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Investigation on Static Stability of Sheet Pile Quay Wall Improved by Cement Treated Sea-Side Ground from Centrifuge Model Tests
SOILS AND FOUNDATIONS Japanese Geotechnical Society
Vol. 48, No. 4, 563–575, Aug. 2008
INVESTIGATION ON STATIC STABILITY OF SHEET PILE QUAY WALL IMPROVED BY CEMENT TREATED SEA-SIDE GROUND FROM CENTRIFUGE MODEL TESTS M. RUHUL AMIN KHANi), KIMITOSHI HAYANOii) and MASAKI KITAZUMEiii) ABSTRACT The static stability of sheet pile quay walls on a thick clay deposit against horizontal loads was studied through a series of centrifuge model tests. In the tests, an overconsolidated Kaolin clay layer was prepared over a layer of dense Toyoura sand in a rectangular container. The model quay wall was set to the bottom of the sand layer. The sea-side area adjacent to the quay wall was improved with cement-treated Kawasaki clay. Under 50 g centrifugal acceleration, the clay deposit was consolidated and horizontal line loads of about 0 to 70 kN/m were applied to the quay wall. The width and the depth of the improved area were varied and its performance was compared with that of a quay wall embedded in unimproved ground. Results of the study indicated that the improved ground provided signiˆcant resistance against horizontal loading. In addition, a numerical model to estimate the mechanical behavior of the sheet pile quay wall is presented. The outcomes of the numerical model show good agreement with the centrifuge test results. Key words: cement deep mixing, centrifuge model, clay ground, quay walls, sheet piles (IGC: K6)
A sheet pile quay wall in the Chiba Port, Japan is one of the examples which require improving its stability. For an existing quay wall, it would be preferable not to close the port for a long period. Then sea-side ground improvement is one of the promising techniques, which will not hamper the port-side activities during its execution, so that the service of the port is uninterrupted for the period of time. However, it is considered necessary to conduct a comprehensive study to investigate the eŠects of sea-side ground improvement on the static and dynamic stabilities of existing sheet pile quay walls. As mentioned above, the sea-side ground improved with the method of cement deep mixing (CDM) (CDIT, 2002) is studied through a series of centrifuge model tests. The static stability of the sheet pile quay wall subjected to horizontal loads is investigated and presented in the paper, while the dynamic stability of the sheet pile quay wall will be presented later. The sheet pile quay wall studied here is without anchorage and tie. Static stability of the improved quay wall is described in terms of structural and foundation ground behavior. A simple numerical method for estimating the behavior of the improved sheet pile quay wall subjected to horizontal loading is suggested. Comparison between the results of numerical calculations and centrifuge model tests is presented to validate the numerical method.
INTRODUCTION Steel sheet pile quay walls are designed and constructed as ‰exible type retaining walls to let ships berth as well as resist earth pressure of the backˆll. In the ˆeld, the structure is designed in such a way that the induced stress and the displacement should not exceed the allowable values. But during many earthquakes in the past, sheet pile quay walls failed with diŠerent degrees of rotation, horizontal displacement and excessive ‰exural stress. For example, sheet pile quay walls at Ohama Wharf and Shimohama Wharf of Akita Port, Japan, failed by excessive horizontal displacement and diŠerent degrees of rotation during the 1983 Nihonkai-Chubu earthquake (PIANC, 2001). The stability of a sheet pile quay wall can generally be improved by: (i) increasing the eŠective angle of internal friction or cohesion of the backˆll soil, (ii) driving the sheet pile into a dense layer of sand, (iii) increasing the thickness of the sheet pile, (iv) supporting the wall by ties and anchorages, (v) increasing the number of anchors, and (vi) increasing the anchor's cross section. Almost all research on improvement of the stability of quay walls are involved in the above-mentioned techniques. However, most of the mentioned techniques require large eŠorts and time, especially in the case of an existing quay wall. i)
ii) iii)
Geotechnical Engineer, Maunsell Australia New Zealand Asia, Australia (formerly Research Engineer, Soil Stabilization Division, Port and Airport Research Institute, Japan). Associate Professor, Yokohama National University, Japan. Director, Geotechnical and Structural Engineering Department, Port and Airport Research Institute, Japan (kitazume＠pari.go.jp). The manuscript for this paper was received for review on August 27, 2007; approved on May 28, 2008. Written discussions on this paper should be submitted before March 1, 2009 to the Japanese Geotechnical Society, 4-38-2, Sengoku, Bunkyoku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month. 563
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CENTRIFUGE MODEL TESTS Geotechnical centrifuge, Mark-II (Kitazume and Miyajima, 1996) in the Port and Airport Research Institute (PARI) was used to perform the model tests. The centrifuge has an eŠective radius of 3.8 m, maximum acceleration of 113 g and maximum payload of 2760 kg. Speciˆcations of the Mark-II centrifuge are listed in Table 1.
ent from that shown in Fig. 1. Through a series of centrifuge tests, a model sheet pile quay wall was used for the model grounds. The sheet pile having relatively low ‰exural rigidity was targeted, so that the eŠect of the DM improvement can be emphasized and evaluated accurately. The sheet pile was a 2 mm thick steel plate instrumented with 13 pairs of strain gauges, S1 to S13, on both sides. The ‰exural rigidity, EI, of the model sheet pile wall was
Model Set-up Figure 1 typically shows the schematic of the model set-up. A strong box of 600 mm in length, 410 mm in depth and 200 mm in width with a transparent front window was used for the tests. Figure 2 shows the photo of another model set-up whose CDM block size was diŠer-
Table 1.
Speciˆcations of Mark-II geotechnical centrifuge
Diameter of rotating arm Maximum eŠective radius Maximum acceleration Maximum payload Maximum capacity Maximum rate of rotation Main motor capacity
9.65 m 3.8 m 113 g 27.1 kN 3060 g.kN 163 rpm DC 450 kW
Fig. 1.
Fig. 2.
Model photo showing various elements
Schematic view of model set-up (in model scale)
STATIC STABILITY OF QUAY WALL Table 2.
Properties of Kaolin clay and Toyoura sand
Kaolin Clay Liquid limit, W L (%) Plastic limit, W P (%) Plastic index, IP (%) Speciˆc gravity, Gs Compression index, Cc Swelling index, Cs Coe‹cient of consolidation, Cv (m2/s) (cu/s?v)NC Critical state friction angle, q?crit
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Toyoura Sand 59.3 26.3 33.0 2.72 0.49 0.12 2.5×10－ 7 0.314 28.69
1.72×104 kNm. Prototype section of this plate becomes the Japanese standard sheet pile of type SP-II (Nippon Steel Corp., 1998). At the bottom of the strong box, the sheet pile wall was set on a 10 mm thick rough surfaced acrylic plate. At the top it was clamped with guide plates, so that it is ˆrmly ˆxed and remains vertical during the model preparation. The model sand ground of 60 mm thick was prepared by pouring dry Toyoura sand in such a way that the relative density of the sand layer becomes about 90z. To saturate the sand layer, water was fed from the bottom through water supply line carefully so as not to disturb the sand. The Kaolin clay was remolded at a water content of about 120z, approximately equal to 2 times the liquid limit and was de-aired. Properties of the Kaolin clay and Toyoura sand are shown in Table 2. Silicone grease was smeared on the walls of the strong box. The clay slurry was then poured over the saturated sand layer in the strong box. In both the sea-side and port-side, ˆlter paper and perforated loading plates were placed over the clay slurry. Pre-consolidation was carried out by compressing the clay with two bello-fram cylinders. The size of the perforated loading plate and ˆlter paper in the sea-side was 398 mm×200 mm and in the port-side 198 mm×200 mm (Fig. 1). Piston of the bello-fram cylinders that incorporated a load cell (20 kN capacity) was set at the center of the loading plates and bello-fram cylinders were clamped with the strong box. Since the loading plate covered almost all the surface of the clay and the walls of the strong box were smeared with grease, load from the pistons compressed the clay one dimensionally. The successive preliminary consolidation pressures applied were 1 kPa, 10 kPa, 30 kPa, 50 kPa, 100 kPa and 150 kPa. Primary consolidation was achieved in each stage. After having completed the preliminary consolidation, the perforated loading plate and ˆlter paper were removed. The surface of consolidated clay was skimmed oŠ to a depth of 160 mm. The strong box was then tilted against a wall and the front transparent window was opened. Horizontal holes were drilled in speciˆed location for inserting pore pressure transducers, P, and earth pressure gauges, E, through the clay by a small hand auger. By using guide tools, pressure transducers P and E were inserted horizontally. Each hole was ˆlled with deaired Kaolin slurry. The pore pressure transducer in the
Speciˆc gravity, Gs D10 (mm) D50 (mm) Coe‹cient of uniformity, Uc Coe‹cient of curvature, U?c Maximum void ratio emax Minimum void ratio emin Friction angle q?
2.65 0.15 0.19 1.56 0.96 0.992 0.624 42.09
sand layer was inserted near the surface carefully. Re‰ective blue colored beads of 6 mm diameter as optical targets were inserted through a template of 20 mm square openings ( see Fig. 2). The window was replaced and the strong box was set upright. The bello-fram cylinders were set again with 150 kPa consolidation pressure to recover the swelling and sensors holes. After releasing the pressure, a speciˆed area in sea-side adjacent to the sheet pile was excavated. Then cement treated Kawasaki clay which is called in this paper as CDM was poured into the excavation. In the tests, the CDM size was changed parametrically as shown in Table 3. For example, the CDM size in Fig. 2 was 10 m×4 m in prototype scale. To prepare the CDM, Kawasaki clay slurry with 130z water content was thoroughly mixed with Portland cement. Amount of Portland cement added was 40z of dry weight of Kawasaki clay. After ˆlling the excavation, su‹cient water was added on top of the clay and CDM for curing. At least seven days curing was allowed to gain su‹cient strength. The unconˆned compression strength qu of the CDMs are listed in Table 3. The unconˆned compression tests were carried out according to the standards of Japanese Geotechnical Society (JGS, 2000). Variation of curing period which ranged from 7 to 12 days aŠected the qu values that were reported in Table 3. To simulate the static earth pressure of backˆll soils, a horizontal loading jack was mounted on the top of the sand box so that the horizontal line load would be applied to the sheet pile during tests. Laser displacement transducers LDs for monitoring the displacement of the CDM and the clay ground, linear variable displacement transducers LVDTs for monitoring the vertical movement of the ground surface and de‰ection of the sheet pile wall at loading point, were ˆrmly set on top of the strong box as shown in Fig. 1.
