- Văn bản
- Lịch sử
Table 7. Analysis parameters of clu
Table 7. Analysis parameters of clump.
Property
Particle size (Long axis)
(Short axis)
Density of soil particles,s
Friction angle between clumps,
Normal and tangential spring
stiffness between clumps
Value
5.5 mm 4.0 mm
2.73 ton/m3 35 degrees
5 105N/m
Normal and tangential spring 5 105 N/m
stiffness between clump and wall
observation in centrifuge tests, the particle size used in DEM should be less than 3 mm. However, the use of clumps consisting of 2 spheres having a diameter of 3 mm took a very long calculation time. Hence, the authors decided to use peanut-shaped clumps having a diameter of 4 mm as shown in Figure 54.
The values of normal spring, tangential spring and the friction coefficient between the clumps were determined through matching analyses of the element tests (results are shown later). The identified analysis parameters are summarised in Table 7. Note that local damping value (Itasca 2003) of 0.7 was employed and any other damping was not used through the analyses.
Calculation timestep used was 5s for all the DEM
analyses except for the analysis of direct shear test
where timestep of 2s was used.
Figure 53. Distributions of shear stresses down the inter-
nal pile surface.
Figure 54. Peanut-shaped clump used in the DEM analyses.
practically impossible, in view of capacity and time of calculation. In centrifuge tests, no scale effect was observed for model footings that had ratios of footing diameter to soil particle size ranging from 30 to 180 (Ovesen 1979).
Diameter of the soil plug in parametric calculation in this paper is about 100 mm. According to the above
166
Maximum density and minimum density tests were
carried out. The minimum density test followed the standard method by Japanese Geotechnical Society (1992). On the other hand, non-standard method was used in the maximum density test. In the standard method, the sand is poured into the mould (40 mm high) with a collar (20 mm high) in 10 layers, and 100 impacts are applied to the mould after pouring each soil layer. In non-standard method used in this research, the sand was poured into the mould with the collar at once, and 1000 impacts were applied to the mould, as shown in Figure 55. Figure 55 shows the ana- lytical models for the minimum and maximum density tests. The hopper, mould and collar were modelled by 'wall elements'. A total of five DEM analyses of min- imum and maximum density tests were carried out.
Clumps were created every time randomly inside the hopper (Fig. 55(a)). Afterwards, the hopper was pulled-up at a speed of 5 mm/s. After the clumps had dropped into the mould with collar (Fig. 55(b)), the clumps in the collar were deleted (Fig. 55(c)) to
obtain the maximum void ratio, emax.
DEM analysis of the maximum density test was
started from the state of Figure 55(b). In order to model the impact on the mould, sinusoidal horizontal displacement having a frequency of 5 Hz and an amplitude of 5 mm was applied to the mould. The
Table 9. The calculated results of maximum density tests.
Analysis
1st
2nd 3rd 4th 5th
Mean
Minimum void ratio
0.678 0.672 0.682 0.671 0.676
0.676
Maximum dry density
1.629 ton/m3 1.635 ton/m3 1.625 ton/m3 1.636 ton/m3 1.631 ton/m3
1.631 ton/m3
Figure 55. Analysis models used for minimum density test and maximum density test.
Table 8. The calculated results of minimum density tests.
Figure 56. The calculated and experimental results of maximum density tests until 200 shaking cycles.
Analysis
1st
2nd 3rd 4th 5th
Mean
Maximum void ratio
0.976 0.946 0.944 0.962 0.960
0.958
Minimum dry density
1.384 ton/m3 1.405 ton/m3 1.406 ton/m3 1.394 ton/m3 1.395 ton/m3
1.397 ton/m3
shaking direction was changed by 36 degrees every
10 cycles of shaking, to simulate the test procedure.
The results of DEM analyses of the minimum den- sity tests are summarised in Table 8. The mean values of maximum void ratio and minimum dry density are 0.958 and 1.397 ton/m3, respectively. These values may be comparable with those obtained from the min- imum density test (see Table 6).
The results of DEM analyses of the maximum dens- ity tests are compared with the test results in Figure 57. Changes in void ratio are plotted against the number of shaking cycles in Figure 57 until the shaking cycle of 200, although 1000 shaking cycles were analysed. The void ratio rapidly decreased with increasing shaking cycle to about 100 cycles and then almost levelled off for further shaking cycles in the non-standard maximum density tests. The results of DEM analyses simulate this measured behaviour well. The minimum void ratio and the corresponding maximum dry density obtained from the DEM analyses are summarised in Table 9.
167
Figure 57. The calculated and experimental results of one- dimensional compression test.
The one-dimensional compression tests and the direct shear tests of the sand were carried out using the consolidation ring and the shear ring having an inner diameter of 60 mm and a height of 20 mm. However, in the DEM analyses, the height of the soil specimen was set at 40 mm in the DEM analyses, because the size of clump (Fig. 54) seemed to be large compared to the actual ring height of 20 mm.
The friction between the clumps and the walls was neglected. The initial void ratio prior to compression was set at 0.693 in the DEM analysis. In the process of DEM analysis of the one-dimensional compression test, a total of 8 loading steps, 9.8 to 1254.4 kPa, were applied to the top loading plate.
Figure 57 shows the comparison between the one- dimensional test results and the DEM analysis results.
Figure 58. DEM modelling of direct shear test.
It can be seen from the figure that the test results are well simulated by the DEM analysis.
Direct shear test was carried out with a vertical stress of 78.4 kPa for the dense sand having
Dr 93% (e 0.608). In the DEM analysis, the ini-
tial void ratio prior to compression was set at 0.693
and vertical stress of 78.4 kPa was applied to the specimen through the top loading plate. After com- pletion of the analysis of the vertical loading, hori- zontal displacement was applied to the upper ring at a displacement rate of 0.4 mm/min (Fig. 58).
Figure 59 shows the comparison between the results of the direct shear test and the DEM analysis. Figure 59(a) shows the relationships between the shear displacement and the shear stress. Figure 59(b) shows the relationships between the shear displace- ment and the vertical strain. It can be seen from Figure 59(a) that the experimental result was simu-
lated well by the DEM analysis and thatpeak value is
estimated as 49 degrees that is larger than the grain-
to-grain friction angle, of 35 degrees. The dila-
tancy behaviour observed in the experiment was also
simulated well by the DEM analysis (Fig. 59(b)).
