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中文譯文 標(biāo)題: 數(shù)控簡單剪切儀動態(tài)土壤測試 作者: 果皮,Pendo M,輝西 斯圖爾特,喬納森·P,加州大學(xué)洛杉磯分校 Venugopal,拉維,Sysendes公司。 出版日期: 01-01-2007 系列: 加州大學(xué)洛杉磯先前發(fā)表的作品 發(fā)布信息: 加州大學(xué)洛杉磯先前發(fā)表的作品,加州大學(xué)洛杉磯 附加信息: 版權(quán)2007年,ASTM,http://journalsip.astm.org/ 原始引用: 果皮,斯圖爾特,摩根,d.h。,Venugopal,r .(2007)。“數(shù)控簡單剪切設(shè)備動態(tài)土壤測試”,Geotech。測試日報(bào),ASTM,30(5),368 - 377。 數(shù)控剪切裝置簡單動態(tài)土壤測試 文摘:我們描述的特征簡單剪切裝置能力運(yùn)用現(xiàn)實(shí)的多向地震荷載對土 標(biāo)本。這個(gè)裝置,文中稱為數(shù)控簡單剪切(直流ss)裝置,包括功能,如伺服液壓控制的驅(qū)動和真正的數(shù)字控制克服控制的局限性,一些之前的動態(tài)土壤測試機(jī)器。該設(shè)備是顯示有能力正弦和寬帶的復(fù)制命令信號在一個(gè)廣泛的頻率和振幅,雖然設(shè)備有限控制能力非常小的命令位移(少于大約0.005毫米)。小變形限制結(jié)果從噪聲介紹了控制系統(tǒng)的反饋信號的模數(shù)轉(zhuǎn)換。我們證明,雙向命令信號準(zhǔn)確地傳授與最小交叉耦合,結(jié)果從一個(gè)創(chuàng)新的多輸入多輸出的數(shù)字控制系統(tǒng)。這個(gè)功能的設(shè)備演示一系列寬帶測試標(biāo)本非飽和土受到uni -和雙向勵磁。 關(guān)鍵詞:數(shù)字控制,簡單的剪切、動態(tài)土壤測試、多向加載 介紹 直接簡單的剪切設(shè)備已經(jīng)成功運(yùn)用多年來描述靜態(tài)和動態(tài)土屬性。這測試方法往往是首選當(dāng)它是可取的標(biāo)本來體驗(yàn)光滑、連續(xù)的旋轉(zhuǎn)主應(yīng)力方向在剪切。初始應(yīng)力可以應(yīng)用模擬靜態(tài)字段條件當(dāng)鋼絲增強(qiáng)利用膜,減少橫向變形樣品(即。,NGI-type配置,Bjerrum和Landva1966)。也許最常見的應(yīng)用程序的簡單剪切試驗(yàn)對仿真的垂直(或近垂直)剪切波傳播通過土柱。優(yōu)點(diǎn)和局限性簡單的剪切測試相對于其他類型的實(shí)驗(yàn)室測試描述了在其他地方,這里不再重復(fù)(比如,菜的et al。1972;沈et al。1978;薩達(dá)et al。1982;Vucetic和拉卡斯提花1982;1985;Budhu Bhatia et al。1985;Amer et al。1987;Airey和木材1987;Budhu和Britto 1987;雅et al。1993)。 最簡單的剪切設(shè)備運(yùn)行在一個(gè)水平方向并應(yīng)用諧波載荷頻率一般慢于動態(tài)過程,如地震搖晃(如。,Tatsuoka和銀1981;Doroudian和Vucetic 1995;和Pfender Lefebvre 1996;瑞艾莫和種子1997;Kusakabe et al。1999年,Hazirbaba和Rathje 2004)。雖然總是有近似參與應(yīng)用在實(shí)驗(yàn)室土壤特性測量對現(xiàn)場條件,對現(xiàn)有設(shè)備無法提供快速、多向加載介紹進(jìn)一步的錯誤未知的意義當(dāng)實(shí)驗(yàn)室測量土壤屬性用于工程模擬。 一個(gè)數(shù)量的簡單剪切設(shè)備已經(jīng)被發(fā)展調(diào)查土壤響應(yīng)多向加載(如。,石原和山崎1980;雅et al。1993;DeGroot et al . 1996)。加州大學(xué)伯克利分校的雙向循環(huán)簡單剪切(UCB-2D)裝置是值得注意的,因?yàn)樗黠@減少了機(jī)械合規(guī)問題,導(dǎo)致相對最高/基地帽搖擺在早期的設(shè)備(如。,石原和山崎1980;石原和“1988)。另一個(gè)顯著的特點(diǎn)UCB-2D設(shè)備是燃燒室壓力控制,方便背壓飽和。 校長UCB-2D設(shè)備本身的限制,早期的設(shè)備,是他們無法應(yīng)用地震像寬帶裝貨嗎在快速位移率。這種限制也存在對大多數(shù)單向簡單剪切設(shè)備。其原因是雙重的:(1)氣動加載系統(tǒng)使用一個(gè)可壓縮流體(即。、空氣) 其中介紹了重大錯誤的反饋回路在高頻段;和(2)數(shù)字監(jiān)督模擬控制器被雇用這有效地限制處理速度和成熟的控制算法。當(dāng)然,振動臺和離心機(jī)實(shí)驗(yàn)都能使用多方向的地震像加載到土壤模型(即。,派克et al。1975;1998年andYanagisawa Jafarzadeh的說法;Kutter 1995;威爾遜et al . 2004)。然而,直接測量土壤元素的響應(yīng)(例如,剪切應(yīng)力剪切應(yīng)變關(guān)系、體積應(yīng)變和孔隙水壓力)在這些類型的實(shí)驗(yàn)需要密集的儀表數(shù)組,可以影響響應(yīng)他們的目的是措施,從而使復(fù)雜數(shù)據(jù)解釋(如。,困難et al . 2005)。 圖1 應(yīng)用的能力,可靠程度的控制,多向加載在一個(gè)很寬的頻率范圍內(nèi),土壤元素在實(shí)驗(yàn)室是至關(guān)重要的推進(jìn)我們的根本理解動態(tài)土壤屬性。例如,寬帶裝載能力是需要調(diào)查率影響土壤手稿收到2006年3月1日,1月28日發(fā)表2007年,2007年5月在線發(fā)表。1研究生研究員,副教授和副主席,分別土木工程系&大學(xué)環(huán)境工程加利福尼亞,洛杉磯,5731年洛杉磯消沉大廳CA 90095。2工程師,指數(shù)失效分析,320年,200套房,歐文戈達(dá)德,CA92618年。3創(chuàng)始人和高級咨詢顧問工程師,Sysendes,Inc .,1804 m,套件4、蒙特利爾、QC H3H 1硅陶瓷、加拿大的觀點(diǎn)和結(jié)論包含在本文檔的作者和不應(yīng)被解釋為一定代表官方的政策,明示或暗示,美國政府。巖土測試日報(bào),卷。30,5號紙ID GTJ100518可以在www.astm.org368年版權(quán)?2007年由ASTM國際,100年巴爾港驅(qū)動器,PO Box,西Conshohocken C700,PA 19428 - 2959。屬性,人們知道這是重要的對于粘土(如。,Lefebvre和Pfender 1996;Sheahan et al . 1996)。此外,效果剪切速率和2 d裝載在孔隙壓力生成或體積改變行為,或兩者兼而有之,是了解較少,需要進(jìn)一步調(diào)查一些土壤類型。為了滿足這些研究需要,一個(gè)簡單的剪切設(shè)備現(xiàn)場數(shù)控與能力室壓力控制和多向激勵一直發(fā)達(dá)。這個(gè)裝置,文中稱為現(xiàn)場數(shù)控簡單剪切(直流ss)裝置合并功能,如伺服液壓控制的驅(qū)動和真正的數(shù)字控制克服的局限性先前的動態(tài)土壤測試機(jī)器。結(jié)果是一個(gè)真正獨(dú)特的簡單剪切裝置的功能應(yīng)用寬帶(地震像)位移要求土壤標(biāo)本在兩個(gè)方向,用最小的交叉耦合水平運(yùn)動。在本文中,我們描述這個(gè)裝置和它的功能動態(tài)土壤測試。 物理描述直流ss裝置 機(jī)械設(shè)計(jì)的直流ss裝置使用了UCB-2D的裝置作為一個(gè)原型(面包師et al . 1993)。這個(gè)直流ss裝置是專為了保留的主要特征UCB-2D設(shè)備如包含細(xì)胞壓力的目的背壓飽和,有限的機(jī)械遵守尊重對簡單剪切邊界條件(如。,頂部和基板“搖擺”),和雙向加載功能。