Test Procedures and Conditions The strong box with the model ground was mounted on the swinging platform of the centrifuge. Centrifugal acceleration was increased up to 50 g. The consolidation in the centrifuge at 50 g was conducted until the degree of consolidation was estimated to have achieved 90z. At 50 g, a horizontal line load was applied gradually by the loading jack to the sheet pile quay wall in the seaward direction. As shown in Fig. 3, loading cycles were applied
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Table 3.
Test conditions in Prototype scale
Test cases
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
Case 7
Clay depth (m) CDM size(width×depth, m 2) qu of CDM (kPa)
8 0 ×0 —
8 10×8 920
8 10×4 617
8 2×4 1173
8 4×4 1536
8 8× 2 1333
8 4× 2 1020
same. All the test results in the following sections are presented in the prototype scale. RESULTS AND DISCUSSIONS
Fig. 3.
Cyclic load applied to the quay wall in Case 4
at several horizontal loads. Each cycle comprised 5 or 6 turns of loading and unloading with the jack speed of 3 mm/min. De‰ection of sheet pile quay wall, vertical movements of the ground surface at the sea-side, earth pressures at various elevations and strains on the surface of the sheet pile wall were monitored during the tests. The positions of the sensors are shown in Fig. 1. Still pictures of the model were taken in every turn of a loading cycle for observing the de‰ection of the wall and displacement of ground with respect to the targets' movement. In this paper, the results of seven centrifuge tests are presented to discuss the eŠects of the sea-side ground improvement on the static stability of the quay wall. The test conditions in the prototype scale are shown in Table 3. All of the test conditions are identical except for the size of the CDM block and the position and number of sensors. Number of sensors arranged for the Test Cases 4–7 was much more than that for the Test Cases 1–3, because the ground behaviour such as earth pressure distributions were investigated in detail for Cases 4–7. Static stability of unimproved and improved sea-side ground has been examined from the unimproved case (Case 1) and the improved cases. The eŠect of width of the CDM block is investigated from Cases 3, 4 and 5, which have the depth of CDM equal to 4 m, and Cases 6 and 7, which have the depth of CDM equal to 2 m. Having the same width of CDM, the in‰uence of the `‰oating type' and full-depth CDM block is likewise examined from Cases 2 and 3. CDM blocks in Cases 5 and 7 also have the same width but diŠerent depth. Cross-sectional area of CDM block in Cases 4, 7 and in Cases 5, 6 is
Undrained Shear Strength of the Clay Stratum In Japan, seashore generally consists of a thick clay layer underlain by a sand layer. In this study, an overconsolidated clay stratum was chosen to easily facilitate the model preparation and the quay wall numerical modeling. The maximum eŠective past pressure experienced by the clay is equal to the preliminary consolidation pressure of 150 kPa as described before. After preliminary consolidation, centrifugal consolidation was conducted on the clay stratum at 50 g. Data from the pore pressure transducers, P, and LVDT2 in the clay were used to estimate the degree of consolidation. Square root of time method was used to estimate the degree of consolidation. Time taken to achieve 90z consolidation in the centrifuge was about 4.5 hours. Since the depth of the clay stratum in all cases is the same (8 m), almost the same amount of consolidation settlement was observed. The clay stratum was found to settle about 0.40 m in the prototype scale. Pore pressure responses during centrifuge consolidation are typically shown in Fig. 4. The data obtained from Cases 4 and 5 are shown. Pore pressure transducer, P4, which was placed near the bottom of the clay stratum ( see Fig. 1), dissipated larger pore pressure than that of P3 and P2. The response from P1 and P5 are almost ‰at which were placed at the ground surface and at the bottom sand layer respectively. This indicates that constant hydrostatic pressure is available at the boundaries of the clay stratum during the test. Theoretical hydrostatic pressures are given in brackets in the ˆgure. Estimated undrained shear strength proˆle of the clay stratum thus consolidated is shown in Fig. 5. The undrained shear strength is estimated as follows. First, K0, was derived for the overconsolidated (OC) clay with a critical state friction angle q?＝28.6, following the equation presented by Mayne and Kulhawy (1982): K0(OC)＝(1－sin q?)OCRsin q?
(1)
where OCR is the overconsolidation ratio (s?p/s?v); the coe‹cient of in-situ earth pressure, and s?v and s?p are the current eŠective vertical stress and the past maximum vertical consolidation pressure respectively. Then, the undrained shear strength, cu, of the clay was derived from the formula of Wroth (1984):
STATIC STABILITY OF QUAY WALL
Fig. 4. Dissipation of excess pore pressure during the centrifuge consolidation stage (Cases 4 and 5)
Fig. 5. Undrained shear strength proˆle of the clay stratum of the model grounds
Ø »
cu cu ＝ s?v s?v
OCRm
(2)
NC
where NC＝normally consolidated clay, with an experimental value of (cu/s?v)NC＝0.314 and m＝0.75(＝(Cc -Cs)/Cc; see Table 2). Theoretical cu values thus obtained have been representatively compared with the test results for Cases 4–7. The cu values for Cases 1–3 were not investigated. To obtain the test results, the cu values were computed from the water content proˆle along the depth both in the sea-side and port-side. First, void ratio, e, and eŠective vertical stress, s?v, for the corresponding sample of water content were derived from the following relation ships:
e＝wGs e＝－0.189Ln(s?v)＋2.076
(3) (4)
Here Gs is the speciˆc gravity and w is the water content of fully saturated kaolin clay. Equation (4) is the e versus loges?v characteristic of the kaolin clay used in the test.
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Then the value of cu was computed from cu＝0.314s?v experimental relationship. After stopping the centrifuge, a few hours passed before sampling for water content. Although some swelling may have taken place in this period, which may result in a smaller cu values than those predicted by theory, the values derived from the test results compared fairly well with the theoretical cu values, which were predicted before the loading stage. The cu value of Case 4 is less than in other cases. This may be because of delayed sampling. The sampling was conducted after about 12 hours from the stopping of centrifuge, while samples of other cases were taken within about 2 to 5 hours. Since the methodology of preparing the model and centrifuging were identical, the cu proˆles are considered to be reasonably similar. The fact implies that the targeted undrained shear strength proˆle of the clay stratum was achieved through the tests.
De‰ection of Sheet Pile Quay Wall De‰ection of the quay wall is examined as the main index in describing stability. Figures 6(a) and (b) show the in-‰ight photo of Case 4 at the initial stage and 68 kN/m loading stage respectively. Various elements are marked in the ˆgures. Some de‰ection of the sheet pile wall from the vertical position can be seen in Fig. 6(b). Figure 7 shows the relationship between horizontal load, Fh, and de‰ection of quay wall at loading point. As mentioned before, the horizontal load induced by the loading jack represented the static earth pressure of back ˆll soils. In the study, about 40–50 kN/m of the static earth pressure was estimated by taking into account the thickness and the strength characteristics of the backˆll soils. Therefore, de‰ection at Fh＝45 kN/m, d45, is chosen to compare with the data of all cases and is tabulated in the ˆgure. De‰ection d45 of the unimproved ground of Case 1 is 0.47 m whereas full-depth CDM improved ground of Case 2 is 0.12 m. StiŠness of the full-depth improved ground becomes almost four times larger than that of the unimproved sea-side ground. Here stiŠness is indicated as horizontal load per unit de‰ection. Cases 4, 5, and 3 with the same depth of CDM (depth: 4 m) but diŠerent width (respective widths: 2 m, 4 m and 10 m) have d45 of 0.29 m, 0.13 m and 0.12 m respectively. Even though the width in Case 3 was more than double that of Case 5, the de‰ection was not decreased proportionally as decreased in Cases 4 and 5. The results indicate that in increasing the width or size of the CDM, a small amount of de‰ection of the quay wall will take place. This is deˆned here as the limit of least de‰ection. Cases 7 and 6 with the same depth of CDM (depth: 2 m) but diŠerent width (respective widths: 4 m and 8 m) have d45 value of 0.24 m, and 0.14 m respectively. The stiŠness oŠered by the quay wall in these cases is almost proportional with the width of CDM. Cases 2 and 3 having ‰oating or half-depth and full-depth CDM (with the same width of treated material) have d45 value of 0.12 m in each case. The eŠect of the depth of CDM is also investigated from Cases 5 and 7 which have the same width
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Fig. 6. In-‰ight photo of the model sheet pile quay wall of Case 4 showing: (a) initial condition before applying the load and (b) at the 68 kN/m loading stage
Fig. 7.
Load de‰ection relationship of the sheet pile quay wall
(＝4 m) but diŠerent depth (depth of CDMs: 4 m and 2 m). The values of d45 of these cases are found as 0.13 m and 0.24 m respectively. De‰ection is increased about double in the case with smaller depth CDM. Increasing the depth of CDM may have stiŠened the ground and reduced the wall de‰ection towards the limit of least de‰ection. Sectional-area wise performance of the CDM can also be compared from Cases 4, 7 and Cases 5, 6. Cases 4 and 7 having the same cross sectional-area (＝8 m2) show d45 values of 0.29 m and 0.24 m. And Cases 5 and 6 (area＝16 m2) show d45 values of 0.13 m and 0.14 m. Almost the same d45 values are observed in each group.
Fig. 8. Variation of shear stress ratio, (sh-sv)/2cu with the applied horizontal load, Fh
Earth Pressures Horizontal and vertical earth pressures around the CDM block and sheet pile quay wall were investigated in detail for Cases 4–7. Due to increasing the horizontal load, Fh, shear deformation of the foundation ground starts to take place. Gradual increasing trend of total horizontal pressure, sh, in the sea-side was observed during the loading stage. Variation of shearing stress ratio, (sh-sv)/2cu with the applied horizontal load, Fh is shown in Fig. 8. Here sh and sv are the total horizontal and ver-
STATIC STABILITY OF QUAY WALL
tical earth pressure respectively. The values of sh are obtained from the earth pressure gauges, E, placed along the depth and the values of sv are calculated by considering the soil densities and the water level. The cu values are determined from the water content proˆle of the clay as stated in Fig. 5. With the de‰ection of the quay wall, rising trends of shear stress ratio are found in the clay. Figure 9 shows the response of vertical earth pressure below the CDM block at the Fh＝45 kN/m loading stage. Earth pressure gauges (E7¿E8, Fig. 1) were set below the CDM to measure the vertical pressures. Rotation of CDM block during the loading stage can be understood by comparing the initial (ini.) and ˆnal values of vertical earth pressure. All of the cases show the deviation from the initial line with an indication of the seaward rotation
Fig. 9. Vertical earth pressure observed below the CDM block at the initial (ini.) and the 45 kN/m loading stage
Fig. 10.