As the element tests of the sand were well simu- lated by DEM as mentioned in the above, DEM analyses of the push-up load tests were attempted using the analytical parameters identified through DEM analyses of the element tests.
Figure 60 shows the analysis model of push-up loading of soil plug. Considering axi-symmetrical
168
Figure 59. The calculated and experimental results of direct shear test.
Figure 60. Analysis model of push-up load test of soil plug.
Figure 61. Results of DEM simulations of push-up load
tests of soil plug.
condition of the problem, only one-fourth of the pile and the soil plug were modelled. The pile was mod- elled by rigid walls. Hence the deformation of the pile body was not taken into account in the analysis. The soil particles (clumps or spheres) were generated inside the model pile in order to create the soil plug. Then, self-weight analysis was conducted without friction between the soil and the inner pile shaft. Finally, the analysis of push-up loading was carried out by applying an upward velocity of 5 mm/s to the rigid loading plate, taking into account the friction between the soil and the inner pile shaft.
Figure 61 shows the comparisons of the results of the push-up load tests and the DEM analyses. In the DEM analyses, coefficient of friction between the
pile and the soil particle,, was set to be 0.6.
Figure 62 shows the distributions of inner shaft
resistance calculated from the DEM analyses, com- pared with the experimental results.
The results of Figures 61 and 62 may encourage the use of DEM to investigate behaviours of the pile and the ground which accompany large deformation and failure of the ground.
Figure 63 shows the distributions of mobilised coefficient of friction between the soil and the inner pile shaft calculated from the DEM analyses. Here, the mobilised coefficient of friction is defined as the ratio of shear stress (inner shaft resistance) to the radial stress acting on the inner pile shaft. The coeffi- cient of friction between the soil particle and the pile was set to be 0.6. However, the mobilised coefficient of friction ranges from 0.4 to 0.55 which are less than the coefficient of friction between the soil particle and the pile. It may be inferred from this result that rotation of the soil particles adjacent to the pile shaft, rather than slippage between the soil particles and the pile shaft, controls the inner shaft resistance.
169
Figure 62. Distributions of inner shaft resistance calcu- lated from the DEM analyses.
The authors are attempting DEM analyses of the penetration of an open-ended pipe pile into the ground from its surface, using analytical models as shown in Figure 64, where the pile is modelled by the rigid walls or particles to allow for the deformation of the pile.
6 BARRIERS IN APPLIC
Property
Particle size (Long axis)
(Short axis)
Density of soil particles,s
Friction angle between clumps,
Normal and tangential spring
stiffness between clumps
Value
5.5 mm 4.0 mm
2.73 ton/m3 35 degrees
5 105N/m
Normal and tangential spring 5 105 N/m
stiffness between clump and wall
observation in centrifuge tests, the particle size used in DEM should be less than 3 mm. However, the use of clumps consisting of 2 spheres having a diameter of 3 mm took a very long calculation time. Hence, the authors decided to use peanut-shaped clumps having a diameter of 4 mm as shown in Figure 54.
The values of normal spring, tangential spring and the friction coefficient between the clumps were determined through matching analyses of the element tests (results are shown later). The identified analysis parameters are summarised in Table 7. Note that local damping value (Itasca 2003) of 0.7 was employed and any other damping was not used through the analyses.
Calculation timestep used was 5s for all the DEM
analyses except for the analysis of direct shear test
where timestep of 2s was used.
Figure 53. Distributions of shear stresses down the inter-
nal pile surface.
Figure 54. Peanut-shaped clump used in the DEM analyses.
practically impossible, in view of capacity and time of calculation. In centrifuge tests, no scale effect was observed for model footings that had ratios of footing diameter to soil particle size ranging from 30 to 180 (Ovesen 1979).
Diameter of the soil plug in parametric calculation in this paper is about 100 mm. According to the above
166
Maximum density and minimum density tests were
carried out. The minimum density test followed the standard method by Japanese Geotechnical Society (1992). On the other hand, non-standard method was used in the maximum density test. In the standard method, the sand is poured into the mould (40 mm high) with a collar (20 mm high) in 10 layers, and 100 impacts are applied to the mould after pouring each soil layer. In non-standard method used in this research, the sand was poured into the mould with the collar at once, and 1000 impacts were applied to the mould, as shown in Figure 55. Figure 55 shows the ana- lytical models for the minimum and maximum density tests. The hopper, mould and collar were modelled by 'wall elements'. A total of five DEM analyses of min- imum and maximum density tests were carried out.
Clumps were created every time randomly inside the hopper (Fig. 55(a)). Afterwards, the hopper was pulled-up at a speed of 5 mm/s. After the clumps had dropped into the mould with collar (Fig. 55(b)), the clumps in the collar were deleted (Fig. 55(c)) to
obtain the maximum void ratio, emax.
DEM analysis of the maximum density test was
started from the state of Figure 55(b). In order to model the impact on the mould, sinusoidal horizontal displacement having a frequency of 5 Hz and an amplitude of 5 mm was applied to the mould. The
Table 9. The calculated results of maximum density tests.
Analysis
1st
2nd 3rd 4th 5th
Mean
Minimum void ratio
0.678 0.672 0.682 0.671 0.676
0.676
Maximum dry density
1.629 ton/m3 1.635 ton/m3 1.625 ton/m3 1.636 ton/m3 1.631 ton/m3
1.631 ton/m3
Figure 55. Analysis models used for minimum density test and maximum density test.
Table 8. The calculated results of minimum density tests.
Figure 56. The calculated and experimental results of maximum density tests until 200 shaking cycles.
Analysis
1st
2nd 3rd 4th 5th
Mean
Maximum void ratio
0.976 0.946 0.944 0.962 0.960
0.958
Minimum dry density
1.384 ton/m3 1.405 ton/m3 1.406 ton/m3 1.394 ton/m3 1.395 ton/m3
1.397 ton/m3
shaking direction was changed by 36 degrees every
10 cycles of shaking, to simulate the test procedure.
The results of DEM analyses of the minimum den- sity tests are summarised in Table 8. The mean values of maximum void ratio and minimum dry density are 0.958 and 1.397 ton/m3, respectively. These values may be comparable with those obtained from the min- imum density test (see Table 6).