除了這些特性,直流ss裝置結(jié)合了幾種改進(jìn)設(shè)計(jì)相對于UCB-2D裝置包括:我使用一個(gè)三郵報(bào)框架與高績效跟蹤軸承(容納垂直位移的頂罩),以進(jìn)一步降低搖擺;二世一個(gè)伺服液壓控制的控制系統(tǒng),使高頻率加載;iii雙重軸負(fù)載細(xì)胞獲得職位摩擦剪切載荷的測量。 圖1顯示了大會的直流ss裝置。照片的直流ss設(shè)備顯示在圖2。直流黨衛(wèi)軍的設(shè)備是用來測試圓柱土壤標(biāo)本與直徑10.2厘米或更少。這個(gè)標(biāo)本是位于相對嚴(yán)格的底部和頂部帽(圖1、圖2(b))和通常局限由一線增強(qiáng)膜。見圖2(c),水平(頂部和底部)面臨的標(biāo)本被限制的帽子,它含有細(xì)磨石epoxied變成一個(gè)休會覆蓋整個(gè)臉的帽子除了保持嘴唇的鋁在邊緣。這些帽子提供一個(gè)“摩擦”表面同時(shí)使排水進(jìn)入多孔石頭如果石頭不飽和(石頭可以飽和對不排水試驗(yàn))。這個(gè)上蓋/樣品/下蓋堆棧頂部之間的位置和底部適配器板圖1所示。底部帽適合一個(gè)休息在底部適配器板。適配器板頂部輕輕地降低,這樣休息在頂端的適配器板適合舒適地覆蓋在頂蓋。頂部和底部帽是緊緊在各自的適配器板由三個(gè)固定螺絲在每個(gè)板。一旦樣品是獲得兩個(gè)適配器板之間,三個(gè)LVDTs間距分布樣品安裝在頂部適配器板和固定在板通過螺釘。這個(gè)標(biāo)本是然后合并垂直應(yīng)力和準(zhǔn)備剪切載荷。 圖2 頂部適配器板是一種垂直表,進(jìn)而是附加到一個(gè)垂直負(fù)載細(xì)胞(圖1)。垂直負(fù)載轉(zhuǎn)移到標(biāo)本通過垂直表,這是附加的三個(gè)等距線性幻燈片。每個(gè)三個(gè)線性幻燈片附屬于一個(gè)單獨(dú)的帖子,有效防止側(cè)運(yùn)動和搖擺的垂直表(因此,實(shí)際上無花果。1原理的直流ss裝置在加利福尼亞大學(xué)洛杉磯分校。果皮ET AL。在數(shù)控簡單剪切儀369來說,標(biāo)本)。這是一個(gè)重要的三郵報(bào)框架改善UCB-2D設(shè)備,雇傭了一個(gè)懸臂系統(tǒng)(垂直表附加到一對跟蹤軸承沿相同的墻)。負(fù)載應(yīng)用于垂直表由氣動執(zhí)行機(jī)構(gòu)安裝在主框架之外。 一個(gè)重要的功能的設(shè)備,直流黨衛(wèi)軍留存從UCB-2D裝置是其雙向加載功能。橫向剪切載荷應(yīng)用在該基地的標(biāo)本通過兩個(gè)獨(dú)立控制的水平表。底部水平表安裝在線性幻燈片附加到主框架的裝置,這表是只自由移動 一個(gè)水平方向。上層水平表也安裝在線性幻燈片,這樣運(yùn)動上層表是完全垂直于下表。兩個(gè)水平表可以控制產(chǎn)生凈合成的運(yùn)動底部適配器板在任何水平方向。加載應(yīng)用較低水平表通過螺紋棒相連致動器,可以應(yīng)用張力和壓縮。有一個(gè)tensioncapable輥之間連接上層表及其執(zhí)行機(jī)構(gòu)以適應(yīng)垂直位移下表。負(fù)載應(yīng)用到表loadcells來衡量安裝執(zhí)行機(jī)構(gòu)和表之間。負(fù)荷測量由loadcells不相同,那些傳授標(biāo)本由于摩擦而在線性的幻燈片。這個(gè)巨大的摩擦加載系統(tǒng)中的表征,觀察到相當(dāng)小(大約2.2 N)。這一點(diǎn)的重要性摩擦負(fù)載取決于什么類型的測試,是理想的。這種摩擦負(fù)載將產(chǎn)生不準(zhǔn)確的(大約0.3 kPa10.2厘米直徑試樣),代表比例可以忽略不計(jì)的剪切應(yīng)力對大多數(shù)應(yīng)用程序。然而,如果很低應(yīng)力測量是必要的,帖子摩擦剪切應(yīng)力可以通過使用一個(gè)雙軸loadcell測量。這種雙軸loadcell適合在頂部之間適配器板和垂直表,一個(gè)空間,否則占用墊塊。這種雙軸loadcell能夠測量兩個(gè)垂直和剪切載荷同時(shí)以最小的相聲這些通道之間。然而,存在的雙軸loadcell介紹系統(tǒng)遵從性(即搖擺和垂直變形),可能是重要的在大中型菌株。因此,大多數(shù)測試執(zhí)行沒有雙軸loadcell到位。 三LVDTs(線性可變差動傳感器),安裝頂部和底部之間的適配器板,用于測量垂直標(biāo)本變形。這些位置的LVDTs最小化錯誤由于機(jī)械合規(guī)。這三個(gè)LVDTs是用,這樣相對搖擺的標(biāo)本在兩個(gè)方向的加載可以測量。三LVDTs數(shù)據(jù)的平均值定義試樣高度在一個(gè)測試。水平變形是衡量兩個(gè)LVDTs安裝在水平表在嗎正交的方向。 設(shè)備的直流黨衛(wèi)軍下運(yùn)作的“應(yīng)變控制”的條件下,這意味著表位移控制和執(zhí)行機(jī)構(gòu)力量必須實(shí)現(xiàn)這些位移測量。這個(gè)運(yùn)動,可以傳授表是有限的不同方面的控制系統(tǒng)對不同頻段。在低頻率f0 24赫茲,限制因素是峰致動器位移umax = 51毫米。在中間頻率0.24 Hzf15赫茲,限制因素是流量的能力伺服閥的Qmax = 158立方厘米/秒。在頻率f15赫茲,的制約因素是壓力能力的液壓泵pmax = 21 MPa。的情況下諧波控制信號,這些數(shù)量可以與相關(guān)的峰值表動作如下: U(t) = D sin（wt） ≤umax (1) u˙ (t) = D w cos（wt）≤ Qmax/A (2) u¨ (t) = ? D w2sin（wt）≤pmaxA/m (3) 圖3 在ut及其衍生產(chǎn)品描述表位移,速度,和加速度,一個(gè)是執(zhí)行機(jī)構(gòu)的橫截面積20.3平方厘米,m是表質(zhì)量5.7公斤,和頻率表運(yùn)動(按弧度/秒)。相應(yīng)的峰值位移值,速度和加速度給出了圖3。控制系統(tǒng)能產(chǎn)生任何運(yùn)動,是在的限制線在圖3。 油柱的理論頻率的致動器表系統(tǒng)給出了孔蒂和特龍貝蒂(2000):哪里是體積彈性模量的液壓流體1.7106 kPa嗎和V是原油的體積是463立方厘米的致動器。身體上,油柱頻率代表自然頻率的三液壓執(zhí)行器系統(tǒng),它可以被可視化為表質(zhì)量與彈簧連接有一個(gè)剛度定義的油柱在致動器室。對于命令信號頻率油柱頻率附近,表現(xiàn)為執(zhí)行機(jī)構(gòu)可以是有限的由于共振行為(如。,孔蒂和特龍貝蒂2000)。 直流ss控制系統(tǒng) 如圖4中,數(shù)字控制系統(tǒng)的直流黨衛(wèi)軍設(shè)備有兩個(gè)目的。第一個(gè)是提供控制信號直接驅(qū)動,驅(qū)動液壓作動器servovalves為每個(gè)軸(直接驅(qū)動servovalves有機(jī)載控制器,糾正跟蹤誤差在控制信號在開車前液壓致動器)。第二個(gè)目的是獲得LVDTs數(shù)據(jù)和loadcells。這里指的物理設(shè)備作為直流黨衛(wèi)軍是最初開發(fā)了一個(gè)基于pc的數(shù)字監(jiān)督模擬控制系統(tǒng)。這個(gè)控制系統(tǒng)使用PID(比例-積分導(dǎo)數(shù))控制算法,跑在一個(gè)Windows?操作系統(tǒng)。主要問題控制系統(tǒng)延時(shí)處理過程中的反饋信號從儀器(如(LVDT)和一代的命令信號。這限制了設(shè)備的能力,準(zhǔn)確復(fù)制一些命令信號。這些問題尤其急性加載功能涉及快速度和2 d搖動。 圖4 該系統(tǒng)已成功用于以前的測試(例如,用力的et al。2004;重?fù)鬳t al。2005),盡管這些應(yīng)用程序涉及單向震動和1.0赫茲加載頻率,所以控制問題相關(guān)的基于pc的系統(tǒng)沒有顯著的?？刂葡到y(tǒng)目前設(shè)備使用一個(gè)系統(tǒng)所為硬實(shí)時(shí)數(shù)字控制。主要區(qū)別基于pc的數(shù)字控制是控制功能被實(shí)現(xiàn)在控制器板相對于個(gè)人電腦操作系統(tǒng)。