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of the CDM block. Movement of the CDM block during the loading stage was monitored by the laser displacement transducers (LD2 and LD3, Fig. 1). In all cases except for Case1, the horizontal movement of the CDM block was measured and in Cases 4–7 vertical movement of the CDM block was also measured. Figures 10(a) and (b) show the horizontal and vertical displacement of a point on the CDM block with the applied load, Fh. The monitored point is (7/8)W away from the sheet pile wall ( see the inset ˆgure). Here W is the width of the CDM block. Horizontal displacement at 45 kN/m loading, dh45 and vertical displacement at 45 kN/m loading, dv45 are also shown in the ˆgures. Comparing the values of dh45 and dv45, the values of the de‰ection of quay wall at loading point, dh ( see Fig. 7) are found to be relatively larger. Case 4 shows the largest dh45 which is 0.12 m and Case 2 shows the smallest value which is 0.002. Horizontal displacements of Cases 2 and 3 are found negligible. Case 4 with the smallest width CDM shows larger displacement both horizontally and vertically. Cases 4 and 5 with 4 m depth CDM show larger vertical displacement than that of Cases 6 and 7 which are having 2 m depth CDM.
Bending Moments, Displacements of Sheet Piles Bending moments are derived from the responses of the strain gauges (S) along the sheet pile wall ( see Fig. 1). Figures 11(a) and (b) show the bending moment and de‰ection distributions of the sheet pile quay wall at the 45 kN/m loading stage derived from all cases. The de‰ection distributions were obtained by conducting two successive integrations on the functions ˆtted to the bending moment distributions. Here quantic spline functions were used to ˆt the bending moment test points as shown in Fig. 11(a). In the ˆgure the spline functions are shown by the curves and the test points are shown by the markers.
Movement of the CDM block during the loading stage: (a) horizontal displacement and (b) vertical displacement of the CDM block
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Fig. 11.
Bending moments and de‰ection distributions of the sheet pile quay walls at the 45 kN/m loading stage
Maximum bending moment experienced by all cases is listed in the ˆgure. Almost similar pattern of bending moment is developed in all cases. However, interaction among the CDM, the sheet pile wall and the clay reduces the bending moments in accordance with the size of the CDM block. For example, the maximum bending moment experienced by the unimproved case (Case 1) is 215 kN-m whereas the cases with improved sea-side ground show much smaller value. Maximum bending moments in the improved cases take place at the ground surface and in the unimproved case it takes place below the ground level. Maximum bending moments in the cases with CDM depth equal to 4 m ranges from 121 to 145 kN-m and in the cases with CDM depth equal to 2 m ranges from 125 to 147 kN-m. The trends of Cases 4 and 7 which have the smallest size CDM show a curvature like the unimproved case. As shown in Fig. 11(b), ˆrm ˆxity at the bottom part, gradual bending near the ground surface and maximum de‰ection at the top can be visualized from the de‰ection distribution of the sheet pile quay wall. De‰ection at the loading point which is 3.5 m above the ground level was recorded at 45 kN/m loading and is shown in Fig. 11(b). Ratio of the test data to the spline data, dtest/dspline, is listed in the ˆgure. The ratios fall in a narrow band and range from 1.1 to 1.4. De‰ection distributions of the sheet pile quay wall show good agreement with the test points.
Horizontal Subgrade Reaction Two successive diŠerentiations of spline-curve of the
bending moment distributions give the horizontal subgrade reaction on the wall below the ground level which is shown in Fig. 12(a). In the ˆgure, negative horizontal subgrade reaction represents that the passive pressure acting on the sheet pile is larger than the active pressure acting on it. Maximum subgrade reaction is observed at the ground level for the improved grounds and it reduces toward the bottom of the sheet pile quay wall to zero or very small value. Maximum subgrade reaction in the unimproved case (Case 1) is found as －43 kN/m2/m whereas in the improved cases it ranges from －60 kN/m2/m to －125 kN/m2/m. For each stage of loading the data set of elevation versus displacement, bending moment and horizontal subgrade reaction were derived with the help of spline functions. For elevation equal to zero, which is the ground level, the displacement and horizontal subgrade reaction from all stages of loading were picked up. Figure 12(b) shows the relationship between the horizontal subgrade reaction and the displacement at the ground surface thus obtained. Then linear least square ˆtting is attempted for the curve of each case with an equation to obtain the coe‹cient of horizontal subgrade reaction, ks, at the ground surface, although nonlinear relationships are observed especially for Cases 1, 4 and 7. For these cases the eŠect of clay stiŠness might be larger rather than that of CDM stiŠness. In the study, the nonlinearity is ignored for the simplicity. However the change of ks with the increase of the displacement should be studied in detail in
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Fig. 12. Determination of horizontal subgrade reaction at the 45 kN/m loading stage: (a) horizontal subgrade reaction along depth and (b) subgrade reaction versus displacement at the ground surface
about full depth. The value of ks at ground surface in the improved cases ranges from 625 to 11000 kN/m3 whereas ks of the unimproved case is 160 kN/m3. The ks in the improved zone increases almost linearly, except for the full depth case (Case 2) where decreasing trend was observed beyond 4 m depth. The reason for the trend of Case 2 is not well understood, but the strength of CDM might be relatively scattered within the block as the largest volume of cement slurry was prepared among all cases. The eŠect of width of the CDM on the coe‹cient of horizontal subgrade reaction, ks, is shown in Fig. 14. For the cases with 4 m depth CDM, the width eŠect is representatively considered at the depth of 0 m, 2 m and 4 m (Fig. 14(a)). Likewise the cases with 2 m depth CDM, the width eŠect is considered at the depth of 0 m, 1 m and 2 m (Fig. 14(b)). With the same depth of CDM, ks increases almost proportionally with increase in width of the CDM, as shown in the ˆtting equations. From the ˆtting relationship between the ks and width of the CDM as shown in the ˆgures, ks corresponding to any other widths are determined and used in the numerical method as described later. Fig. 13. Coe‹cient of horizontal subgrade reaction, ks along depth at the 45 kN/m loading stage
NUMERICAL METHOD
the further study to input ks more precisely for numerical simulations. In the same way as shown in Fig. 12(b), the coe‹cient of horizontal subgrade reaction, ks, is also determined along the depth. Figure 13 shows the coe‹cient of horizontal subgrade reaction, ks thus obtained, against depth. The resistance from the CDM can be visualized from the ˆgure up to a depth of about 4 m for Cases 3, 4, 5 and 2 m for Cases 6, 7, except for Case 2 with up to
Formation of Equations Elastic equilibrium of forces acting on the horizontal slice of sub-divided layers below the ground level is considered. Portion of the sheet pile quay wall above the ground level is treated simply as a cantilever beam. In simulation of the centrifuge model condition, a concentrated force Fh is applied at 3.5 m above the ground level in the same way as the centrifuge model tests. Figure 15 schematically shows the position of Fh and sub-divided layers in the clay stratum. According to the
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Fig. 14. Variation of coe‹cient of horizontal subgrade reaction, ks with the width of CDM block: (a) depth of the CDM block is 4 m and (b) depth of the CDM block is 2 m
boundary conditions and Q＝P/(24EI). Behavior of sheet pile quay wall below the ground level is modeled by the method of horizontal subgrade reaction (Chang, 1937). Underground de‰ection of the sheet pile quay wall can be expressed as:
EI
d 4y ＝－ksy dx4
(7)
where ks is the coe‹cient of horizontal subgrade reaction on the sheet pile wall. General solution of Eq. (7) is obtained as:
y＝Cie bx cos bx＋Cje bx sin bx＋ Cke－bx cos bx＋Cle－bx sin bx
(8)
where b＝4 ks/(4EI), Ci¿Cl are integral constants obtained from the boundary conditions in each layer of the clay ground (§C1¿C16 are used in the application). Similar general solution can be written as Eq. (9) for the sand layer with the integral constants R1 to R4. Fig. 15.
y＝R1e bx cos bx＋R2e bx sin bx＋ R3e－bx cos bx＋R4e－bx sin bx
Numerical model of the sheet pile quay wall
theory of elastic beam, equation of de‰ection, y of the sheet pile quay wall above the ground level is obtained as follows:
EI
d 4y ＝P dx4
(5)
where EI is the ‰exural rigidity of the sheet pile, P is the pressure due to external loads applied to sheet pile, x is the vertical coordinate of elevation and y is the de‰ection of the sheet pile as shown in Fig. 15. General solution of Eq. (5) is obtained as:
y＝A1x3＋A2x2＋A3x＋A4＋Qx4
(6)
where A1¿A4 are integral constants obtained from the
(9)
Boundary Conditions and Solutions To put the appropriate value of ks to the equations, the clay ground has been divided into four layers. Number of layers can be varied according to ˆeld conditions and required degree of accuracy of the prediction. As shown in Fig. 15, integral constants used in this model are A1¿A4, C1¿C16 and R1¿R4. In the ˆgure, y, y?, y!, y?!, y!! represent zero, 1st, 2nd, 3rd, and 4th degree of derivative whose respective physical meanings are de‰ection, angle of de‰ection, bending moment, shear force and distributed load on the sheet pile quay wall. At the top of the wall: y! top＝0, y? t! op＝Fh, P＝0 and two equations are formed with constants A1¿A4. Left hand sides of these two equations are the 2nd and 3rd deriva-
STATIC STABILITY OF QUAY WALL
tive of Eq. (6). At each of the ˆve layer-interfaces, four equations are formed with the following boundary conditions: yU＝yL, y?U＝y?L, y! !＝y?L!; where `U' U＝y! L, y? U represents upper layer and `L' the lower layer of a particular layer-interface. In layer-interface 1 (ground level), diŠerent degrees of derivative of Eqs. (6) and (8) are set on both sides of the boundary equations. A1¿A4, and C1¿C4 appears in the interface 1. Likewise C1¿C16 and R1¿R4 are appeared in the equations of the remaining interfaces. In the ˆve layer-interfaces, twenty equations are formed. At the bottom of the wall: ybot＝0, y! bot＝0 and two equations are formed with constants R1¿R4. Left hand side of these boundary conditions is the zero and 2nd derivative of Eq. (9). Twenty four unknowns are then derived from the set of twenty four equations. Particular solutions are obtained by using these constants (unknown) to the equation of de‰ection in each layer.