The results of DEM analyses of the maximum dens- ity tests are compared with the test results in Figure 57. Changes in void ratio are plotted against the number of shaking cycles in Figure 57 until the shaking cycle of 200, although 1000 shaking cycles were analysed. The void ratio rapidly decreased with increasing shaking cycle to about 100 cycles and then almost levelled off for further shaking cycles in the non-standard maximum density tests. The results of DEM analyses simulate this measured behaviour well. The minimum void ratio and the corresponding maximum dry density obtained from the DEM analyses are summarised in Table 9.
167
Figure 57. The calculated and experimental results of one- dimensional compression test.
The one-dimensional compression tests and the direct shear tests of the sand were carried out using the consolidation ring and the shear ring having an inner diameter of 60 mm and a height of 20 mm. However, in the DEM analyses, the height of the soil specimen was set at 40 mm in the DEM analyses, because the size of clump (Fig. 54) seemed to be large compared to the actual ring height of 20 mm.
The friction between the clumps and the walls was neglected. The initial void ratio prior to compression was set at 0.693 in the DEM analysis. In the process of DEM analysis of the one-dimensional compression test, a total of 8 loading steps, 9.8 to 1254.4 kPa, were applied to the top loading plate.
Figure 57 shows the comparison between the one- dimensional test results and the DEM analysis results.
Figure 58. DEM modelling of direct shear test.
It can be seen from the figure that the test results are well simulated by the DEM analysis.
Direct shear test was carried out with a vertical stress of 78.4 kPa for the dense sand having
Dr 93% (e 0.608). In the DEM analysis, the ini-
tial void ratio prior to compression was set at 0.693
and vertical stress of 78.4 kPa was applied to the specimen through the top loading plate. After com- pletion of the analysis of the vertical loading, hori- zontal displacement was applied to the upper ring at a displacement rate of 0.4 mm/min (Fig. 58).
Figure 59 shows the comparison between the results of the direct shear test and the DEM analysis. Figure 59(a) shows the relationships between the shear displacement and the shear stress. Figure 59(b) shows the relationships between the shear displace- ment and the vertical strain. It can be seen from Figure 59(a) that the experimental result was simu-
lated well by the DEM analysis and thatpeak value is
estimated as 49 degrees that is larger than the grain-
to-grain friction angle, of 35 degrees. The dila-
tancy behaviour observed in the experiment was also
simulated well by the DEM analysis (Fig. 59(b)).
As the element tests of the sand were well simu- lated by DEM as mentioned in the above, DEM analyses of the push-up load tests were attempted using the analytical parameters identified through DEM analyses of the element tests.
Figure 60 shows the analysis model of push-up loading of soil plug. Considering axi-symmetrical
168
Figure 59. The calculated and experimental results of direct shear test.
Figure 60. Analysis model of push-up load test of soil plug.
Figure 61. Results of DEM simulations of push-up load
tests of soil plug.
condition of the problem, only one-fourth of the pile and the soil plug were modelled. The pile was mod- elled by rigid walls. Hence the deformation of the pile body was not taken into account in the analysis. The soil particles (clumps or spheres) were generated inside the model pile in order to create the soil plug. Then, self-weight analysis was conducted without friction between the soil and the inner pile shaft. Finally, the analysis of push-up loading was carried out by applying an upward velocity of 5 mm/s to the rigid loading plate, taking into account the friction between the soil and the inner pile shaft.
Figure 61 shows the comparisons of the results of the push-up load tests and the DEM analyses. In the DEM analyses, coefficient of friction between the
pile and the soil particle,, was set to be 0.6.
Figure 62 shows the distributions of inner shaft
resistance calculated from the DEM analyses, com- pared with the experimental results.
The results of Figures 61 and 62 may encourage the use of DEM to investigate behaviours of the pile and the ground which accompany large deformation and failure of the ground.
Figure 63 shows the distributions of mobilised coefficient of friction between the soil and the inner pile shaft calculated from the DEM analyses. Here, the mobilised coefficient of friction is defined as the ratio of shear stress (inner shaft resistance) to the radial stress acting on the inner pile shaft. The coeffi- cient of friction between the soil particle and the pile was set to be 0.6. However, the mobilised coefficient of friction ranges from 0.4 to 0.55 which are less than the coefficient of friction between the soil particle and the pile. It may be inferred from this result that rotation of the soil particles adjacent to the pile shaft, rather than slippage between the soil particles and the pile shaft, controls the inner shaft resistance.
169
Figure 62. Distributions of inner shaft resistance calcu- lated from the DEM analyses.
The authors are attempting DEM analyses of the penetration of an open-ended pipe pile into the ground from its surface, using analytical models as shown in Figure 64, where the pile is modelled by the rigid walls or particles to allow for the deformation of the pile.
