Frontiers in Civil Engineering

Volume: 1

Applications of Plasticity Theory and Limit Analysis to the Bearing Capacity of Shallow Foundations

Author(s): Y.M. Cheng, H. Wong, C.J. Leo and C.K. Lau

Pp: 310-391 (82)

DOI: 10.2174/9781681083032116010007

* (Excluding Mailing and Handling)

Abstract

In this chapter, the plasticity theory (slip line analysis) and limit analysis will be applied to the bearing capacity problems for illustration. Through these applications, the readers will be able to strengthen their understanding on the various types of stability analysis methods.


Keywords: Axisymmetry, Bearing capacity, Footings/foundations, Geotechnical centrifuge modelling, Method of characteristics, Numerical modelling, Physical modelling, Plane strain, Plasticity, Sands, Shear strength, Silts, Stress analysis.

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      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Trial Access" as access_base_text, CASE j.type WHEN 111 THEN true ELSE false END as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_trail` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 51739267 and j.to_ip >=51739267 )) and ((j.from_date <= 1739848555 and j.to_date >= 1739848555 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 9312) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Subscribed" as access_base_text, false as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_corporate` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 51739267 and j.to_ip >=51739267 )) and ((j.from_date <= 1739848555 and j.to_date >= 1739848555 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 9312) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Token Based Access" as access_base_text, false as terms_popup, "R" as content_download_type, j.uc_id as restricted_user_access_key, "v" as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_token` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 51739267 and j.to_ip >=51739267 )) and ((j.from_date <= 1739848555 and j.to_date >= 1739848555 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 9312)
      580μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
      Backtrace
      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 2000 and `b`.`banner_from_date` <= 1739848555 and `b`.`banner_to_date` >= 1739848555 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.16msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 2000
      • 3: 1739848555
      • 4: 1739848555
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='bf0bcdd465001b461db6c22278d99fa2'
      220μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Keywords
    13Keywords.php#?
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
        DPkFlRnjNW7abqbWBnRq9wu59IwwpgsbgynxYVfU
        uc_cart_id
        bf0bcdd465001b461db6c22278d99fa2
        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/9312" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /chapter/9312
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:16 [ "x-https" => array:1 [ 0 => "1" ] "host" => array:1 [ 0 => "alpha.eurekaselect.com" ] "priority" => array:1 [ 0 => "u=0, i" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] ]
        request_cookies
        []
        