Input Parameters The coe‹cient of horizontal subgrade reaction, ks can be obtained from the relationships of various parameters like shear modulus, Poisson's ratio, shear strength, friction angle, and cohesion along the depth of the ground. For example, the ks can be determined by the following model of Bowles (1974). ks＝As＋Bs z n
(10)
where As＝ constant for structural member, Bs＝ coe‹cient for depth, z＝depth of interest below ground and n＝ exponent to give ks the best ˆt (if load test or other data are available). Bowles (1974) has shown that this model is reasonably accurate by using it to analyze full-scale ˆeld walls and for reanalyzing model sheet pile walls reported by TschebotarioŠ (1949) and by Rowe (1952). Based on the concept of this model, the CDM zone can be treated either as a layer like soil or a hybrid zone whose
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property will be obtained by considering the interaction among the sheet pile wall, the CDM and the surrounding clay. Here, two diŠerent methods to determine the coe‹cient of horizontal subgrade reaction, ks are introduced. I. Simpliˆcation with CDM area: This method is described in Fig. 16. Largest displacement of the sheet pile quay wall was observed in the unimproved case (Case 1). Since the displacement of the quay wall in the deeper ground is very small and ks is very sensitive to the magnitude of the displacement, the ks values below about 5 m depth are di‹cult to be precisely determined with the linear ˆtting although the results are shown in the ˆgure. As a result, the unreasonable change of the ks with the depth below about 5 m depth is observed. Hence, in the study, test data of ks until about 5 m depth is considered to extrapolate the ks variation with depth in unimproved case (Fig. 16(a)). The relationship derived for the unimproved ground is:
ks＝100＋235z
(11)
where z is the depth from the ground level. All of the ks data of improved cases are normalized by the cross sectional area, A, and unit area, A0, of the CDM block and plotted against the depth, z (Fig. 16(b)). Here unit area, A0 of 1 m2 is chosen. The average trend line gives the following relationship:
ks＝(133＋132z)A/A0
(12)
From these two equations (Eqs. (11) and (12)) simpli-
Table 4.
Parameters used in Numerical Analysis Steel Sheet Pile Wall
I (m4/m) E (kN/m2) EI (kN.m)
8333×10－ 8 2.1×108 17170
Fig. 16. Simpliˆcation of coe‹cient of horizontal subgrade reaction, ks: (a) simpliˆed ks along depth for the unimproved case, (b) ks normalized by sectional area of the CDM block, A1, (A0＝unit area) along depth and (c) simpliˆed ks along depth for 4 m depth CDM
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Fig. 17. Simpliˆcation of coe‹cient of horizontal subgrade reaction, ks: (a) simpliˆed ks along depth for the unimproved case, (b) ks normalized by width of the CDM block, W , (W0＝unit width) along depth and (c) simpliˆed ks along depth for 8 m depth CDM
Fig. 18. EŠect of the width of CDM block at the 45 kN/m loading: (a) simpliˆed calculation with respect to the sectional area of the CDM block and (b) simpliˆed calculation with respect to the width of the CDM block
ˆed ks values are produced along the depth and shown in Fig. 16(c). In the ˆgure, simpliˆed ks values are shown for various width of a 4 m depth CDM block. Below the CDM block, the ks value is assumed as the value of unimproved case (Eq. (11)). II. Simpliˆcation with CDM width: This method is described in Fig. 17. The simpliˆed relationship derived for the unimproved ground is same as described in the ˆrst method with Eq. (11). All of the ks data of improved cases are normalized by the width, W, and unit width, W 0, of the CDM block and plotted against the depth, z (Fig. 17(b)). Here unit width, W0 of 1 m is chosen. The average trend line gives the following relationship:
ks＝(200＋850z)W/W0
(13)
From Eqs. (11) and (13) simpliˆed ks values are pro-
duced along the depth and shown in Fig. 17(c). In the ˆgure, simpliˆed ks values are shown for various width of an 8 m depth CDM block. Below the CDM block, the ks value is assumed as the value of unimproved case (Eq. (11)). Steel sheet pile properties used in numerical method are listed in Table 4. Prototype section of a steel sheet pile was considered in deriving the modulus, E and ‰exural rigidity, EI. NUMERICAL RESULTS De‰ection of the quay wall is obtained numerically for various width and depth of the CDM by using the ks value. The ks values are obtained from the above methods. Figure 18 shows the relationship between
STATIC STABILITY OF QUAY WALL
de‰ection at loading point at the 45 kN/m loading stage and the width of the CDM block. Centrifuge test data and numerical predictions are plotted in the ˆgure. Simpliˆed calculation with respect to the CDM area (method-I) is shown in Fig. 18(a) for the depth of 2 m, 4 m and 8 m. Reasonable predictions are observed throughout the width of the CDM. This ˆgure implied that beyond 4 m width, CDM of 2 m depth is more e‹cient than that of 4 m depth or full-depth in reducing the de‰ection of the sheet pile quay wall. Since Cases 2 and 3, which have the same width but diŠerent depths (full- and halfdepth), show the same de‰ection, from an economical feasibility point of view half-depth or the ‰oating type CDM is more e‹cient for the ˆeld situation. Both of the experiment and numerical simulation results indicate that the improved grounds sustain the de‰ection of the sheet pile, but that there is still a certain degree of de‰ection even in the full-depth case. This is considered due to a limitation of the eŠect of sea-side ground improvement, although lower displacement might be achieved when the rigidity of the sheet pile is relatively higher. Simpliˆed calculation with respect to the CDM width (method-II) is shown in Fig. 18(b) for the depth of 2 m, 4 m and 8 m. These three lines show a tendency of merging at about 6 m width of the CDM. It means beyond 6 m width, de‰ection is same for any depth of the CDM and the lowest de‰ection is about 0.2 m. Numerical prediction with area based simpliˆcation (method-I) agrees well with the test data and shows better prediction than that of width based simpliˆcation (method-II). These facts indicate that the concept of the simple numerical modeling shown here would work very well to predict actual ˆeld behaviour of improved ground, although the input parameters such as the coe‹cients of subgrade force reaction should be carefully determined based on ˆeld tests and/or laboratory tests. CONCLUSIONS The eŠects of sea-side ground improvement on the static stability of existing sheet pile quay walls have been presented with reference to the load-de‰ection behavior, eŠect of size of cement deep mixing zone, and wall de‰ection, bending moment, horizontal subgrade reaction and earth pressure distributions in a series of centrifuge tests. The eŠects of sea-side ground improvement on the static stability of existing sheet pile quay wall also have been numerically predicted. Simple numerical predictions compare satisfactorily with the centrifuge test results. The method can be used for predicting the important design parameters like de‰ection of the sheet pile quay wall. The conclusions of the study are as follows: 1. Compared with the case of a wall embedded in unimproved ground, signiˆcant resistance against horizontal load was observed to develop in the CDM improved cases, i.e., the horizontal de‰ection was eŠectively reduced.
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2. The horizontal de‰ection of the model quay wall decreased with increase in width of the CDM area until it reaches a certain limit. 3. In the cases of improved ground, the maximum bending moment of the model quay wall was reduced up to about half of the value of the unimproved ground case. 4. The horizontal load was mainly resisted by the improved soil zone, which oŠered large horizontal subgrade reactions. 5. Seaward rotational tendency of the CDM block was observed in the improved ground cases. 6. Proposed numerical model of the sheet pile quay wall can predict the eŠect of the sea-side ground improvement and prediction by the numerical model agrees fairly well with the results of centrifuge model tests. These indicate that the concept of the simple numerical modeling shown here would work very well to predict actual ˆeld behaviour of improved ground, although the input parameters such as the coe‹cients of subgrade force reaction should be carefully determined based on ˆeld tests and/or laboratory tests. ACKNOWLEDGEMENTS The authors are thankful to Mr. K. Maruyama who cooperated in this research signiˆcantly. The authors also acknowledge the Ministry of Land, Infrastructure and Transport, Japan for providing the ˆnancial support in pursuing the study. REFERENCES 1) Bowles, J. E. (1974): Analytical and Computer Methods in Foundation Engineering, McGraw-Hill Book Co., NY. 2) Chang, Y. L. (1937): Discussion of `Lateral pile loading tests by L.B. Feagin'. Transactions of ASCE, 102, 272–278. 3) Coastal Development Institute of Technology (CDIT), Japan (2002): The Deep Mixing Method-Principle, Design & Construction, Balkema, Rotterdam. 4) Japanese Geotechnical Society (JGS), Japan, (2000): Standards of Japanese Geotechnical Society for Laboratory Shear Test, JGS, Tokyo, Japan. 5) Kitazume, M. and Miyajima, S. (1996): Development of PHRI Mark II Geotechnical centrifuge, Technical Note of the Port and Harbour Research Institute, (817), 4–33. 6) Mayne, P. W. and Kulhawy, F. H. (1982): K0–OCR relationships in soil, Journal of Geotechnical Engineering Div., ASCE, 108(G76), 851–872. 7) Nippon Steel Corporation, Japan (1998): Steel Sheet Pile–Design and Manufacture (Kou Ya ita) Nippon Steel Corporation Handbook, p. 465 (in Japanese). 8) PIANC, International Navigation Association (2001): Seismic Design Guidelines for Port Structures, Balkema, Rotterdam. 9) Rowe, P. W. (1952): Anchored sheet pile walls, Proc. Institution of Civil Engineers, 1(1), 27–70. 10) TschebotarioŠ, G. P. (1949): Large scale earth pressure tests with model ‰exible bulkheads, Final Report to Bureau of Yards and Docks U.S. Navy, Princeton University. 11) Wroth, C. P. (1984): The interpretation of in situ soil tests, 24th Rankine lecture, Geotechnique, 34(4), 449–489.