這使保證采樣頻率的內(nèi)部反饋回路的5 kHz使用位移反饋水平LVDTs,而基于pc的數(shù)字監(jiān)督模擬控制系統(tǒng)通常不能可靠地執(zhí)行計(jì)算需要復(fù)雜的控制反饋采樣頻率高于200赫茲,根據(jù)處理器時(shí)鐘速度,控制算法復(fù)雜,數(shù)量的后臺進(jìn)行由個(gè)人電腦操作系統(tǒng)等。數(shù)字控制系統(tǒng)利用兩個(gè)dSPACE DS1104控制器板。每個(gè)板包含一個(gè)PowerPC 603 e處理器,四個(gè)16位2 s模擬數(shù)字(A / D)轉(zhuǎn)換器,四個(gè)12位A / D轉(zhuǎn)換器800 ns和8個(gè)16位位十年代數(shù)模轉(zhuǎn)換(D / A)轉(zhuǎn)換器,除了其他輸入/輸出端口。這兩個(gè)板安裝在在一個(gè)PCI插槽主機(jī)電腦但運(yùn)行他們自己的實(shí)時(shí)內(nèi)核(即。,一個(gè)操作系統(tǒng)專門針對控制功能)獨(dú)立于主機(jī)電腦的操作系統(tǒng)。 一個(gè)PID控制算法實(shí)現(xiàn)了兩個(gè)基于pc和硬實(shí)時(shí)數(shù)字控制。這被稱為隨后隨著“PID控制器”。收益為PID控制器是調(diào)諧為獲得最佳性能試錯用階梯函數(shù)命令信號。PID控制器的輸出是一個(gè)數(shù)字電壓命令,發(fā)送到一個(gè)穆格公司電壓放大器通過的D / A頻道在dSPACE板。電壓放大器,反過來,發(fā)送一個(gè)電壓驅(qū)動信號到適當(dāng)?shù)膱?zhí)行機(jī)構(gòu)伺服閥。見圖5(一個(gè))、PID控制的兩個(gè)軸都是獨(dú)立的,從而控制系統(tǒng)作為一個(gè)整體無法補(bǔ)償對于交叉耦合效應(yīng)(即：影響,運(yùn)動沿一個(gè)軸在運(yùn)動沿著第二軸)。 圖5 為了減少交叉耦合效應(yīng),數(shù)字控制系統(tǒng)是通過引入一個(gè)多輸入多multipleoutput增強(qiáng)(MIMO)控制算法與PID控制器的接口。見圖5(b),該控制器采用線性差動變換器反饋兩軸和生成一個(gè)補(bǔ)償指令信號對于每個(gè)PID控制器,考慮到交叉耦合效果。控制器的設(shè)計(jì)和實(shí)現(xiàn)為一個(gè)離散狀態(tài)空間系統(tǒng)使用LQG(線性二次-高斯)最優(yōu)控制方法(富蘭克林et al . 1990)。這方法需要估計(jì)的數(shù)量,反映四個(gè)經(jīng)驗(yàn)系統(tǒng)屬性。這是通過使用N4SID系統(tǒng)識別算法(Van Overschee和德沼澤1995)系統(tǒng)辨識算法操作輸入-輸出數(shù)據(jù)序列;用于此目的的數(shù)據(jù)是兩個(gè)不相關(guān)的隨機(jī)輸入(生成的PID控制器)和相應(yīng)的線性差動變換器輸出信號。 結(jié)合MIMO的控制算法,以及兩個(gè)PID控制器是指后來的“mimo PID”控制器。設(shè)備配置的直流黨衛(wèi)軍,MIMO算法可以打開或關(guān)閉。因此,要么PID或mimo PID嗎數(shù)字控制的實(shí)驗(yàn)是可能的。數(shù)據(jù)采集功能無論是模式總結(jié)如下: ?輸入運(yùn)動時(shí)間步:不實(shí)用的下限; ?數(shù)量的輸入運(yùn)動數(shù)據(jù)點(diǎn):不實(shí)用的上限; ?反饋采樣頻率(即。,內(nèi)部頻率對反饋回路):5 kHz; ?數(shù)據(jù)記錄頻率:上界是5 kHz,可以downsampled作為需要。 直流ss系統(tǒng)性能 性能的評價(jià)系統(tǒng)的直流黨衛(wèi)軍(即。,控制器,泵、致動器、伺服閥),兩個(gè)諧波和寬帶地震輸入運(yùn)動被指定為PID控制器和的控制器和由此產(chǎn)生的mimo pid反饋信號測量。單向測試進(jìn)行評估性能每個(gè)軸的獨(dú)立,并提供基線結(jié)果相互影響的評估。雙向加載軸之間的交叉耦合進(jìn)行評估。 鳴謝 開發(fā)的設(shè)備支持直流黨衛(wèi)軍職業(yè)美國國家科學(xué)基金會的資助下,第二個(gè)作者(NSF獲獎號:9733113),亨利Samueli學(xué)校的工程和應(yīng)用科學(xué)大學(xué)洛杉磯分校和美國地質(zhì)調(diào)查顯示,國家地震災(zāi)害減少計(jì)劃,獎號。1434 - hg - 98 gr - 00037、05 hqgr0050。這種支持是感激地承認(rèn)。這個(gè)觀點(diǎn)和結(jié)論包含在這個(gè)文檔是作者的,不應(yīng)該解釋為一定代表官方的政策,要么表示或暗示,美國政府。帕特里克·m·史密斯和哈羅德·卡斯珀是感謝他們的相當(dāng)大的貢獻(xiàn)發(fā)展的物理設(shè)備。我們感謝三匿名評論者對他們有用的手稿評論。 英文原文 Title: Digitally controlled simple shear apparatus for dynamic soil testing Author: Duku, Pendo M, Fugro West Stewart, Jonathan P, University of California, Los Angeles Venugopal, Ravi, Sysendes, Inc. Publication Date: 01-01-2007 Series: UC Los Angeles Previously Published Works Publication Info: UC Los Angeles Previously Published Works, UC Los Angeles Additional Info: Copyright 2007, ASTM, http://journalsip.astm.org/ Original Citation: Duku, P.M., Stewart, J.P., Whang, D.H., Venugopal, R. (2007). “Digitally controlled simple shear apparatus for dynamic soil testing,” Geotech. Testing Journal, ASTM, 30 (5), 368-377. Digitally Controlled Simple Shear Apparatus for Dynamic Soil Testing ABSTRACT:We describe the characteristics of a simple shear apparatus capable of applying realistic multidirectional earthquake loading to soil specimens. This device, herein termed the Digitally Controlled Simple Shear (DC-SS) apparatus, incorporates features such as servohydraulic actuation and true digital control to overcome control limitations of some previous dynamic soil testing machines. The device is shown to be capable of reproducing sinusoidal and broadband command signals across a wide range of frequencies and amplitudes, although the device has limited control capabilities for very small command displacements (less than approximately 0.005 mm). The small deformation limitation results from noise introduced to the control