6 BARRIERS IN APPLIC
0/5000
Bảng 7. Phân tích các thông số của cụm. Bất động sản Kích thước hạt (trục dài) (Ngắn trục) Mật độ của đất hạt, s Ma sát góc giữa khối, Mùa xuân bình thường và tiếp tuyến độ cứng giữa khối Giá trị 5.5 mm 4.0 mm 2,73 tấn / m3 35 độ 5 105N/m Mùa xuân bình thường và tiếp tuyến 5 105 N/m độ cứng giữa cụm và tường quan sát trong máy ly tâm kiểm tra, kích thước hạt được sử dụng trong DEM nên là ít hơn 3 mm. Tuy nhiên, việc sử dụng các khối bao gồm 2 các lĩnh vực có đường kính 3 mm mất một thời gian rất dài tính toán. Do đó, các tác giả quyết định sử dụng đậu phộng-hình khối có đường kính 4 mm như minh hoạ trong hình 54. Các giá trị bình thường mùa xuân, mùa xuân tiếp tuyến và hệ số ma sát giữa các khối đã được xác định thông qua kết hợp các phân tích của các cuộc thử nghiệm nguyên tố (kết quả được hiển thị sau này). Các tham số được xác định phân tích được tóm tắt trong bảng 7. Lưu ý rằng giá trị damping địa phương (Itasca 2003) của 0.7 được sử dụng và bất kỳ dao khác đã không được sử dụng thông qua những phân tích. Tính toán timestep được sử dụng là 5s cho tất cả DEM phân tích ngoại trừ các phân tích của bài kiểm tra trực tiếp cắt nơi timestep của 2s đã được sử dụng. Con số 53. Phân phối của cắt căng thẳng xuống inter- Nal đống bề mặt. Con số 54. Hình đậu phộng cụm được sử dụng trong phân tích DEM. thực tế không thể, theo quan điểm công suất và thời gian tính toán. Trong các thử nghiệm máy ly tâm, không có tác dụng quy mô đã được quan sát cho footings mô hình có tỷ lệ đường kính chân đất hạt kích thước khác nhau, từ 30 đến 180 (Ovesen năm 1979). Đường kính của các plug đất trong các tính toán tham số trong bài báo này là khoảng 100 mm. Theo ở trên 166 Mật độ tối đa và tối thiểu mật độ thử nghiệm thực hiện. Kiểm tra mật độ tối thiểu theo phương pháp tiêu chuẩn xã hội Nhật bản địa (1992). Mặt khác, không đúng tiêu chuẩn phương pháp được sử dụng trong thử nghiệm lớn nhất. Trong phương pháp tiêu chuẩn, cát được đổ vào khuôn (40 mm cao) với một cổ áo (20 mm cao) trong 10 lớp, và 100 tác động được áp dụng cho khuôn sau khi đổ mỗi lớp đất. Trong Phi tiêu chuẩn phương pháp được sử dụng trong nghiên cứu này, cát được đổ vào khuôn với cổ áo cùng một lúc, và 1000 tác động đã được áp dụng cho khuôn mẫu, như minh hoạ trong hình 55. Con số 55 cho thấy ana - lytical mô hình cho các bài kiểm tra mật độ tối thiểu và tối đa. Hopper, khuôn mẫu và cổ áo được mô hình bởi 'tường yếu tố'. Tổng cộng năm DEM phân tích của min-imum và thử nghiệm lớn nhất được thực hiện. Khối được tạo ra mỗi khi ngẫu nhiên trong các phễu (hình 55(a)). Sau đó, các phễu được kéo lên một độ 5 mm/s. Sau khi các khối đã bỏ vào khuôn với cổ áo (hình 55(b)), các khối trong các cổ áo đã bị xóa (hình 55(c)) để có được tỷ lệ tối đa khoảng trống, emax. DEM phân tích của kiểm tra mật độ tối đa là bắt đầu từ nhà nước của con số 55(b). Để mô hình ảnh hưởng trên khuôn, Sin trọng lượng rẽ nước ngang có một tần số của 5 Hz và một biên độ của 5 mm được áp dụng cho khuôn. Các Bảng 9. Kết quả tính toán cuộc thử nghiệm lớn nhất. Phân tích 1st 2 3 4 5 Có nghĩa là Tỷ lệ tối thiểu khoảng trống 0.678 0.672 0.682 0.671 0.676 0.676 Mật độ khô tối đa 1.629 tấn / m3 1.635 tấn / m3 1.625 tấn / m3 1.636 tấn / m3 1.631 tấn / m3 1.631 tấn / m3 Con số 55. Phân tích các mô hình được sử dụng để kiểm tra mật độ tối thiểu và kiểm tra mật độ tối đa. 8 bảng. Các kết quả tính toán của bài kiểm tra mật độ tối thiểu. Con số 56. Các kết quả tính toán và thử nghiệm lớn nhất thử nghiệm cho đến 200 lắc chu kỳ. Phân tích 1st 2 3 4 5 Có nghĩa là Tối đa tỷ lệ vô hiệu 0.976 0.946 0.944 0.962 0.960 0.958 Tối thiểu mật độ khô 1.384 tấn / m3 1.405 tấn / m3 1.406 tấn / m3 1.394 tấn / m3 1.395 tấn / m3 1.397 tấn / m3 lắc hướng đã được thay đổi bởi 36 độ mỗi 10 chu kỳ lắc, để mô phỏng các thủ tục thử nghiệm. Kết quả của DEM phân tích của các tối thiểu den - xét nghiệm sity được tóm tắt trong bảng 8. Các giá trị có nghĩa là tỷ lệ khoảng trống tối đa và tối thiểu mật độ khô là 0.958 và 1.397 tấn / m3, tương ứng. Những giá trị này có thể được so sánh với những người thu được từ mật độ min-imum kiểm tra (xem bảng 6). Kết quả của DEM phân tích của các bài kiểm tra tối đa dens-Anh được so sánh với kết quả thử nghiệm trong con số 57. Những thay đổi trong tỷ lệ khoảng trống được âm mưu chống lại số lượng lắc chu kỳ trong con số 57 cho đến khi chu kỳ bắt của 200, mặc dù 1000 chu kỳ bắt được phân tích. Tỷ lệ vô hiệu nhanh chóng giảm với sự gia tăng các chu kỳ lắc để chu kỳ khoảng 100 và sau đó hầu như lấp cho thêm lắc chu kỳ trong các bài kiểm tra mật độ tối đa không chuẩn. Kết quả phân tích DEM mô phỏng hành vi đo này cũng. Tỷ lệ tối thiểu void và mật độ khô tối đa tương ứng thu được từ phân tích DEM được tóm tắt trong bảng 9. 