Vol. 48, No. 4, 563–575, Aug. 2008
INVESTIGATION ON STATIC STABILITY OF SHEET PILE QUAY WALL IMPROVED BY CEMENT TREATED SEA-SIDE GROUND FROM CENTRIFUGE MODEL TESTS M. RUHUL AMIN KHANi), KIMITOSHI HAYANOii) and MASAKI KITAZUMEiii) ABSTRACT The static stability of sheet pile quay walls on a thick clay deposit against horizontal loads was studied through a series of centrifuge model tests. In the tests, an overconsolidated Kaolin clay layer was prepared over a layer of dense Toyoura sand in a rectangular container. The model quay wall was set to the bottom of the sand layer. The sea-side area adjacent to the quay wall was improved with cement-treated Kawasaki clay. Under 50 g centrifugal acceleration, the clay deposit was consolidated and horizontal line loads of about 0 to 70 kN/m were applied to the quay wall. The width and the depth of the improved area were varied and its performance was compared with that of a quay wall embedded in unimproved ground. Results of the study indicated that the improved ground provided signiˆcant resistance against horizontal loading. In addition, a numerical model to estimate the mechanical behavior of the sheet pile quay wall is presented. The outcomes of the numerical model show good agreement with the centrifuge test results. Key words: cement deep mixing, centrifuge model, clay ground, quay walls, sheet piles (IGC: K6)
A sheet pile quay wall in the Chiba Port, Japan is one of the examples which require improving its stability. For an existing quay wall, it would be preferable not to close the port for a long period. Then sea-side ground improvement is one of the promising techniques, which will not hamper the port-side activities during its execution, so that the service of the port is uninterrupted for the period of time. However, it is considered necessary to conduct a comprehensive study to investigate the eŠects of sea-side ground improvement on the static and dynamic stabilities of existing sheet pile quay walls. As mentioned above, the sea-side ground improved with the method of cement deep mixing (CDM) (CDIT, 2002) is studied through a series of centrifuge model tests. The static stability of the sheet pile quay wall subjected to horizontal loads is investigated and presented in the paper, while the dynamic stability of the sheet pile quay wall will be presented later. The sheet pile quay wall studied here is without anchorage and tie. Static stability of the improved quay wall is described in terms of structural and foundation ground behavior. A simple numerical method for estimating the behavior of the improved sheet pile quay wall subjected to horizontal loading is suggested. Comparison between the results of numerical calculations and centrifuge model tests is presented to validate the numerical method.
INTRODUCTION Steel sheet pile quay walls are designed and constructed as ‰exible type retaining walls to let ships berth as well as resist earth pressure of the backˆll. In the ˆeld, the structure is designed in such a way that the induced stress and the displacement should not exceed the allowable values. But during many earthquakes in the past, sheet pile quay walls failed with diŠerent degrees of rotation, horizontal displacement and excessive ‰exural stress. For example, sheet pile quay walls at Ohama Wharf and Shimohama Wharf of Akita Port, Japan, failed by excessive horizontal displacement and diŠerent degrees of rotation during the 1983 Nihonkai-Chubu earthquake (PIANC, 2001). The stability of a sheet pile quay wall can generally be improved by: (i) increasing the eŠective angle of internal friction or cohesion of the backˆll soil, (ii) driving the sheet pile into a dense layer of sand, (iii) increasing the thickness of the sheet pile, (iv) supporting the wall by ties and anchorages, (v) increasing the number of anchors, and (vi) increasing the anchor's cross section. Almost all research on improvement of the stability of quay walls are involved in the above-mentioned techniques. However, most of the mentioned techniques require large eŠorts and time, especially in the case of an existing quay wall. i)
ii) iii)
Geotechnical Engineer, Maunsell Australia New Zealand Asia, Australia (formerly Research Engineer, Soil Stabilization Division, Port and Airport Research Institute, Japan). Associate Professor, Yokohama National University, Japan. Director, Geotechnical and Structural Engineering Department, Port and Airport Research Institute, Japan (kitazume＠pari.go.jp). The manuscript for this paper was received for review on August 27, 2007; approved on May 28, 2008. Written discussions on this paper should be submitted before March 1, 2009 to the Japanese Geotechnical Society, 4-38-2, Sengoku, Bunkyoku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month. 563
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CENTRIFUGE MODEL TESTS Geotechnical centrifuge, Mark-II (Kitazume and Miyajima, 1996) in the Port and Airport Research Institute (PARI) was used to perform the model tests. The centrifuge has an eŠective radius of 3.8 m, maximum acceleration of 113 g and maximum payload of 2760 kg. Speciˆcations of the Mark-II centrifuge are listed in Table 1.
ent from that shown in Fig. 1. Through a series of centrifuge tests, a model sheet pile quay wall was used for the model grounds. The sheet pile having relatively low ‰exural rigidity was targeted, so that the eŠect of the DM improvement can be emphasized and evaluated accurately. The sheet pile was a 2 mm thick steel plate instrumented with 13 pairs of strain gauges, S1 to S13, on both sides. The ‰exural rigidity, EI, of the model sheet pile wall was
Model Set-up Figure 1 typically shows the schematic of the model set-up. A strong box of 600 mm in length, 410 mm in depth and 200 mm in width with a transparent front window was used for the tests. Figure 2 shows the photo of another model set-up whose CDM block size was diŠer-
Table 1.
Speciˆcations of Mark-II geotechnical centrifuge
Diameter of rotating arm Maximum eŠective radius Maximum acceleration Maximum payload Maximum capacity Maximum rate of rotation Main motor capacity
9.65 m 3.8 m 113 g 27.1 kN 3060 g.kN 163 rpm DC 450 kW
Fig. 1.
Fig. 2.
Model photo showing various elements
Schematic view of model set-up (in model scale)
STATIC STABILITY OF QUAY WALL Table 2.
Properties of Kaolin clay and Toyoura sand
Kaolin Clay Liquid limit, W L (%) Plastic limit, W P (%) Plastic index, IP (%) Speciˆc gravity, Gs Compression index, Cc Swelling index, Cs Coe‹cient of consolidation, Cv (m2/s) (cu/s?v)NC Critical state friction angle, q?crit
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Toyoura Sand 59.3 26.3 33.0 2.72 0.49 0.12 2.5×10－ 7 0.314 28.69
1.72×104 kNm. Prototype section of this plate becomes the Japanese standard sheet pile of type SP-II (Nippon Steel Corp., 1998). At the bottom of the strong box, the sheet pile wall was set on a 10 mm thick rough surfaced acrylic plate. At the top it was clamped with guide plates, so that it is ˆrmly ˆxed and remains vertical during the model preparation. The model sand ground of 60 mm thick was prepared by pouring dry Toyoura sand in such a way that the relative density of the sand layer becomes about 90z. To saturate the sand layer, water was fed from the bottom through water supply line carefully so as not to disturb the sand. The Kaolin clay was remolded at a water content of about 120z, approximately equal to 2 times the liquid limit and was de-aired. Properties of the Kaolin clay and Toyoura sand are shown in Table 2. Silicone grease was smeared on the walls of the strong box. The clay slurry was then poured over the saturated sand layer in the strong box. In both the sea-side and port-side, ˆlter paper and perforated loading plates were placed over the clay slurry. Pre-consolidation was carried out by compressing the clay with two bello-fram cylinders. The size of the perforated loading plate and ˆlter paper in the sea-side was 398 mm×200 mm and in the port-side 198 mm×200 mm (Fig. 1). Piston of the bello-fram cylinders that incorporated a load cell (20 kN capacity) was set at the center of the loading plates and bello-fram cylinders were clamped with the strong box. Since the loading plate covered almost all the surface of the clay and the walls of the strong box were smeared with grease, load from the pistons compressed the clay one dimensionally. The successive preliminary consolidation pressures applied were 1 kPa, 10 kPa, 30 kPa, 50 kPa, 100 kPa and 150 kPa. Primary consolidation was achieved in each stage. After having completed the preliminary consolidation, the perforated loading plate and ˆlter paper were removed. The surface of consolidated clay was skimmed oŠ to a depth of 160 mm. The strong box was then tilted against a wall and the front transparent window was opened. Horizontal holes were drilled in speciˆed location for inserting pore pressure transducers, P, and earth pressure gauges, E, through the clay by a small hand auger. By using guide tools, pressure transducers P and E were inserted horizontally. Each hole was ˆlled with deaired Kaolin slurry. The pore pressure transducer in the
Speciˆc gravity, Gs D10 (mm) D50 (mm) Coe‹cient of uniformity, Uc Coe‹cient of curvature, U?c Maximum void ratio emax Minimum void ratio emin Friction angle q?
2.65 0.15 0.19 1.56 0.96 0.992 0.624 42.09
sand layer was inserted near the surface carefully. Re‰ective blue colored beads of 6 mm diameter as optical targets were inserted through a template of 20 mm square openings ( see Fig. 2). The window was replaced and the strong box was set upright. The bello-fram cylinders were set again with 150 kPa consolidation pressure to recover the swelling and sensors holes. After releasing the pressure, a speciˆed area in sea-side adjacent to the sheet pile was excavated. Then cement treated Kawasaki clay which is called in this paper as CDM was poured into the excavation. In the tests, the CDM size was changed parametrically as shown in Table 3. For example, the CDM size in Fig. 2 was 10 m×4 m in prototype scale. To prepare the CDM, Kawasaki clay slurry with 130z water content was thoroughly mixed with Portland cement. Amount of Portland cement added was 40z of dry weight of Kawasaki clay. After ˆlling the excavation, su‹cient water was added on top of the clay and CDM for curing. At least seven days curing was allowed to gain su‹cient strength. The unconˆned compression strength qu of the CDMs are listed in Table 3. The unconˆned compression tests were carried out according to the standards of Japanese Geotechnical Society (JGS, 2000). Variation of curing period which ranged from 7 to 12 days aŠected the qu values that were reported in Table 3. To simulate the static earth pressure of backˆll soils, a horizontal loading jack was mounted on the top of the sand box so that the horizontal line load would be applied to the sheet pile during tests. Laser displacement transducers LDs for monitoring the displacement of the CDM and the clay ground, linear variable displacement transducers LVDTs for monitoring the vertical movement of the ground surface and de‰ection of the sheet pile wall at loading point, were ˆrmly set on top of the strong box as shown in Fig. 1.