system from analog-to-digital conversion of feedback signals.We demonstrate that bidirectional command signals can be accurately imparted with minimal cross coupling, which results from an innovative multiple-input, multiple-output digital control system. The capabilities of the device are demonstrated with a series of broadband tests on unsaturated soil specimens subjected to uni- and bidirectional excitation. KEYWORDS: digital control, simple shear, dynamic soil testing, multidirectional loading Introduction Direct simple shear apparatuses have been utilized successfully formany years to characterize static and dynamic soil properties. Thismethod of testing is often preferred when it is desirable for thespecimen to experience a smooth and continuous rotation of theprincipal stress directions during shear. Initial stresses can be applied to simulate at-rest field conditions when wire reinforcedmembranes are utilized that minimize lateral distortion of thesample (i.e., the NGI-type configuration, Bjerrum and Landva1966). Perhaps the most common application of simple shear testing has been for the simulation of vertical (or nearly vertical) shearwave propagation through a soil column. Advantages and limitations of simple shear tests relative to other types of laboratory tests have been described elsewhere and are not repeated here (e.g., Lucks et al. 1972; Shen et al. 1978; Saada et al. 1982; Vucetic and Lacasse 1982; Budhu 1985; Bhatia et al. 1985; Amer et al. 1987; Airey and Wood 1987; Budhu and Britto 1987; Boulanger et al. 1993). Most simple shear apparatuses operate in a single horizontal direction and apply harmonic loading at frequencies which are typically slower than dynamic processes such as earthquake shaking (e.g., Tatsuoka and Silver 1981; Doroudian and Vucetic 1995; Lefebvre and Pfender 1996; Riemer and Seed 1997; Kusakabe et al. 1999; Hazirbaba and Rathje 2004). While there are always approximations involved in applying soil properties measured in the laboratory to field conditions, the inability of existing devices to provide rapid, multidirectional loading introduces further errors of unknown significance when laboratory-measured soil properties are used in engineering simulations. A number of simple shear apparatuses have been developed to investigate soil response to multidirectional loading (e.g., Ishihara and Yamazaki 1980; Boulanger et al. 1993; DeGroot et al. 1996). The University of California, Berkeley bidirectional cyclic simple shear (UCB-2D) device is noteworthy since it significantly reduced mechanical compliance issues that caused relative top/base cap rocking in earlier devices (e.g., Ishihara and Yamazaki 1980; Ishihara and Nagase 1988). Another significant feature of the UCB-2D device is chamber pressure control, which facilitates back pressure saturation . The principal limitation of the UCB-2D device, and earlier devices, is their inability to apply earthquake-like broadband loading at rapid displacement rates. This limitation also exists for most unidirectional simple shear devices. The reasons for this are twofold :(1) pneumatic loading systems use a compressible fluid (i.e., air) which introduces significant errors to the feedback loop at high frequencies; and (2) digitally-supervised analog controllers were employed which effectively limit the processing speed and sophistication of the control algorithms. Of course, shaking table and centrifuge experiments are capable of applying multidirectional earthquake-like loading to soil models (i.e., Pyke et al. 1975;Jafarzadeh andYanagisawa 1998; Kutter 1995;Wilson et al. 2004).However, direct measurements of the soil