167 Con số 57. Các tính toán và thử nghiệm kết quả của một thử nghiệm nén chiều. Các bài kiểm tra hết nén và các bài kiểm tra trực tiếp cắt của cát được thực hiện bằng cách sử dụng vòng củng cố và cắt vòng có một đường kính bên trong của 60 mm và độ cao 20 mm. Tuy nhiên, trong các phân tích DEM, chiều cao của mẫu đất đã được thiết lập tại 40 mm trong các phân tích DEM, vì kích thước của cụm (hình 54) có vẻ là lớn so với chiều cao thực tế vòng 20 mm. Ma sát giữa các khối và các bức tường được bỏ rơi. Tỷ lệ vô hiệu ban đầu trước khi nén đã được đặt ở 0.693 trong phân tích DEM. Trong quá trình phân tích DEM của thử nghiệm nén hết, tổng cộng 8 nâng bước, 9.8 để 1254.4 kPa, được áp dụng cho đầu tải tấm. Con số 57 cho thấy so sánh giữa kết quả một chiều kiểm tra và kết quả phân tích DEM. Con số 58. DEM mô hình của bài kiểm tra trực tiếp cắt. Nó có thể được nhìn thấy từ con số các kết quả thử nghiệm là tốt mô phỏng bằng cách phân tích DEM. Kiểm tra trực tiếp cắt được thực hiện với một căng thẳng dọc là 78,4 kPa cát dày đặc đã Tiến sĩ 93% (e 0.608). Trong phân tích DEM, ini- chướng void tỷ lệ trước khi nén đã được thiết lập tại 0.693 và dọc căng thẳng là 78,4 kPa được áp dụng cho các mẫu vật thông qua đầu tải tấm. Sau khi com-pletion phân tích nạp theo chiều dọc, trọng lượng rẽ nước hori-zontal được áp dụng để chiếc nhẫn trên tại một tỷ lệ trọng lượng rẽ nước cách 0.4 mm/min (hình 58). Con số 59 cho thấy so sánh giữa các kết quả của bài kiểm tra trực tiếp cắt và phân tích DEM. Tìm 59(a) cho thấy mối quan hệ giữa trọng lượng rẽ nước cắt và suất cắt. Tìm 59(b) cho thấy mối quan hệ giữa cắt thuyên-ment và căng thẳng đứng. Nó có thể được nhìn thấy từ con số 59(a) rằng kết quả thử nghiệm là simu- lated tốt bởi DEM phân tích và thatpeak giá trị là ước tính là 49 độ lớn hơn hạt- để hạt ma sát góc, của 35 độ. Dila- Zotello hành vi quan sát thấy trong các thử nghiệm cũng Mô phỏng tốt bằng cách phân tích DEM (hình 59(b)). Theo các yếu tố xét nghiệm của cát đã tốt simu-lated bởi DEM như đã đề cập ở trên, DEM phân tích của vật tải push-up xét nghiệm đã thử bằng cách sử dụng các thông số phân tích xác định thông qua DEM phân tích của các cuộc thử nghiệm nguyên tố. Con số 60 cho thấy các mô hình phân tích của push-up tải của đất cắm. Xem xét đối xứng axi 168 Con số 59. Các kết quả tính toán và thử nghiệm của bài kiểm tra trực tiếp cắt. Con số 60. Phân tích các mô hình của push-up tải thử nghiệm đất cắm. Con số 61. Kết quả của DEM mô phỏng của push-up tải Các xét nghiệm của đất cắm. Các điều kiện của vấn đề, chỉ một phần tư của cọc và phần đất được mô hình. Các cọc là mod-elled bởi bức tường cứng nhắc. Do đó sự biến dạng của cơ thể đống đã không đưa vào tài khoản trong phân tích. Các hạt đất (khối hoặc lĩnh vực) đã được tạo ra bên trong đống mô hình để tạo ra các plug đất. Sau đó, tự trọng lượng phân tích được thực hiện mà không có ma sát giữa đất và bên trong đống trục. Cuối cùng, các phân tích của push-up tải được thực hiện bằng cách áp dụng một vận tốc trở lên của 5 mm/s tấm nâng cứng nhắc, tham gia vào tài khoản ma sát giữa đất và bên trong đống trục. Con số 61 cho thấy so sánh kết quả của các xét nghiệm tải push-up và phân tích DEM. Trong các phân tích DEM, Hệ số của ma sát giữa các đống và đất hạt, , đã được thiết lập để là 0,6. Con số 62 cho thấy các bản phân phối của bên trong trục kháng chiến xác định từ những phân tích DEM, com - pared với các kết quả thử nghiệm. Kết quả của con số 61 và 62 có thể khuyến khích việc sử dụng của DEM để điều tra các hành vi của các cọc và mặt đất mà đi kèm với biến dạng lớn và thất bại của mặt đất. Con số 63 cho thấy các bản phân phối của huy động việc truy của hệ số ma sát giữa đất và trục bên trong đống xác định từ những phân tích DEM. Ở đây, ma sát của hệ số mobilised được định nghĩa là tỷ lệ của ứng suất cắt (bên trong trục kháng) để sự căng thẳng xuyên tâm tác động lên bên trong đống trục. Gói coeffi ma sát giữa các hạt đất và cọc đã được thiết lập để là 0,6. Tuy nhiên, ma sát mobilised của hệ số dao động từ 0,4 đến 0,55 có ít hơn của hệ số ma sát giữa các hạt đất và cọc. Nó có thể được suy ra từ kết quả này chuyển động của các hạt đất liền kề với các đống trục, chứ không phải là trượt giữa các hạt đất và các cọc sợi, kiểm soát sức đề kháng bên trong trục. 169 Con số 62. Phân phối của bên trong trục kháng calcu-lated từ những phân tích DEM. Các tác giả đang cố DEM phân tích của sự xâm nhập của một đống mở ống xuống đất từ bề mặt của nó, bằng cách sử dụng phân tích các mô hình như minh hoạ trong hình 64, nơi cọc mô hình cứng nhắc bức tường hoặc hạt để cho phép cho sự biến dạng của các cọc. CÁC RÀO CẢN 6 TRONG TH
đang được dịch, vui lòng đợi..
Table 7. Analysis parameters of clump.
Property
Particle size (Long axis)
(Short axis)
Density of soil particles,s
Friction angle between clumps,
Normal and tangential spring
stiffness between clumps
Value
5.5 mm 4.0 mm
2.73 ton/m3 35 degrees
5 105N/m
Normal and tangential spring 5 105 N/m
stiffness between clump and wall
observation in centrifuge tests, the particle size used in DEM should be less than 3 mm. However, the use of clumps consisting of 2 spheres having a diameter of 3 mm took a very long calculation time. Hence, the authors decided to use peanut-shaped clumps having a diameter of 4 mm as shown in Figure 54.
The values of normal spring, tangential spring and the friction coefficient between the clumps were determined through matching analyses of the element tests (results are shown later). The identified analysis parameters are summarised in Table 7. Note that local damping value (Itasca 2003) of 0.7 was employed and any other damping was not used through the analyses.
Calculation timestep used was 5s for all the DEM
analyses except for the analysis of direct shear test
where timestep of 2s was used.