Test Procedures and Conditions The strong box with the model ground was mounted on the swinging platform of the centrifuge. Centrifugal acceleration was increased up to 50 g. The consolidation in the centrifuge at 50 g was conducted until the degree of consolidation was estimated to have achieved 90z. At 50 g, a horizontal line load was applied gradually by the loading jack to the sheet pile quay wall in the seaward direction. As shown in Fig. 3, loading cycles were applied
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Table 3.
Test conditions in Prototype scale
Test cases
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
Case 7
Clay depth (m) CDM size(width×depth, m 2) qu of CDM (kPa)
8 0 ×0 —
8 10×8 920
8 10×4 617
8 2×4 1173
8 4×4 1536
8 8× 2 1333
8 4× 2 1020
same. All the test results in the following sections are presented in the prototype scale. RESULTS AND DISCUSSIONS
Fig. 3.
Cyclic load applied to the quay wall in Case 4
at several horizontal loads. Each cycle comprised 5 or 6 turns of loading and unloading with the jack speed of 3 mm/min. De‰ection of sheet pile quay wall, vertical movements of the ground surface at the sea-side, earth pressures at various elevations and strains on the surface of the sheet pile wall were monitored during the tests. The positions of the sensors are shown in Fig. 1. Still pictures of the model were taken in every turn of a loading cycle for observing the de‰ection of the wall and displacement of ground with respect to the targets' movement. In this paper, the results of seven centrifuge tests are presented to discuss the eŠects of the sea-side ground improvement on the static stability of the quay wall. The test conditions in the prototype scale are shown in Table 3. All of the test conditions are identical except for the size of the CDM block and the position and number of sensors. Number of sensors arranged for the Test Cases 4–7 was much more than that for the Test Cases 1–3, because the ground behaviour such as earth pressure distributions were investigated in detail for Cases 4–7. Static stability of unimproved and improved sea-side ground has been examined from the unimproved case (Case 1) and the improved cases. The eŠect of width of the CDM block is investigated from Cases 3, 4 and 5, which have the depth of CDM equal to 4 m, and Cases 6 and 7, which have the depth of CDM equal to 2 m. Having the same width of CDM, the in‰uence of the `‰oating type' and full-depth CDM block is likewise examined from Cases 2 and 3. CDM blocks in Cases 5 and 7 also have the same width but diŠerent depth. Cross-sectional area of CDM block in Cases 4, 7 and in Cases 5, 6 is
Undrained Shear Strength of the Clay Stratum In Japan, seashore generally consists of a thick clay layer underlain by a sand layer. In this study, an overconsolidated clay stratum was chosen to easily facilitate the model preparation and the quay wall numerical modeling. The maximum eŠective past pressure experienced by the clay is equal to the preliminary consolidation pressure of 150 kPa as described before. After preliminary consolidation, centrifugal consolidation was conducted on the clay stratum at 50 g. Data from the pore pressure transducers, P, and LVDT2 in the clay were used to estimate the degree of consolidation. Square root of time method was used to estimate the degree of consolidation. Time taken to achieve 90z consolidation in the centrifuge was about 4.5 hours. Since the depth of the clay stratum in all cases is the same (8 m), almost the same amount of consolidation settlement was observed. The clay stratum was found to settle about 0.40 m in the prototype scale. Pore pressure responses during centrifuge consolidation are typically shown in Fig. 4. The data obtained from Cases 4 and 5 are shown. Pore pressure transducer, P4, which was placed near the bottom of the clay stratum ( see Fig. 1), dissipated larger pore pressure than that of P3 and P2. The response from P1 and P5 are almost ‰at which were placed at the ground surface and at the bottom sand layer respectively. This indicates that constant hydrostatic pressure is available at the boundaries of the clay stratum during the test. Theoretical hydrostatic pressures are given in brackets in the ˆgure. Estimated undrained shear strength proˆle of the clay stratum thus consolidated is shown in Fig. 5. The undrained shear strength is estimated as follows. First, K0, was derived for the overconsolidated (OC) clay with a critical state friction angle q?＝28.6, following the equation presented by Mayne and Kulhawy (1982): K0(OC)＝(1－sin q?)OCRsin q?
(1)
where OCR is the overconsolidation ratio (s?p/s?v); the coe‹cient of in-situ earth pressure, and s?v and s?p are the current eŠective vertical stress and the past maximum vertical consolidation pressure respectively. Then, the undrained shear strength, cu, of the clay was derived from the formula of Wroth (1984):
STATIC STABILITY OF QUAY WALL
Fig. 4. Dissipation of excess pore pressure during the centrifuge consolidation stage (Cases 4 and 5)
Fig. 5. Undrained shear strength proˆle of the clay stratum of the model grounds
Ø »
cu cu ＝ s?v s?v
OCRm
(2)
NC
where NC＝normally consolidated clay, with an experimental value of (cu/s?v)NC＝0.314 and m＝0.75(＝(Cc -Cs)/Cc; see Table 2). Theoretical cu values thus obtained have been representatively compared with the test results for Cases 4–7. The cu values for Cases 1–3 were not investigated. To obtain the test results, the cu values were computed from the water content proˆle along the depth both in the sea-side and port-side. First, void ratio, e, and eŠective vertical stress, s?v, for the corresponding sample of water content were derived from the following relation ships:
e＝wGs e＝－0.189Ln(s?v)＋2.076
(3) (4)
Here Gs is the speciˆc gravity and w is the water content of fully saturated kaolin clay. Equation (4) is the e versus loges?v characteristic of the kaolin clay used in the test.
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Then the value of cu was computed from cu＝0.314s?v experimental relationship. After stopping the centrifuge, a few hours passed before sampling for water content. Although some swelling may have taken place in this period, which may result in a smaller cu values than those predicted by theory, the values derived from the test results compared fairly well with the theoretical cu values, which were predicted before the loading stage. The cu value of Case 4 is less than in other cases. This may be because of delayed sampling. The sampling was conducted after about 12 hours from the stopping of centrifuge, while samples of other cases were taken within about 2 to 5 hours. Since the methodology of preparing the model and centrifuging were identical, the cu proˆles are considered to be reasonably similar. The fact implies that the targeted undrained shear strength proˆle of the clay stratum was achieved through the tests.
De‰ection of Sheet Pile Quay Wall De‰ection of the quay wall is examined as the main index in describing stability. Figures 6(a) and (b) show the in-‰ight photo of Case 4 at the initial stage and 68 kN/m loading stage respectively. Various elements are marked in the ˆgures. Some de‰ection of the sheet pile wall from the vertical position can be seen in Fig. 6(b). Figure 7 shows the relationship between horizontal load, Fh, and de‰ection of quay wall at loading point. As mentioned before, the horizontal load induced by the loading jack represented the static earth pressure of back ˆll soils. In the study, about 40–50 kN/m of the static earth pressure was estimated by taking into account the thickness and the strength characteristics of the backˆll soils. Therefore, de‰ection at Fh＝45 kN/m, d45, is chosen to compare with the data of all cases and is tabulated in the ˆgure. De‰ection d45 of the unimproved ground of Case 1 is 0.47 m whereas full-depth CDM improved ground of Case 2 is 0.12 m. StiŠness of the full-depth improved ground becomes almost four times larger than that of the unimproved sea-side ground. Here stiŠness is indicated as horizontal load per unit de‰ection. Cases 4, 5, and 3 with the same depth of CDM (depth: 4 m) but diŠerent width (respective widths: 2 m, 4 m and 10 m) have d45 of 0.29 m, 0.13 m and 0.12 m respectively. Even though the width in Case 3 was more than double that of Case 5, the de‰ection was not decreased proportionally as decreased in Cases 4 and 5. The results indicate that in increasing the width or size of the CDM, a small amount of de‰ection of the quay wall will take place. This is deˆned here as the limit of least de‰ection. Cases 7 and 6 with the same depth of CDM (depth: 2 m) but diŠerent width (respective widths: 4 m and 8 m) have d45 value of 0.24 m, and 0.14 m respectively. The stiŠness oŠered by the quay wall in these cases is almost proportional with the width of CDM. Cases 2 and 3 having ‰oating or half-depth and full-depth CDM (with the same width of treated material) have d45 value of 0.12 m in each case. The eŠect of the depth of CDM is also investigated from Cases 5 and 7 which have the same width
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Fig. 6. In-‰ight photo of the model sheet pile quay wall of Case 4 showing: (a) initial condition before applying the load and (b) at the 68 kN/m loading stage
Fig. 7.
Load de‰ection relationship of the sheet pile quay wall
(＝4 m) but diŠerent depth (depth of CDMs: 4 m and 2 m). The values of d45 of these cases are found as 0.13 m and 0.24 m respectively. De‰ection is increased about double in the case with smaller depth CDM. Increasing the depth of CDM may have stiŠened the ground and reduced the wall de‰ection towards the limit of least de‰ection. Sectional-area wise performance of the CDM can also be compared from Cases 4, 7 and Cases 5, 6. Cases 4 and 7 having the same cross sectional-area (＝8 m2) show d45 values of 0.29 m and 0.24 m. And Cases 5 and 6 (area＝16 m2) show d45 values of 0.13 m and 0.14 m. Almost the same d45 values are observed in each group.
Fig. 8. Variation of shear stress ratio, (sh-sv)/2cu with the applied horizontal load, Fh
Earth Pressures Horizontal and vertical earth pressures around the CDM block and sheet pile quay wall were investigated in detail for Cases 4–7. Due to increasing the horizontal load, Fh, shear deformation of the foundation ground starts to take place. Gradual increasing trend of total horizontal pressure, sh, in the sea-side was observed during the loading stage. Variation of shearing stress ratio, (sh-sv)/2cu with the applied horizontal load, Fh is shown in Fig. 8. Here sh and sv are the total horizontal and ver-
STATIC STABILITY OF QUAY WALL
tical earth pressure respectively. The values of sh are obtained from the earth pressure gauges, E, placed along the depth and the values of sv are calculated by considering the soil densities and the water level. The cu values are determined from the water content proˆle of the clay as stated in Fig. 5. With the de‰ection of the quay wall, rising trends of shear stress ratio are found in the clay. Figure 9 shows the response of vertical earth pressure below the CDM block at the Fh＝45 kN/m loading stage. Earth pressure gauges (E7¿E8, Fig. 1) were set below the CDM to measure the vertical pressures. Rotation of CDM block during the loading stage can be understood by comparing the initial (ini.) and ˆnal values of vertical earth pressure. All of the cases show the deviation from the initial line with an indication of the seaward rotation
Fig. 9. Vertical earth pressure observed below the CDM block at the initial (ini.) and the 45 kN/m loading stage
Fig. 10.
