 Test0 0 Test Test Test Test Pile-subsoil Relative Displacement(mm) Fig.. Influence of geosynthetic reinforcement tensile strength on stress concentration ratio: (a) for h/s ¼ 0.7 and (b) for h/s ¼.. concentration ratio in embankments with different heights is different. In the case of h/s ¼ 0.7, the inclusion of a reinforcement with a tensile strength of. kn/m can increase the maximum stress concentration ratio from. (Test ) to.9 (Test 0), equivalent to 9%. However, with the same reinforcement as used for the case of h/s ¼., the maximum stress concentration ratio was increased from 7. (Test ) to. (Test ), an increase of %. This suggests that the use of geosynthetic reinforcement to improve the stress concentration ratio is more significant for embankments with a relatively high height than for embankments with a relatively low height. The influence of geosynthetic reinforcements with different tensile strengths on the settlements when pile subsoil relative displacement Ds ¼ mm, is shown in Table. It can be seen that irrespective of embankment height, the inclusion of reinforcement can reduce the maximum settlement and the maximum differential settlement, but

70 C. Yun-min et al. / Geotextiles and Geomembranes (00) 7 Table Influence of geosynthetic reinforcement tensile strength on embankment settlement Test no. 9 0 Geosynthetic tensile strength (kn/m) 0... 0... Maximum settlement (mm) 7 9 Maximum differential settlement (mm) 9 o o o o the effect is more pronounced for the case of h/s ¼ 0.7, than for the case of h/s ¼.. As Collin et al. (99) and Hufenus et al. (00) have suggested, reinforcement effects depend on tensile strength and degree of lateral anchoring of the reinforcement. The two lateral sides of the reinforcement in these tests were fixed on the side cap beams, so the effects of improvement of stress concentration ratio and reduction in differential settlements could be over-predicted compared with real embankments in which fully lateral anchoring of the reinforcement is not possible... The influence of cap beam width on stress concentration ratio and settlements Fig. 7 shows the results of Tests, and. It is observed that the larger the ratio of cap beam width to clear spacing, the higher the stress concentration ratio. At a cap beam width to clear spacing ratio of / (Test), the maximum stress concentration ratio was., and at a cap beam width to clear spacing ratio of /. (Test ) and / (Test ), the maximum stress concentration ratio was increased to.7 and., respectively. Jones et al. (990) reported similar findings for stress concentration ratio. The influence of the ratio of the cap beam width to clear spacing on the settlements is shown in Table. As can be seen, the larger the ratio, the smaller the differential and the total settlement. It seems that the reduction effect is more significant on the differential settlement than on the total settlement. When increasing the cap beam width to clear spacing ratio from / to /, the maximum settlement was reduced from 7 to mm, equivalent to %. Meanwhile, the maximum differential settlement was reduced from to mm, equivalent to %. For a given embankment height, increasing the cap beam width to clear spacing ratio, which means soil arch in the embankment has a tendency to transform from an incomplete to a full condition with an inevitable decrease of differential settlement.. Several current design methods of stress concentration ratio.. Method of Low et al. (99) Low et al. (99) improved the calculation method of soil arching based on semi-spherical crown model Test Test Test Pile-subsoil Relative Displcement (mm) Fig. 7. Influence of cap beam width on stress concentration ratio. Table Influence of cap beam width on embankment settlement Test no. Cap beam width to clear spacing ratio / /. / Maximum settlement (mm) 7 7 Maximum differential settlement (mm) introduced by Hewlett and Randolph (9). The main points are reproduced here. A plane semi-cylindrical sand arch with a thickness equal to half the width of the cap beam is assumed in the embankment fill as depicted in Fig.. Low et al. (99) argued that the sand element critical state would be reached at the crown of the arch or just above the cap beam. The radial equilibrium of an element in the crown of the arch requires ds r dr þ s r s y ¼ g, () r where s r is the radial stress, s y the tangential stress, r the radial distance and g the embankment fill unit weight. s y ¼ K p s r, K p ¼ðþsin fþ=ð sin fþ,andfthe sand fill friction angle.