Figure 53. Distributions of shear stresses down the inter-
nal pile surface.
Figure 54. Peanut-shaped clump used in the DEM analyses.
practically impossible, in view of capacity and time of calculation. In centrifuge tests, no scale effect was observed for model footings that had ratios of footing diameter to soil particle size ranging from 30 to 180 (Ovesen 1979).
Diameter of the soil plug in parametric calculation in this paper is about 100 mm. According to the above
166
Maximum density and minimum density tests were
carried out. The minimum density test followed the standard method by Japanese Geotechnical Society (1992). On the other hand, non-standard method was used in the maximum density test. In the standard method, the sand is poured into the mould (40 mm high) with a collar (20 mm high) in 10 layers, and 100 impacts are applied to the mould after pouring each soil layer. In non-standard method used in this research, the sand was poured into the mould with the collar at once, and 1000 impacts were applied to the mould, as shown in Figure 55. Figure 55 shows the ana- lytical models for the minimum and maximum density tests. The hopper, mould and collar were modelled by 'wall elements'. A total of five DEM analyses of min- imum and maximum density tests were carried out.
Clumps were created every time randomly inside the hopper (Fig. 55(a)). Afterwards, the hopper was pulled-up at a speed of 5 mm/s. After the clumps had dropped into the mould with collar (Fig. 55(b)), the clumps in the collar were deleted (Fig. 55(c)) to
obtain the maximum void ratio, emax.
DEM analysis of the maximum density test was
started from the state of Figure 55(b). In order to model the impact on the mould, sinusoidal horizontal displacement having a frequency of 5 Hz and an amplitude of 5 mm was applied to the mould. The
Table 9. The calculated results of maximum density tests.
Analysis
1st
2nd 3rd 4th 5th
Mean
Minimum void ratio
0.678 0.672 0.682 0.671 0.676
0.676
Maximum dry density
1.629 ton/m3 1.635 ton/m3 1.625 ton/m3 1.636 ton/m3 1.631 ton/m3
1.631 ton/m3
Figure 55. Analysis models used for minimum density test and maximum density test.
Table 8. The calculated results of minimum density tests.
Figure 56. The calculated and experimental results of maximum density tests until 200 shaking cycles.
Analysis
1st
2nd 3rd 4th 5th
Mean
Maximum void ratio
0.976 0.946 0.944 0.962 0.960
0.958
Minimum dry density
1.384 ton/m3 1.405 ton/m3 1.406 ton/m3 1.394 ton/m3 1.395 ton/m3
1.397 ton/m3
shaking direction was changed by 36 degrees every
10 cycles of shaking, to simulate the test procedure.
The results of DEM analyses of the minimum den- sity tests are summarised in Table 8. The mean values of maximum void ratio and minimum dry density are 0.958 and 1.397 ton/m3, respectively. These values may be comparable with those obtained from the min- imum density test (see Table 6).
The results of DEM analyses of the maximum dens- ity tests are compared with the test results in Figure 57. Changes in void ratio are plotted against the number of shaking cycles in Figure 57 until the shaking cycle of 200, although 1000 shaking cycles were analysed. The void ratio rapidly decreased with increasing shaking cycle to about 100 cycles and then almost levelled off for further shaking cycles in the non-standard maximum density tests. The results of DEM analyses simulate this measured behaviour well. The minimum void ratio and the corresponding maximum dry density obtained from the DEM analyses are summarised in Table 9.
167
Figure 57. The calculated and experimental results of one- dimensional compression test.
The one-dimensional compression tests and the direct shear tests of the sand were carried out using the consolidation ring and the shear ring having an inner diameter of 60 mm and a height of 20 mm. However, in the DEM analyses, the height of the soil specimen was set at 40 mm in the DEM analyses, because the size of clump (Fig. 54) seemed to be large compared to the actual ring height of 20 mm.
The friction between the clumps and the walls was neglected. The initial void ratio prior to compression was set at 0.693 in the DEM analysis. In the process of DEM analysis of the one-dimensional compression test, a total of 8 loading steps, 9.8 to 1254.4 kPa, were applied to the top loading plate.
Figure 57 shows the comparison between the one- dimensional test results and the DEM analysis results.
Figure 58. DEM modelling of direct shear test.
It can be seen from the figure that the test results are well simulated by the DEM analysis.
Direct shear test was carried out with a vertical stress of 78.4 kPa for the dense sand having
Dr 93% (e 0.608). In the DEM analysis, the ini-
tial void ratio prior to compression was set at 0.693
and vertical stress of 78.4 kPa was applied to the specimen through the top loading plate. After com- pletion of the analysis of the vertical loading, hori- zontal displacement was applied to the upper ring at a displacement rate of 0.4 mm/min (Fig. 58).
Figure 59 shows the comparison between the results of the direct shear test and the DEM analysis. Figure 59(a) shows the relationships between the shear displacement and the shear stress. Figure 59(b) shows the relationships between the shear displace- ment and the vertical strain. It can be seen from Figure 59(a) that the experimental result was simu-
lated well by the DEM analysis and thatpeak value is
estimated as 49 degrees that is larger than the grain-
to-grain friction angle, of 35 degrees. The dila-
tancy behaviour observed in the experiment was also
simulated well by the DEM analysis (Fig. 59(b)).
As the element tests of the sand were well simu- lated by DEM as mentioned in the above, DEM analyses of the push-up load tests were attempted using the analytical parameters identified through DEM analyses of the element tests.
Figure 60 shows the analysis model of push-up loading of soil plug. Considering axi-symmetrical
168
Figure 59. The calculated and experimental results of direct shear test.
Figure 60. Analysis model of push-up load test of soil plug.
Figure 61. Results of DEM simulations of push-up load
tests of soil plug.
condition of the problem, only one-fourth of the pile and the soil plug were modelled. The pile was mod- elled by rigid walls. Hence the deformation of the pile body was not taken into account in the analysis. The soil particles (clumps or spheres) were generated inside the model pile in order to create the soil plug. Then, self-weight analysis was conducted without friction between the soil and the inner pile shaft. Finally, the analysis of push-up loading was carried out by applying an upward velocity of 5 mm/s to the rigid loading plate, taking into account the friction between the soil and the inner pile shaft.