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of the CDM block. Movement of the CDM block during the loading stage was monitored by the laser displacement transducers (LD2 and LD3, Fig. 1). In all cases except for Case1, the horizontal movement of the CDM block was measured and in Cases 4–7 vertical movement of the CDM block was also measured. Figures 10(a) and (b) show the horizontal and vertical displacement of a point on the CDM block with the applied load, Fh. The monitored point is (7/8)W away from the sheet pile wall ( see the inset ˆgure). Here W is the width of the CDM block. Horizontal displacement at 45 kN/m loading, dh45 and vertical displacement at 45 kN/m loading, dv45 are also shown in the ˆgures. Comparing the values of dh45 and dv45, the values of the de‰ection of quay wall at loading point, dh ( see Fig. 7) are found to be relatively larger. Case 4 shows the largest dh45 which is 0.12 m and Case 2 shows the smallest value which is 0.002. Horizontal displacements of Cases 2 and 3 are found negligible. Case 4 with the smallest width CDM shows larger displacement both horizontally and vertically. Cases 4 and 5 with 4 m depth CDM show larger vertical displacement than that of Cases 6 and 7 which are having 2 m depth CDM.
Bending Moments, Displacements of Sheet Piles Bending moments are derived from the responses of the strain gauges (S) along the sheet pile wall ( see Fig. 1). Figures 11(a) and (b) show the bending moment and de‰ection distributions of the sheet pile quay wall at the 45 kN/m loading stage derived from all cases. The de‰ection distributions were obtained by conducting two successive integrations on the functions ˆtted to the bending moment distributions. Here quantic spline functions were used to ˆt the bending moment test points as shown in Fig. 11(a). In the ˆgure the spline functions are shown by the curves and the test points are shown by the markers.
Movement of the CDM block during the loading stage: (a) horizontal displacement and (b) vertical displacement of the CDM block
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Fig. 11.
Bending moments and de‰ection distributions of the sheet pile quay walls at the 45 kN/m loading stage
Maximum bending moment experienced by all cases is listed in the ˆgure. Almost similar pattern of bending moment is developed in all cases. However, interaction among the CDM, the sheet pile wall and the clay reduces the bending moments in accordance with the size of the CDM block. For example, the maximum bending moment experienced by the unimproved case (Case 1) is 215 kN-m whereas the cases with improved sea-side ground show much smaller value. Maximum bending moments in the improved cases take place at the ground surface and in the unimproved case it takes place below the ground level. Maximum bending moments in the cases with CDM depth equal to 4 m ranges from 121 to 145 kN-m and in the cases with CDM depth equal to 2 m ranges from 125 to 147 kN-m. The trends of Cases 4 and 7 which have the smallest size CDM show a curvature like the unimproved case. As shown in Fig. 11(b), ˆrm ˆxity at the bottom part, gradual bending near the ground surface and maximum de‰ection at the top can be visualized from the de‰ection distribution of the sheet pile quay wall. De‰ection at the loading point which is 3.5 m above the ground level was recorded at 45 kN/m loading and is shown in Fig. 11(b). Ratio of the test data to the spline data, dtest/dspline, is listed in the ˆgure. The ratios fall in a narrow band and range from 1.1 to 1.4. De‰ection distributions of the sheet pile quay wall show good agreement with the test points.
Horizontal Subgrade Reaction Two successive diŠerentiations of spline-curve of the
bending moment distributions give the horizontal subgrade reaction on the wall below the ground level which is shown in Fig. 12(a). In the ˆgure, negative horizontal subgrade reaction represents that the passive pressure acting on the sheet pile is larger than the active pressure acting on it. Maximum subgrade reaction is observed at the ground level for the improved grounds and it reduces toward the bottom of the sheet pile quay wall to zero or very small value. Maximum subgrade reaction in the unimproved case (Case 1) is found as －43 kN/m2/m whereas in the improved cases it ranges from －60 kN/m2/m to －125 kN/m2/m. For each stage of loading the data set of elevation versus displacement, bending moment and horizontal subgrade reaction were derived with the help of spline functions. For elevation equal to zero, which is the ground level, the displacement and horizontal subgrade reaction from all stages of loading were picked up. Figure 12(b) shows the relationship between the horizontal subgrade reaction and the displacement at the ground surface thus obtained. Then linear least square ˆtting is attempted for the curve of each case with an equation to obtain the coe‹cient of horizontal subgrade reaction, ks, at the ground surface, although nonlinear relationships are observed especially for Cases 1, 4 and 7. For these cases the eŠect of clay stiŠness might be larger rather than that of CDM stiŠness. In the study, the nonlinearity is ignored for the simplicity. However the change of ks with the increase of the displacement should be studied in detail in
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Fig. 12. Determination of horizontal subgrade reaction at the 45 kN/m loading stage: (a) horizontal subgrade reaction along depth and (b) subgrade reaction versus displacement at the ground surface
about full depth. The value of ks at ground surface in the improved cases ranges from 625 to 11000 kN/m3 whereas ks of the unimproved case is 160 kN/m3. The ks in the improved zone increases almost linearly, except for the full depth case (Case 2) where decreasing trend was observed beyond 4 m depth. The reason for the trend of Case 2 is not well understood, but the strength of CDM might be relatively scattered within the block as the largest volume of cement slurry was prepared among all cases. The eŠect of width of the CDM on the coe‹cient of horizontal subgrade reaction, ks, is shown in Fig. 14. For the cases with 4 m depth CDM, the width eŠect is representatively considered at the depth of 0 m, 2 m and 4 m (Fig. 14(a)). Likewise the cases with 2 m depth CDM, the width eŠect is considered at the depth of 0 m, 1 m and 2 m (Fig. 14(b)). With the same depth of CDM, ks increases almost proportionally with increase in width of the CDM, as shown in the ˆtting equations. From the ˆtting relationship between the ks and width of the CDM as shown in the ˆgures, ks corresponding to any other widths are determined and used in the numerical method as described later. Fig. 13. Coe‹cient of horizontal subgrade reaction, ks along depth at the 45 kN/m loading stage
NUMERICAL METHOD
the further study to input ks more precisely for numerical simulations. In the same way as shown in Fig. 12(b), the coe‹cient of horizontal subgrade reaction, ks, is also determined along the depth. Figure 13 shows the coe‹cient of horizontal subgrade reaction, ks thus obtained, against depth. The resistance from the CDM can be visualized from the ˆgure up to a depth of about 4 m for Cases 3, 4, 5 and 2 m for Cases 6, 7, except for Case 2 with up to
Formation of Equations Elastic equilibrium of forces acting on the horizontal slice of sub-divided layers below the ground level is considered. Portion of the sheet pile quay wall above the ground level is treated simply as a cantilever beam. In simulation of the centrifuge model condition, a concentrated force Fh is applied at 3.5 m above the ground level in the same way as the centrifuge model tests. Figure 15 schematically shows the position of Fh and sub-divided layers in the clay stratum. According to the
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Fig. 14. Variation of coe‹cient of horizontal subgrade reaction, ks with the width of CDM block: (a) depth of the CDM block is 4 m and (b) depth of the CDM block is 2 m
boundary conditions and Q＝P/(24EI). Behavior of sheet pile quay wall below the ground level is modeled by the method of horizontal subgrade reaction (Chang, 1937). Underground de‰ection of the sheet pile quay wall can be expressed as:
EI
d 4y ＝－ksy dx4
(7)
where ks is the coe‹cient of horizontal subgrade reaction on the sheet pile wall. General solution of Eq. (7) is obtained as:
y＝Cie bx cos bx＋Cje bx sin bx＋ Cke－bx cos bx＋Cle－bx sin bx
(8)
where b＝4 ks/(4EI), Ci¿Cl are integral constants obtained from the boundary conditions in each layer of the clay ground (§C1¿C16 are used in the application). Similar general solution can be written as Eq. (9) for the sand layer with the integral constants R1 to R4. Fig. 15.
y＝R1e bx cos bx＋R2e bx sin bx＋ R3e－bx cos bx＋R4e－bx sin bx
Numerical model of the sheet pile quay wall
theory of elastic beam, equation of de‰ection, y of the sheet pile quay wall above the ground level is obtained as follows:
EI
d 4y ＝P dx4
(5)
where EI is the ‰exural rigidity of the sheet pile, P is the pressure due to external loads applied to sheet pile, x is the vertical coordinate of elevation and y is the de‰ection of the sheet pile as shown in Fig. 15. General solution of Eq. (5) is obtained as:
y＝A1x3＋A2x2＋A3x＋A4＋Qx4
(6)
where A1¿A4 are integral constants obtained from the
(9)
Boundary Conditions and Solutions To put the appropriate value of ks to the equations, the clay ground has been divided into four layers. Number of layers can be varied according to ˆeld conditions and required degree of accuracy of the prediction. As shown in Fig. 15, integral constants used in this model are A1¿A4, C1¿C16 and R1¿R4. In the ˆgure, y, y?, y!, y?!, y!! represent zero, 1st, 2nd, 3rd, and 4th degree of derivative whose respective physical meanings are de‰ection, angle of de‰ection, bending moment, shear force and distributed load on the sheet pile quay wall. At the top of the wall: y! top＝0, y? t! op＝Fh, P＝0 and two equations are formed with constants A1¿A4. Left hand sides of these two equations are the 2nd and 3rd deriva-
STATIC STABILITY OF QUAY WALL
tive of Eq. (6). At each of the ˆve layer-interfaces, four equations are formed with the following boundary conditions: yU＝yL, y?U＝y?L, y! !＝y?L!; where `U' U＝y! L, y? U represents upper layer and `L' the lower layer of a particular layer-interface. In layer-interface 1 (ground level), diŠerent degrees of derivative of Eqs. (6) and (8) are set on both sides of the boundary equations. A1¿A4, and C1¿C4 appears in the interface 1. Likewise C1¿C16 and R1¿R4 are appeared in the equations of the remaining interfaces. In the ˆve layer-interfaces, twenty equations are formed. At the bottom of the wall: ybot＝0, y! bot＝0 and two equations are formed with constants R1¿R4. Left hand side of these boundary conditions is the zero and 2nd derivative of Eq. (9). Twenty four unknowns are then derived from the set of twenty four equations. Particular solutions are obtained by using these constants (unknown) to the equation of de‰ection in each layer.