        response_headers
        0 of 0
        array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Tue, 18 Feb 2025 03:15:55 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6Im1qaG8xNDZjSEJhMjRqNUFIYkdLVlE9PSIsInZhbHVlIjoiQzdyY1RsZ2lCT3NPTUtEamFvL2Y3UU9IM3Yzb3hySVIrY3EwVnBSMmZQamxRMHp3WmZ0a2RSUDhMcndHWUJaa3RicGZSTXZhTVo1RThwZS9tQUsrSFNUUzNZcks0Qmh3cldQVjUycmh1RnYrR3h5QXB6TldvMnI5cmc0amhuZU8iLCJtYWMiOiI1YTQ2NzMyYjExZDcxZmNiYzQ5MWFiYTQ5MmVlMDVkYTMwOGQ2MTljODlkNjkyYjM5YmY5MjM0ZWM1YmVkODJlIiwidGFnIjoiIn0%3D; expires=Thu, 20 Feb 2025 15:15:55 GMT; Max-Age=216000; path=/; secure; samesite=laxXSRF-TOKEN=eyJpdiI6Im1qaG8xNDZjSEJhMjRqNUFIYkdLVlE9PSIsInZhbHVlIjoiQzdyY1RsZ2lCT3NPTUtEamFvL2Y3UU9IM3Yzb3hySVIrY3EwVnBSMmZQamxRMHp3WmZ0a2RSUDhMcndHWUJaa3RicGZST" 1 => "alphaeurekaselectnet_session=eyJpdiI6ImZ3L0RxTHdQRzFMYlRqK24vTWlndHc9PSIsInZhbHVlIjoiSm5Ma0xlK2RyOUJiWEdBKzhCWnE5L1k2OTNzL25vVGszZ3ZVeTR2QnB2ai8vdmJoZmdrUEtWVVZDY3FpWi9MeFE2MWs4aHJqOGk2OTdwWWRVWEdHbmxSV3RhUGFkWVRGREliNUlFRmQySHMwTS9LRVJkc3BKdFRhYzVOMjlFWnkiLCJtYWMiOiI4NzI3MDhiZTBlOTQ2OWYxNjUxNGRjYzI0M2M4ZWFkNDc3YzhkMGEzZmMxNDRmMGE0OTAyNTk3NWM1MTVlN2JjIiwidGFnIjoiIn0%3D; path=/; secure; httponly; samesite=laxalphaeurekaselectnet_session=eyJpdiI6ImZ3L0RxTHdQRzFMYlRqK24vTWlndHc9PSIsInZhbHVlIjoiSm5Ma0xlK2RyOUJiWEdBKzhCWnE5L1k2OTNzL25vVGszZ3ZVeTR2QnB2ai8vdmJoZmdrUEtWVVZ" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6Im1qaG8xNDZjSEJhMjRqNUFIYkdLVlE9PSIsInZhbHVlIjoiQzdyY1RsZ2lCT3NPTUtEamFvL2Y3UU9IM3Yzb3hySVIrY3EwVnBSMmZQamxRMHp3WmZ0a2RSUDhMcndHWUJaa3RicGZSTXZhTVo1RThwZS9tQUsrSFNUUzNZcks0Qmh3cldQVjUycmh1RnYrR3h5QXB6TldvMnI5cmc0amhuZU8iLCJtYWMiOiI1YTQ2NzMyYjExZDcxZmNiYzQ5MWFiYTQ5MmVlMDVkYTMwOGQ2MTljODlkNjkyYjM5YmY5MjM0ZWM1YmVkODJlIiwidGFnIjoiIn0%3D; expires=Thu, 20-Feb-2025 15:15:55 GMT; path=/; secureXSRF-TOKEN=eyJpdiI6Im1qaG8xNDZjSEJhMjRqNUFIYkdLVlE9PSIsInZhbHVlIjoiQzdyY1RsZ2lCT3NPTUtEamFvL2Y3UU9IM3Yzb3hySVIrY3EwVnBSMmZQamxRMHp3WmZ0a2RSUDhMcndHWUJaa3RicGZST" 1 => "alphaeurekaselectnet_session=eyJpdiI6ImZ3L0RxTHdQRzFMYlRqK24vTWlndHc9PSIsInZhbHVlIjoiSm5Ma0xlK2RyOUJiWEdBKzhCWnE5L1k2OTNzL25vVGszZ3ZVeTR2QnB2ai8vdmJoZmdrUEtWVVZDY3FpWi9MeFE2MWs4aHJqOGk2OTdwWWRVWEdHbmxSV3RhUGFkWVRGREliNUlFRmQySHMwTS9LRVJkc3BKdFRhYzVOMjlFWnkiLCJtYWMiOiI4NzI3MDhiZTBlOTQ2OWYxNjUxNGRjYzI0M2M4ZWFkNDc3YzhkMGEzZmMxNDRmMGE0OTAyNTk3NWM1MTVlN2JjIiwidGFnIjoiIn0%3D; path=/; secure; httponlyalphaeurekaselectnet_session=eyJpdiI6ImZ3L0RxTHdQRzFMYlRqK24vTWlndHc9PSIsInZhbHVlIjoiSm5Ma0xlK2RyOUJiWEdBKzhCWnE5L1k2OTNzL25vVGszZ3ZVeTR2QnB2ai8vdmJoZmdrUEtWVVZ" ] ]
        session_attributes
        0 of 0
        array:5 [ "_token" => "DPkFlRnjNW7abqbWBnRq9wu59IwwpgsbgynxYVfU" "uc_cart_id" => "bf0bcdd465001b461db6c22278d99fa2" "_previous" => array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/9312" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]
        ClearShow all
        Date ↕MethodURLData
        #12025-02-18 03:15:55GET/chapter/93121121915