element response (e.g.,shear stress-shear strain relationships, volumetric strain, and porewater pressure) in these types of experiments requires dense instrumentationarrays that can affect the response they are intended to measure, which in turn complicates data interpretation (e.g., Elgamal et al. 2005). The capability of applying, with a reliable degree of control, multidirectional loading across a wide range of frequencies to soil elements in the laboratory is critical to advancing our fundamental understanding of dynamic soil properties. For example, broadband loading capabilities are needed to investigate rate effects on soil properties, which are known to be significant for clays (e.g., Lefebvre and Pfender 1996; Sheahan et al. 1996). Moreover, the effect of shear rate and 2D loading on pore pressure generation or volume change behavior, or both, is less well understood and requires further investigation for some soil types.To meet these research needs, a digitally-controlled simple shear device with capabilities for chamber pressure control and multidirectional excitation has been developed. This device, herein termed the Digitally-Controlled Simple Shear (DC-SS) apparatus incorporates features such as servohydraulic actuation and true digital control to overcome the limitations of previous dynamic soil testing machines. The result is a truly unique simple shear apparatus with the capability to apply broadband (earthquake-like) displacement demands on soil specimens in two directions and with minimal cross coupling between the horizontal motions. In this paper, we describe this device and its capabilities for dynamic soil testing. Physical Description of DC-SS Device The mechanical design of the DC-SS device was developed using the UCB-2D device as a prototype (Boulanger et al. 1993). The DC-SS device was designed to retain the main features of the UCB-2D device such as inclusion of cell pressure for purposes of back pressure saturation, limited mechanical compliance with respect to simple shear boundary conditions (e.g., top and base platen “rocking”), and bidirectional loading capability. In addition to these features, the DC-SS device incorporates several design improvements relative to the UCB-2D device including: _i_ the use of a tri-post frame with high performance track bearings (which accommodate vertical displacements of the top cap) to further reduce rocking; _ii_ a servohydraulic control system to allow for high frequency loading; and _iii_ a dual axis load cell to obtain post-friction shear load measurements. Figure 1 shows the general assembly of the DC-SS apparatus. Photographs of the DC-SS device are shown in Fig. 2. The DC-SS device was designed to test cylindrical soil specimens with a diameter of 10.2 cm or less. The specimen is located between relatively rigid bottom and top caps (Fig. 1, Fig. 2(b)) and is typically confined by a wire reinforced membrane. As shown in Fig. 2(c), the horizontal (top and bottom) faces of the specimen are confined by the caps, which contain fine porous stones epoxied into a recess covering the entire face of the cap except for a retaining lip of aluminum around the edge. These caps provide a “frictional” surface while allowing for drainage into the porous stones if the stones are unsaturated (the stones can be saturated for undrained tests). The top cap/specimen/bottom cap stack is positioned between the top and bottom adapter plates shown in Fig. 1. The bottom cap fits into a recess within the bottom adapter plate. The top adapter plate is gently lowered such that a recess within the top adapter plate fits snugly over the top cap. The top and