Figure 61 shows the comparisons of the results of the push-up load tests and the DEM analyses. In the DEM analyses, coefficient of friction between the
pile and the soil particle,, was set to be 0.6.
Figure 62 shows the distributions of inner shaft
resistance calculated from the DEM analyses, com- pared with the experimental results.
The results of Figures 61 and 62 may encourage the use of DEM to investigate behaviours of the pile and the ground which accompany large deformation and failure of the ground.
Figure 63 shows the distributions of mobilised coefficient of friction between the soil and the inner pile shaft calculated from the DEM analyses. Here, the mobilised coefficient of friction is defined as the ratio of shear stress (inner shaft resistance) to the radial stress acting on the inner pile shaft. The coeffi- cient of friction between the soil particle and the pile was set to be 0.6. However, the mobilised coefficient of friction ranges from 0.4 to 0.55 which are less than the coefficient of friction between the soil particle and the pile. It may be inferred from this result that rotation of the soil particles adjacent to the pile shaft, rather than slippage between the soil particles and the pile shaft, controls the inner shaft resistance.
169
Figure 62. Distributions of inner shaft resistance calcu- lated from the DEM analyses.
The authors are attempting DEM analyses of the penetration of an open-ended pipe pile into the ground from its surface, using analytical models as shown in Figure 64, where the pile is modelled by the rigid walls or particles to allow for the deformation of the pile.
6 BARRIERS IN APPLIC
Property
Particle size (Long axis)
(Short axis)
Density of soil particles,s
Friction angle between clumps,
Normal and tangential spring
stiffness between clumps
Value
5.5 mm 4.0 mm
2.73 ton/m3 35 degrees
5 105N/m
Normal and tangential spring 5 105 N/m
stiffness between clump and wall
observation in centrifuge tests, the particle size used in DEM should be less than 3 mm. However, the use of clumps consisting of 2 spheres having a diameter of 3 mm took a very long calculation time. Hence, the authors decided to use peanut-shaped clumps having a diameter of 4 mm as shown in Figure 54.
The values of normal spring, tangential spring and the friction coefficient between the clumps were determined through matching analyses of the element tests (results are shown later). The identified analysis parameters are summarised in Table 7. Note that local damping value (Itasca 2003) of 0.7 was employed and any other damping was not used through the analyses.
Calculation timestep used was 5s for all the DEM
analyses except for the analysis of direct shear test
where timestep of 2s was used.
Figure 53. Distributions of shear stresses down the inter-
nal pile surface.
Figure 54. Peanut-shaped clump used in the DEM analyses.
practically impossible, in view of capacity and time of calculation. In centrifuge tests, no scale effect was observed for model footings that had ratios of footing diameter to soil particle size ranging from 30 to 180 (Ovesen 1979).
Diameter of the soil plug in parametric calculation in this paper is about 100 mm. According to the above
166
Maximum density and minimum density tests were
carried out. The minimum density test followed the standard method by Japanese Geotechnical Society (1992). On the other hand, non-standard method was used in the maximum density test. In the standard method, the sand is poured into the mould (40 mm high) with a collar (20 mm high) in 10 layers, and 100 impacts are applied to the mould after pouring each soil layer. In non-standard method used in this research, the sand was poured into the mould with the collar at once, and 1000 impacts were applied to the mould, as shown in Figure 55. Figure 55 shows the ana- lytical models for the minimum and maximum density tests. The hopper, mould and collar were modelled by 'wall elements'. A total of five DEM analyses of min- imum and maximum density tests were carried out.
Clumps were created every time randomly inside the hopper (Fig. 55(a)). Afterwards, the hopper was pulled-up at a speed of 5 mm/s. After the clumps had dropped into the mould with collar (Fig. 55(b)), the clumps in the collar were deleted (Fig. 55(c)) to
obtain the maximum void ratio, emax.
DEM analysis of the maximum density test was
started from the state of Figure 55(b). In order to model the impact on the mould, sinusoidal horizontal displacement having a frequency of 5 Hz and an amplitude of 5 mm was applied to the mould. The
Table 9. The calculated results of maximum density tests.
Analysis
1st
2nd 3rd 4th 5th
Mean
Minimum void ratio
0.678 0.672 0.682 0.671 0.676
0.676
Maximum dry density
1.629 ton/m3 1.635 ton/m3 1.625 ton/m3 1.636 ton/m3 1.631 ton/m3
1.631 ton/m3
Figure 55. Analysis models used for minimum density test and maximum density test.
Table 8. The calculated results of minimum density tests.
Figure 56. The calculated and experimental results of maximum density tests until 200 shaking cycles.
Analysis
1st
2nd 3rd 4th 5th
Mean
Maximum void ratio
0.976 0.946 0.944 0.962 0.960
0.958
Minimum dry density
1.384 ton/m3 1.405 ton/m3 1.406 ton/m3 1.394 ton/m3 1.395 ton/m3
1.397 ton/m3
shaking direction was changed by 36 degrees every
10 cycles of shaking, to simulate the test procedure.
The results of DEM analyses of the minimum den- sity tests are summarised in Table 8. The mean values of maximum void ratio and minimum dry density are 0.958 and 1.397 ton/m3, respectively. These values may be comparable with those obtained from the min- imum density test (see Table 6).
The results of DEM analyses of the maximum dens- ity tests are compared with the test results in Figure 57. Changes in void ratio are plotted against the number of shaking cycles in Figure 57 until the shaking cycle of 200, although 1000 shaking cycles were analysed. The void ratio rapidly decreased with increasing shaking cycle to about 100 cycles and then almost levelled off for further shaking cycles in the non-standard maximum density tests. The results of DEM analyses simulate this measured behaviour well. The minimum void ratio and the corresponding maximum dry density obtained from the DEM analyses are summarised in Table 9.
167
Figure 57. The calculated and experimental results of one- dimensional compression test.
The one-dimensional compression tests and the direct shear tests of the sand were carried out using the consolidation ring and the shear ring having an inner diameter of 60 mm and a height of 20 mm. However, in the DEM analyses, the height of the soil specimen was set at 40 mm in the DEM analyses, because the size of clump (Fig. 54) seemed to be large compared to the actual ring height of 20 mm.