C. Yun-min et al. / Geotextiles and Geomembranes (00) 7 7 Fig. 9. Trench model for soil arching (Terzaghi, 9). Considering the boundary condition at the top of the crown (r ¼ (s/b)/ s r ¼ g(h (s+b)/)), Eq. () can be solved and soil pressure on the foundation soil s s can be expressed as follows: s s ¼ ag ðk p Þð dþðs þ bþ ðk p Þ þð dþ Kp h s þ b s þ b ðk p Þ, ðþ where d ¼ b/(s+b), a is the coefficient of distribution uniformity of soil pressure on the foundation soil and can be taken as 0. in the following calculation as Low et al. (99) recommended. So the soil pressure on the cap beam s p is given by s p ¼ ðs þ bþhg s ss. () b Then, stress concentration ratio can be obtained easily by n ¼ s p /s s. For the sand element just above the cap beam, another stress concentration ratio can be obtained by using a similar procedure and the minor stress concentration ratio is the real one... Method of Terzaghi (9) Terzaghi (9) proposed an analytical solution based on the famous Trap door experiment. He assumed that two vertical shear planes and as shown in Fig. 9 occurred in the soil as the Trap door descended slightly and the shear stress applied on the soil mass directly above the Trap door by the adjoining stationary soil mass decreases the soil pressure on the Trap door and increases the pressure on the adjoining stationary soil mass. The force equilibrium in the vertical direction for the infinitesimal slice of thickness dz is ds v dz Fig.. Semi-cylindrical arch in embankment (Low et al., 99). tan f þ K s v ¼ g, () s where g is the embankment fill unit weight, f the fill friction angle and K the empirical constant and can be taken as 0.7 according to Terzaghi (9). Solving the linear differential equation and imposing the boundary condition that s v ¼ 0atz¼0, one obtains the average pressure on the trap door s vh ¼ s v j z¼h ¼ sg K tan f tan f e Kðh=sÞ. () The descent of the Trap door is similar to the settlement of foundation soil, and the pressure on the Trap door is similar to the soil pressure on foundation soil. Consequently, soil pressure on the cap beam is given by s p ¼ hðs þ bþg s vhs, (7) b where h is the embankment height and b the cap beam width. Stress concentration ratio can be easily obtained by n ¼ s p /s vh. Eq. () is only valid for hps... British Standard design method, BS00 Marston s formula was adopted and modified in BS00 (99) to calculate the average pressure acting on a pile cap (s p ) and is given by: s p gh ¼ a cb, () h where b is the pile cap width, h the embankment height, g the embankment fill unit weight, a c the arching coefficient, a c ¼ :9ðh=bÞ 0: for end-bearing piles and a c ¼ :ðh=bþ 0:07 for friction piles. Eq. () is suitable for the D case; for the D situation, s p is given by s p gh ¼ a cb h. (9) Then, the average pressure on foundation soils s s can be written as s s ¼ ðs þ bþhg s pb, (0) s where s is the cap clear spacing. BS00 defines a critical height h c ¼.s, Eqs. () (0) are valid only for hph c.

7 ARTICLE IN PRESS C. Yun-min et al. / Geotextiles and Geomembranes (00) 7 Test Low et al. Terzaghi BS00(D) Test Low et al. Terzaghi BS00( D) 7 Test Low et al. Terzaghi BS00(D) 7 Test Low et al. Terzaghi BS00( D) 9 7 Test Low et al. Terzaghi BS00( D) 0 9 7 Test Low et al. Terzaghi BS00( D) 0 9 7 Test7 Low et al. Terzaghi BS00(D) Fig. 0. Comparison between the test results and design methods for stress concentration ratio: (a) Test, (b) Test, (c) Test, (d) Test, (e) Test, (f) Test and (g) Test 7.

C. Yun-min et al. / Geotextiles and Geomembranes (00) 7 7 The weight of the embankment fill above h c and the surface load are both completely transferred to the pile caps. A limitation of the BS00 is that the fill strength parameters were not taken into consideration... Comparison of predictions of design methods with experimental results None of the design methods for soil arching stated above considers the influence of reinforcements. Consequently, only the results of Tests 7 are compared with analytical predictions. It should be noted that Eq. (9) was used when test results were compared to BS00. Fig. 0 compares the experimental results to the calculated results of the design methods mentioned in Sections.., assuming c ¼ 0 kpa, f ¼ and g ¼. kn/m. Although the stress concentration ratios obtained from the design methods are not related to the pile subsoil relative displacement, horizontal lines represent the calculated stress concentration ratios, plotted in Fig. 0 for comparison. Fig. 0 shows that Terzaghi (9) method always overpredicts the stress concentration ratio. However, when h/sx., the results of this method show good agreement with the maximum stress concentration ratio from model tests. Method of Low et al. (99) gives slightly larger result compared to experimental values for h/so0.9. This is attributed to the limit analysis of soil element assumed in the arch. In fact, at a low embankment height, neither the soil element at the arch crown nor the soil element on the cap beam reach a limit state. Nevertheless, results of Low et al. (99) are by far the most relevant when compared to experimental results for h/sx.. As a whole, the stress concentration is strongly underestimated by BS00 when compared to the test results. From Fig. 0, it is also observed that method of Terzaghi (9) can be used to predict the upper bound of the stress concentration ratio. However, none of the three methods can predict the lower bound of the stress concentration ratio accurately.. Conclusions A series of D model tests have been undertaken to investigate soil arching in piled embankments with or without geosynthetic reinforcements. The test results have been compared with several current design methods. Model tests show that stress concentration ratios and settlements are influenced significantly by embankment height, cap beam width and clear spacing, and reinforcement tensile strength. Moreover, stress concentration ratio is strongly dependent on the pile subsoil relative displacement and has upper and lower bounds. Comparison of test results to current design methods shows a good agreement with the results of the method of Low et al. (99). The Terzaghi (9) trench model can be used to capture the maximum stress concentration ratio. And it seems that the method for D situation in BS00 underestimates stress concentration ratio. Although the scaling relations between the physical model and prototype have not been considered rigorously, the results obtained from the model tests are helpful to gain a better understanding of the mechanism of soil arching in piled embankments and can be used to verify the validity of design methods. Further studies using centrifuge or fullscale prototypes would be useful to evaluate the validity of the current design methods to real structures. Acknowledgments The study was supported by the National Natural Science Foundation of China (Project Nos. 0, 000, 000) and is greatly appreciated. The authors would also like to thank the reviewers for their valuable suggestions. References Bolton, M.D., 9. The strength and dilatancy of sands. Geotechnique (), 7. British Standard BS00, 99. Code of Practice for Strengthened/ Reinforced Soils and Other Fills. British Standard Institution, London. Chen, Y.M., Jia, N., Chen, R.P., 00. Soil arch analysis of piled embankment. 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