Input Parameters The coe‹cient of horizontal subgrade reaction, ks can be obtained from the relationships of various parameters like shear modulus, Poisson's ratio, shear strength, friction angle, and cohesion along the depth of the ground. For example, the ks can be determined by the following model of Bowles (1974). ks＝As＋Bs z n
(10)
where As＝ constant for structural member, Bs＝ coe‹cient for depth, z＝depth of interest below ground and n＝ exponent to give ks the best ˆt (if load test or other data are available). Bowles (1974) has shown that this model is reasonably accurate by using it to analyze full-scale ˆeld walls and for reanalyzing model sheet pile walls reported by TschebotarioŠ (1949) and by Rowe (1952). Based on the concept of this model, the CDM zone can be treated either as a layer like soil or a hybrid zone whose
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property will be obtained by considering the interaction among the sheet pile wall, the CDM and the surrounding clay. Here, two diŠerent methods to determine the coe‹cient of horizontal subgrade reaction, ks are introduced. I. Simpliˆcation with CDM area: This method is described in Fig. 16. Largest displacement of the sheet pile quay wall was observed in the unimproved case (Case 1). Since the displacement of the quay wall in the deeper ground is very small and ks is very sensitive to the magnitude of the displacement, the ks values below about 5 m depth are di‹cult to be precisely determined with the linear ˆtting although the results are shown in the ˆgure. As a result, the unreasonable change of the ks with the depth below about 5 m depth is observed. Hence, in the study, test data of ks until about 5 m depth is considered to extrapolate the ks variation with depth in unimproved case (Fig. 16(a)). The relationship derived for the unimproved ground is:
ks＝100＋235z
(11)
where z is the depth from the ground level. All of the ks data of improved cases are normalized by the cross sectional area, A, and unit area, A0, of the CDM block and plotted against the depth, z (Fig. 16(b)). Here unit area, A0 of 1 m2 is chosen. The average trend line gives the following relationship:
ks＝(133＋132z)A/A0
(12)
From these two equations (Eqs. (11) and (12)) simpli-
Table 4.
Parameters used in Numerical Analysis Steel Sheet Pile Wall
I (m4/m) E (kN/m2) EI (kN.m)
8333×10－ 8 2.1×108 17170
Fig. 16. Simpliˆcation of coe‹cient of horizontal subgrade reaction, ks: (a) simpliˆed ks along depth for the unimproved case, (b) ks normalized by sectional area of the CDM block, A1, (A0＝unit area) along depth and (c) simpliˆed ks along depth for 4 m depth CDM
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Fig. 17. Simpliˆcation of coe‹cient of horizontal subgrade reaction, ks: (a) simpliˆed ks along depth for the unimproved case, (b) ks normalized by width of the CDM block, W , (W0＝unit width) along depth and (c) simpliˆed ks along depth for 8 m depth CDM
Fig. 18. EŠect of the width of CDM block at the 45 kN/m loading: (a) simpliˆed calculation with respect to the sectional area of the CDM block and (b) simpliˆed calculation with respect to the width of the CDM block
ˆed ks values are produced along the depth and shown in Fig. 16(c). In the ˆgure, simpliˆed ks values are shown for various width of a 4 m depth CDM block. Below the CDM block, the ks value is assumed as the value of unimproved case (Eq. (11)). II. Simpliˆcation with CDM width: This method is described in Fig. 17. The simpliˆed relationship derived for the unimproved ground is same as described in the ˆrst method with Eq. (11). All of the ks data of improved cases are normalized by the width, W, and unit width, W 0, of the CDM block and plotted against the depth, z (Fig. 17(b)). Here unit width, W0 of 1 m is chosen. The average trend line gives the following relationship:
ks＝(200＋850z)W/W0
(13)
From Eqs. (11) and (13) simpliˆed ks values are pro-
duced along the depth and shown in Fig. 17(c). In the ˆgure, simpliˆed ks values are shown for various width of an 8 m depth CDM block. Below the CDM block, the ks value is assumed as the value of unimproved case (Eq. (11)). Steel sheet pile properties used in numerical method are listed in Table 4. Prototype section of a steel sheet pile was considered in deriving the modulus, E and ‰exural rigidity, EI. NUMERICAL RESULTS De‰ection of the quay wall is obtained numerically for various width and depth of the CDM by using the ks value. The ks values are obtained from the above methods. Figure 18 shows the relationship between
STATIC STABILITY OF QUAY WALL
de‰ection at loading point at the 45 kN/m loading stage and the width of the CDM block. Centrifuge test data and numerical predictions are plotted in the ˆgure. Simpliˆed calculation with respect to the CDM area (method-I) is shown in Fig. 18(a) for the depth of 2 m, 4 m and 8 m. Reasonable predictions are observed throughout the width of the CDM. This ˆgure implied that beyond 4 m width, CDM of 2 m depth is more e‹cient than that of 4 m depth or full-depth in reducing the de‰ection of the sheet pile quay wall. Since Cases 2 and 3, which have the same width but diŠerent depths (full- and halfdepth), show the same de‰ection, from an economical feasibility point of view half-depth or the ‰oating type CDM is more e‹cient for the ˆeld situation. Both of the experiment and numerical simulation results indicate that the improved grounds sustain the de‰ection of the sheet pile, but that there is still a certain degree of de‰ection even in the full-depth case. This is considered due to a limitation of the eŠect of sea-side ground improvement, although lower displacement might be achieved when the rigidity of the sheet pile is relatively higher. Simpliˆed calculation with respect to the CDM width (method-II) is shown in Fig. 18(b) for the depth of 2 m, 4 m and 8 m. These three lines show a tendency of merging at about 6 m width of the CDM. It means beyond 6 m width, de‰ection is same for any depth of the CDM and the lowest de‰ection is about 0.2 m. Numerical prediction with area based simpliˆcation (method-I) agrees well with the test data and shows better prediction than that of width based simpliˆcation (method-II). These facts indicate that the concept of the simple numerical modeling shown here would work very well to predict actual ˆeld behaviour of improved ground, although the input parameters such as the coe‹cients of subgrade force reaction should be carefully determined based on ˆeld tests and/or laboratory tests. CONCLUSIONS The eŠects of sea-side ground improvement on the static stability of existing sheet pile quay walls have been presented with reference to the load-de‰ection behavior, eŠect of size of cement deep mixing zone, and wall de‰ection, bending moment, horizontal subgrade reaction and earth pressure distributions in a series of centrifuge tests. The eŠects of sea-side ground improvement on the static stability of existing sheet pile quay wall also have been numerically predicted. Simple numerical predictions compare satisfactorily with the centrifuge test results. The method can be used for predicting the important design parameters like de‰ection of the sheet pile quay wall. The conclusions of the study are as follows: 1. Compared with the case of a wall embedded in unimproved ground, signiˆcant resistance against horizontal load was observed to develop in the CDM improved cases, i.e., the horizontal de‰ection was eŠectively reduced.
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2. The horizontal de‰ection of the model quay wall decreased with increase in width of the CDM area until it reaches a certain limit. 3. In the cases of improved ground, the maximum bending moment of the model quay wall was reduced up to about half of the value of the unimproved ground case. 4. The horizontal load was mainly resisted by the improved soil zone, which oŠered large horizontal subgrade reactions. 5. Seaward rotational tendency of the CDM block was observed in the improved ground cases. 6. Proposed numerical model of the sheet pile quay wall can predict the eŠect of the sea-side ground improvement and prediction by the numerical model agrees fairly well with the results of centrifuge model tests. These indicate that the concept of the simple numerical modeling shown here would work very well to predict actual ˆeld behaviour of improved ground, although the input parameters such as the coe‹cients of subgrade force reaction should be carefully determined based on ˆeld tests and/or laboratory tests. ACKNOWLEDGEMENTS The authors are thankful to Mr. K. Maruyama who cooperated in this research signiˆcantly. The authors also acknowledge the Ministry of Land, Infrastructure and Transport, Japan for providing the ˆnancial support in pursuing the study. REFERENCES 1) Bowles, J. E. (1974): Analytical and Computer Methods in Foundation Engineering, McGraw-Hill Book Co., NY. 2) Chang, Y. L. (1937): Discussion of `Lateral pile loading tests by L.B. Feagin'. Transactions of ASCE, 102, 272–278. 3) Coastal Development Institute of Technology (CDIT), Japan (2002): The Deep Mixing Method-Principle, Design & Construction, Balkema, Rotterdam. 4) Japanese Geotechnical Society (JGS), Japan, (2000): Standards of Japanese Geotechnical Society for Laboratory Shear Test, JGS, Tokyo, Japan. 5) Kitazume, M. and Miyajima, S. (1996): Development of PHRI Mark II Geotechnical centrifuge, Technical Note of the Port and Harbour Research Institute, (817), 4–33. 6) Mayne, P. W. and Kulhawy, F. H. (1982): K0–OCR relationships in soil, Journal of Geotechnical Engineering Div., ASCE, 108(G76), 851–872. 7) Nippon Steel Corporation, Japan (1998): Steel Sheet Pile–Design and Manufacture (Kou Ya ita) Nippon Steel Corporation Handbook, p. 465 (in Japanese). 8) PIANC, International Navigation Association (2001): Seismic Design Guidelines for Port Structures, Balkema, Rotterdam. 9) Rowe, P. W. (1952): Anchored sheet pile walls, Proc. Institution of Civil Engineers, 1(1), 27–70. 10) TschebotarioŠ, G. P. (1949): Large scale earth pressure tests with model ‰exible bulkheads, Final Report to Bureau of Yards and Docks U.S. Navy, Princeton University. 11) Wroth, C. P. (1984): The interpretation of in situ soil tests, 24th Rankine lecture, Geotechnique, 34(4), 449–489.