bottom caps are held tightly on their respective adapter plates by three set screws on each plate. Once the specimen is secured between the two adapter plates, three LVDTs equally spaced around the specimen are mounted on the top adapter plate and fixed to the plate by set screws. The specimen is then consolidated by a vertical stress and is ready for shear loading. Above the top adapter plate is a vertical table, which in turn is attached to a vertical load cell (Fig. 1). Vertical loads are transferred to the specimen through the vertical table, which is attached to three equally spaced linear slides. Each of the three linear slides is attached to a separate post, which effectively precludes lateral movements and rocking of the vertical table (and hence, practically speaking, the specimen as well). This tri-post frame is a significant improvement over the UCB-2D device, which employed a cantilever system (vertical table attached to a pair of track bearings along the same wall). Loads are applied to the vertical table by a pneumatic actuator mounted outside the main frame. An important feature of the DC-SS device that was retained from the UCB-2D device is its bidirectional loading capability. Horizontal shear loads are applied at the base of the specimen through two independently controlled horizontal tables. The bottom horizontal table is mounted on linear slides attached to the main frame of the apparatus, and this table is free to move in only one horizontal direction. The upper horizontal table is also mounted on linear slides such that the movement of the upper table is exactly perpendicular to the lower table. The two horizontal tables can be controlled to produce net resultant movements of the bottom adapter plate in any horizontal direction. Loads are applied to the lower horizontal table by threaded rods that are attached to an actuator that can apply tension and compression. There is a tensioncapable roller connection between the upper table and its actuator to accommodate perpendicular displacements of the lower table. The loads applied to the tables are measured by loadcells mounted between the actuators and the tables. The loads measured by the loadcells are not identical to those imparted to the specimen due to friction in the linear slides. The magnitude of the frictional load within the system was characterized and observed to be quite small (approximately 2.2 N). The significance of this frictional load is dependent on what type of testing is desired. This frictional load will produce inaccuracies of approximately 0.3 kPa (for a10.2-cm diameter specimen), which represents a negligible percentage of the shear stress for most applications. However, if very low stress measurements are needed, post-friction shear stresses can be measured by using a dual-axis loadcell. The dual-axis loadcell fits in between the top adapter plate and the vertical table, a space which is otherwise occupied by a spacer block. The dual-axis loadcell is capable of measuring both the vertical and shear loads simultaneously with minimal cross talk between these channels. However, the presence of the dual-axis loadcell introduces system compliance (i.e., rocking and vertical deformations) that may be significant at medium to large strains. Therefore, most tests are performed without the dual-axis loadcell in place. Three LVDTs (linear variable differential transducers), mounted between the top and bottom adapter plates, are used to measure the vertical specimen deformations. These locations of LVDTs minimize errors due to mechanical compliance. The three LVDTs are used so that relative rocking of the specimen