The friction between the clumps and the walls was neglected. The initial void ratio prior to compression was set at 0.693 in the DEM analysis. In the process of DEM analysis of the one-dimensional compression test, a total of 8 loading steps, 9.8 to 1254.4 kPa, were applied to the top loading plate.
Figure 57 shows the comparison between the one- dimensional test results and the DEM analysis results.
Figure 58. DEM modelling of direct shear test.
It can be seen from the figure that the test results are well simulated by the DEM analysis.
Direct shear test was carried out with a vertical stress of 78.4 kPa for the dense sand having
Dr 93% (e 0.608). In the DEM analysis, the ini-
tial void ratio prior to compression was set at 0.693
and vertical stress of 78.4 kPa was applied to the specimen through the top loading plate. After com- pletion of the analysis of the vertical loading, hori- zontal displacement was applied to the upper ring at a displacement rate of 0.4 mm/min (Fig. 58).
Figure 59 shows the comparison between the results of the direct shear test and the DEM analysis. Figure 59(a) shows the relationships between the shear displacement and the shear stress. Figure 59(b) shows the relationships between the shear displace- ment and the vertical strain. It can be seen from Figure 59(a) that the experimental result was simu-
lated well by the DEM analysis and thatpeak value is
estimated as 49 degrees that is larger than the grain-
to-grain friction angle, of 35 degrees. The dila-
tancy behaviour observed in the experiment was also
simulated well by the DEM analysis (Fig. 59(b)).
As the element tests of the sand were well simu- lated by DEM as mentioned in the above, DEM analyses of the push-up load tests were attempted using the analytical parameters identified through DEM analyses of the element tests.
Figure 60 shows the analysis model of push-up loading of soil plug. Considering axi-symmetrical
168
Figure 59. The calculated and experimental results of direct shear test.
Figure 60. Analysis model of push-up load test of soil plug.
Figure 61. Results of DEM simulations of push-up load
tests of soil plug.
condition of the problem, only one-fourth of the pile and the soil plug were modelled. The pile was mod- elled by rigid walls. Hence the deformation of the pile body was not taken into account in the analysis. The soil particles (clumps or spheres) were generated inside the model pile in order to create the soil plug. Then, self-weight analysis was conducted without friction between the soil and the inner pile shaft. Finally, the analysis of push-up loading was carried out by applying an upward velocity of 5 mm/s to the rigid loading plate, taking into account the friction between the soil and the inner pile shaft.
Figure 61 shows the comparisons of the results of the push-up load tests and the DEM analyses. In the DEM analyses, coefficient of friction between the
pile and the soil particle,, was set to be 0.6.
Figure 62 shows the distributions of inner shaft
resistance calculated from the DEM analyses, com- pared with the experimental results.
The results of Figures 61 and 62 may encourage the use of DEM to investigate behaviours of the pile and the ground which accompany large deformation and failure of the ground.
Figure 63 shows the distributions of mobilised coefficient of friction between the soil and the inner pile shaft calculated from the DEM analyses. Here, the mobilised coefficient of friction is defined as the ratio of shear stress (inner shaft resistance) to the radial stress acting on the inner pile shaft. The coeffi- cient of friction between the soil particle and the pile was set to be 0.6. However, the mobilised coefficient of friction ranges from 0.4 to 0.55 which are less than the coefficient of friction between the soil particle and the pile. It may be inferred from this result that rotation of the soil particles adjacent to the pile shaft, rather than slippage between the soil particles and the pile shaft, controls the inner shaft resistance.
169
Figure 62. Distributions of inner shaft resistance calcu- lated from the DEM analyses.
The authors are attempting DEM analyses of the penetration of an open-ended pipe pile into the ground from its surface, using analytical models as shown in Figure 64, where the pile is modelled by the rigid walls or particles to allow for the deformation of the pile.
6 BARRIERS IN APPLIC
đang được dịch, vui lòng đợi..
Các ngôn ngữ khác
Hỗ trợ công cụ dịch thuật: Albania, Amharic, Anh, Armenia, Azerbaijan, Ba Lan, Ba Tư, Bantu, Basque, Belarus, Bengal, Bosnia, Bulgaria, Bồ Đào Nha, Catalan, Cebuano, Chichewa, Corsi, Creole (Haiti), Croatia, Do Thái, Estonia, Filipino, Frisia, Gael Scotland, Galicia, George, Gujarat, Hausa, Hawaii, Hindi, Hmong, Hungary, Hy Lạp, Hà Lan, Hà Lan (Nam Phi), Hàn, Iceland, Igbo, Ireland, Java, Kannada, Kazakh, Khmer, Kinyarwanda, Klingon, Kurd, Kyrgyz, Latinh, Latvia, Litva, Luxembourg, Lào, Macedonia, Malagasy, Malayalam, Malta, Maori, Marathi, Myanmar, Mã Lai, Mông Cổ, Na Uy, Nepal, Nga, Nhật, Odia (Oriya), Pashto, Pháp, Phát hiện ngôn ngữ, Phần Lan, Punjab, Quốc tế ngữ, Rumani, Samoa, Serbia, Sesotho, Shona, Sindhi, Sinhala, Slovak, Slovenia, Somali, Sunda, Swahili, Séc, Tajik, Tamil, Tatar, Telugu, Thái, Thổ Nhĩ Kỳ, Thụy Điển, Tiếng Indonesia, Tiếng Ý, Trung, Trung (Phồn thể), Turkmen, Tây Ban Nha, Ukraina, Urdu, Uyghur, Uzbek, Việt, Xứ Wales, Yiddish, Yoruba, Zulu, Đan Mạch, Đức, Ả Rập, dịch ngôn ngữ.
- không, đừng nghĩ như vậy. khi một ai đó
- anh yeu em
- không, đừng nghĩ như vậy. khi một ai đó
- served
- không, đừng nghĩ như vậy. khi một ai đó
- 산세
- capital
- bạn trông khá lớn so với tuổi
- distortion
- 건조온도
- residence
- If i were you. I would apply for that jo
- economic deals primarily with the concep
- you can give money for me
- 작업조 건관리
- produce
- When you come to my hometown , you shoul
- We both just really loved each other and
- 산세농도
- We both just really loved each other and
- economic deals primarily with the concep
- sẽ có rất nhiều phụ nữ theo đuổi bạn
- you give money for me
- alternatives