in either direction of loading can be measured. Data from the three LVDTs are averaged to define specimen height during a test. Horizontal deformations are measured by two LVDTs mounted to the horizontal tables in orthogonal directions. The DC-SS device operates under “strain-control” conditions, meaning that table displacements are controlled and the actuator forces required to achieve those displacements are measured. The motions that can be imparted to the tables are limited by different aspects of the control system for different frequency bands. At low frequencies （f≤0.24Hz）, the limiting factor is the peak actuator displacement （Umax=51 mm）. At intermediate frequencies (0.24Hz≤f≤15Hz) the limiting factor is the flow rate capacity of the servo-valve (_Qmax=158 cm3/s). At frequencies (f<15 )Hz, the limiting factor is the pressure capacity of the hydraulic pump (Pmax=21 MPa)_. For the case of harmonic control signals, these quantities can be related to the peak table motions as follows: Ut=Dsinwt≤Umax (1) Utdx=Dwcos(wt)≤Qmax/A (2) U(t)dx2=-Dw2sin(wt)≤PmaxA/m (3) where U(t) and its derivatives describe the table displacement, velocity, and acceleration, A is the cross-sectional area of the actuator( 20.3 cm2), m is the table mass( 5.7 kg), and _ is the frequency of table motion (in radians/s). The corresponding peak values of displacement, velocity, and acceleration are given in Fig. 3. The control system is capable of producing any motion that lies below the limit lines in Fig. 3 . DC-SS Control System As illustrated in Fig. 4, the digital control system for the DC-SS device serves two purposes. The first is to provide control signals to direct drive servovalves that drive hydraulic actuators for each axis (direct drive servovalves have an onboard controller that corrects tracking errors in the control signal before driving the hydraulic actuators). The second purpose is to acquire data from the LVDTs and loadcells. The physical device referred to here as DC-SS was originally developed with a PC-based digitally-supervised analog control system. This control system used a PID (Proportional- Integral-Derivative) control algorithm that ran within a Windows? operating system. The principal problem with that control system was latency in the processing of feedback signals from instruments (such as an LVDT) and the generation of command signals. This limited the ability of the device to accurately replicate some command signals. These problems were especially acute for loading functions involving fast velocities and 2D shaking. The system was successfully used in previous testing (e.g., Whang et al. 2004; Whang et al. 2005), although those applications involved unidirectional shaking and a 1.0 Hz loading frequency, so control problems associated with the PC-based system were not significant. The control system for the present device uses a system referred to as hard real-time digital control. The principal difference from PC-based digital control is that the control functions are implemented on the controller board as opposed to a PC operating system. This enables guaranteed sampling frequencies for the internal feedback loop of 5 kHz using displacement feedback from the horizontal LVDTs,whereas PC-based digitally-supervised analog control systems typically cannot reliably execute the computations required for complex control at feedback sampling frequencies higher than 200 Hz, depending on the processor clock speed, control algorithm sophistication, number of background processes handled by the PC operating system, etc. The digital control system utilizes two dSPACE DS1104 controller boards. Each board contains a PowerPC 603e processor, four 16-bit 2 _s analog-to-digital (A/D) converters, four 12-bit 800 ns A/D converters and eight 16 -bit 10 _s digital-to-analog (D/A) converters, in addition to other input/output ports. The two boards are mounted in PCI slots in a host PC but run their own real-time kernel (i.e., an operating system specifically tailored for control functions) independent of the host PC’s operating system. A PID control algorithm was implemented for both PC-based and hard real time digital control. This is referred to subsequently as the “PID controller”. Gains for the PID controller are tuned by trial-and-error for optimal performance using a step function command signal. The output of the PID controller is a digital voltage command that is sent to a Moog voltage amplifier via one of the D/A channels on the dSPACE board. The voltage amplifier, in turn, sends a voltage drive signal to the appropriate actuator servovalve. As illustrated in Fig. 5(a), PID control of the two axes are independent, and hence the control system as a whole is unable to compensate one axis on the motion along the second axis). In order to minimize cross-coupling effects, the digital control system was enhanced by introducing a multiple-input multipleoutput (MIMO) control algorithm that interfaces with the PID controllers. As illustrated in Fig. 5(b), this controller uses LVDT feedback from both axes and generates a compensated command signal for each of the PID controllers, taking into account cross-coupling effects. The controller is designed and implemented as a discretetime state space system using the LQG (Linear-Quadratic- Gaussian) optimal control method (Franklin et al. 1990). This method requires the estimation of four empirical quantities that reflect system properties. This is accomplished using the N4SID system identification algorithm (Van Overschee and De Moor 1995). System identification algorithms operate on input-output data sequences; the data used for this purpose were two uncorrelated random inputs (generated by the PID controllers) and the corresponding LVDT output signals. The combination of the MIMO control algorithm and the two PID controllers is referred to subsequently as the “MIMO-PID” controller. The DC-SS device is configured so that the MIMO algorithm can be turned on or off. Hence, either PID or MIMO-PID digital control of experiments is possible. Data acquisition capabilities for either mode are summarized below: ? Input motion time step: no practical lower limit; ? Number of input motion data points: no practical upper limit; ? Feedback sampling frequency (i.e., the internal frequency for the feedback loop): 5 kHz; ? Data logging frequency: upper bound is 5 kHz, can be downsampled as needed. DC-SS System Performance To evaluate the performance of the DC-SS system (i.e., controller, pump, actuators, and servo-valves), both harmonic and broadband earthquake input motions were specified to the PID controller and the MIMO-PID controller and the resulting feedback signals were measured. Unidirectional tests were performed to evaluate the performance of each axis independently, and to provide baseline results for evaluating interaction effects. Bidirectional loading was performed to evaluate cross-coupling between axes. Acknowledgments The development of the DC-SS device was supported by a CAREER grant from the National Science Foundation to the second author (NSF Award No. 9733113), the Henry Samueli School of Engineering and Applied Science at UCLA, and the U.S. Geological Survey, National Earthquake Hazards Reduction Program, Award Nos. 1434-HG-98-GR-00037 and 05HQGR0050